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Optimization Model for Fresh Fruit Supply Chains: Case-Study of Dragon Fruit in Vietnam

Optimization Model for Fresh Fruit Supply Chains: Case-Study of Dragon Fruit in Vietnam AgriEngineering Article Optimization Model for Fresh Fruit Supply Chains: Case-Study of Dragon Fruit in Vietnam 1 , 2 1 2 , 1 Tri-Dung Nguyen , Uday Venkatadri , Tri Nguyen-Quang *, Claver Diallo and Michelle Adams Department of Industrial Engineering, Dalhousie University, PO BOX 15000, Halifax, NS B3H 4R2, Canada; TD.Nguyen@dal.ca (T.-D.N.); uday.venkatadri@dal.ca (U.V.); claver.diallo@dal.ca (C.D.) Biofluids and Biosystems Modeling Lab. (BBML), Department of Engineering, Faculty of Agriculture, Dalhousie University, 39 Cox Road, Truro, NS B2N 5E3, Canada School for Resource and Environmental Studies, Dalhousie University, 6100 University Ave, PO BOX 15000, Halifax, NS B3H 4R2, Canada; Michelle.Adams@dal.ca * Correspondence: tri.nguyen-quang@dal.ca Received: 4 November 2019; Accepted: 16 December 2019; Published: 20 December 2019 Abstract: We present an optimization model for dragon fruit plantations in Vietnam. The timing of cultivating and harvesting decisions are taken into account as the dragon fruit plant has an approximately ten-year life cycle with maximum average yield in the fourth year. Another consideration also included is the prevalence of forward-buying contracts with locked-in prices. The dragon fruit supply chain faces several diculties as yield, price, and demand are highly sensitive to weather conditions and global uncertainty factors. The risk factors in the dragon fruit supply chain also depend on species—for example, the red varieties, while more profitable than the white varieties, also have higher export risk because they are subject to global prices and adverse geopolitical conditions. Keywords: dragon fruit (DF); optimization model; fresh fruit supply chain; Vietnam 1. Introduction In recent years, along with the development of the supply chain management and logistics industry, the agri-food supply chain in general and the fresh fruit chain in particular have been recognized as strategic components of the national economy of many developing countries such as Vietnam. Compared to staple crops, fruit production brings greater economic benefits. However, the fruit and vegetable production sector also faces particular risks such as climate change, water scarcity, increase in land-use for industrial and urban development, and consumer behavior and price volatility. Moreover, the planning and managing of production, distribution, and pricing of fresh fruits are more complicated because of their very short shelf-life. The value can be increased if the value chain of fruit and vegetable production and distribution is better organized from farmers to retailers. Countries where agriculture is in development, i.e., Vietnam, are still facing challenges such as: The influence of traditional trade practices—there are many intermediate nodes involved in the network, making the food supply chain longer and more complex than in other developed countries. The high cost of storage after harvesting and transportation—this is due to the tropical climate with high temperature and humidity. AgriEngineering 2020, 2, 1; doi:10.3390/agriengineering2010001 www.mdpi.com/journal/agriengineering AgriEngineering 2020, 2, 1 1 of 25 The continued use of low paid labor. Though labor is cheap, there is a high workforce turnaround. The workforce shortages are acute at the beginning and end of the harvest season when labor demand is high due to competition. During these periods, workers often change employers for better pay. The poor availability of information within the value chain from growers to collectors/traders, wholesalers, retailers, and supermarkets about the harvest, preliminary processing, packing, labeling, preserving, and transportation. The inability of farmers to set produce prices—farmers play the most important role in the food supply chain but most of them are small, with little influence on price. They must sell their products at prices determined by traders due to lack of market information and experience. Due to the lack of long-term orientation at the macro-level of management, farmers target profits based on market demand. In the dragon fruit case, this may imply cutting existing varieties of the fruit and changing over to other varieties, based on anticipated demand. Since dragon fruit is a perennial plant, the impact of these decisions can last several years. It can be said that making decisions for a fresh fruit supply chain management is a more dicult and complex problem than with other supply chains [1]. This is a great challenge for fresh fruit supply chain (FFSC) managers over the past 40 years, given the increasing globalization and rapidly increasing demand. They need a tool to support modern and accurate decision-making for long-term production. There are several articles in the literature related to FFSCs with many di erent approaches or methods that could support optimization of a part or the whole chain. The deterministic approach is a very common and often used in the FFSC research; formulations are based on both linear programming [2–7] and mixed integer programming [8–17]. There are two essential types of fruit used for case studies: perennial crops such as apples [18–21], oranges [6,12], pome fruit [10], pears [16,22,23], cherries [24] and grapes [4,25,26] or annual crops such as pineapple [27], strawberries [28], melon [29], and tomato [13,30,31]. Dragon fruit is a tropical fast-growing perennial crop, other examples being asparagus [32], Persian lime [33], Thai soursop, Taiwan pear-shaped guava, etc. During the last several years, the fresh produce cold chain has received attention from researchers around the world to enhance the quality and freshness of fruits and vegetables delivered to customers. The cold chain issues considered by most researchers have to do with controlling the temperature and gas flow in containers [34–36], minimizing the energy used to refrigerate containers [37], and optimizing the transport system in the chain [38]. The dragon fruit (Figure 1) is a tropical fruit grown extensively in Vietnam. With 36.5 thousand hectares of cultivated land and 630 thousand tons of total yield, Vietnam is the world’s leading exporter of dragon fruit [39]. However, dragon fruit production and processing are still in a nascent stage of development and face issues around severe price fluctuations due to conditions such as: a. Product development is still nascent; b. Market price fluctuations; c. Chinese imports are subject to price and currency exchange risks; d. High competition with other exporting countries (such as Thailand, Malaysia, etc.) driving down value despite increased export volumes; e. Export has been increasing both in volume and value but the increase in value has been declining. This paper presents an optimization model for dragon fruit crop planning to support farmers make decisions on the allocation of land to crop varieties. The objective of the model is to maximize profit, while satisfying customer demand. Given that dragon fruit is perennial but fast growing, there is an opportunity to change the crop mix based on anticipated future prices. However, there could be a loss in yield depending on the maturity of the crops in a plantation mix. The remainder of this paper is organized as follows: Section 2 introduces dragon fruit plantation and crop planning. Section 3 AgriEngineering 2020, 2, 1 2 of 25 presents a linear programming optimization model for crop harvesting and replantation decisions. Section 4 presents the results and discussions from example scenarios. Section 5 concludes the paper AgriEngineering 2019, 2 FOR PEER REVIEW 3 and outlines areas for further study. AgriEngineering 2019, 2 FOR PEER REVIEW 3 95 Figure 1. Dragon fruit trees blossoming (left) and fruiting (right) in June–July. Photos taken in 2016 in 95 Figure 1. Dragon fruit trees blossoming (left) and fruiting (right) in June–July. Photos taken in 2016 in Figure 1. Dragon fruit trees blossoming (left) and fruiting (right) in June–July. Photos taken in 2016 in 96 Binh Thuan province, Vietnam. 96 Binh Thuan province, Vietnam. Binh Thuan province, Vietnam. 97 2. Dragon Fruit Plantation Characteristics 2. Dragon Fruit Plantation Characteristics 97 2. Dragon Fruit Plantation Characteristics 98 2.1. Fruit Distribution Context 2.1. Fruit Distribution Context 98 2.1. Fruit Distribution Context 99 The dragon fruit supply chain starts with farmers who make plantation decisions based on The dragon fruit supply chain starts with farmers who make plantation decisions based on 99 The dragon fruit supply chain starts with farmers who make plantation decisions based on 100 forward buy-in contracts with traders. The traders sell fruit to by-products and wholesalers who in forward buy-in contracts with traders. The traders sell fruit to by-products and wholesalers who in 100 forward buy-in contracts with traders. The traders sell fruit to by-products and wholesalers who in 101 turn distribute the fruit and by-products to retail, export, and by-product producers. The dragon fruit turn distribute the fruit and by-products to retail, export, and by-product producers. The dragon fruit 101 turn distribute the fruit and by-products to retail, export, and by-product producers. The dragon fruit 102 supply chain is depicted in Figure 2. Typical dragon fruit by-products are wine and packaged dried supply chain is depicted in Figure 2. Typical dragon fruit by-products are wine and packaged dried 102 supply chain is depicted in Figure 2. Typical dragon fruit by-products are wine and packaged dried 103 fruit snacks. fruit snacks. 103 fruit snacks. Export markets Export markets Collectors/ Farmers Wholesalers Retailers Collectors/ Traders Farmers Wholesalers Retailers Traders By-product By-product producers producers Figure 2. Simplified dragon fruit supply chain [40]. 105 Figure 2. Simplified dragon fruit supply chain [40]. 105 Figure 2. Simplified dragon fruit supply chain [40]. Dragon fruit is typically planted twice a year in Vietnam. Harvesting starts one year after 106 Dragon fruit is typically planted twice a year in Vietnam. Harvesting starts one year after 106 Dragon fruit is typically planted twice a year in Vietnam. Harvesting starts one year after plantation, but the fruit is at the quality required for commercial purposes 2–10 years after harvest. 107 plantation, but the fruit is at the quality required for commercial purposes 2–10 years after harvest. 107 plantation, but the fruit is at the quality required for commercial purposes 2–10 years after harvest. 108 Dragon fruit yield typically depends on age and a tree is usually only considered productive until 108 Dragon fruit yield typically depends on age and a tree is usually only considered productive until 109 the age of 12 years. Figure 3 shows the typical yield curve as a function of tree age (based on [41]). 109 the age of 12 years. Figure 3 shows the typical yield curve as a function of tree age (based on [41]). AgriEngineering 2020, 2, 1 3 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 4 Dragon fruit yield typically depends on age and a tree is usually only considered productive until the AgriEngineering 2019, 2 FOR PEER REVIEW 4 age of 12 years. Figure 3 shows the typical yield curve as a function of tree age (based on [41]). 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Year Year 111 Figure Figure3. 3. Typ Typical ical dragon dragon fru fruit it yield yield aas s aa fun function ction of oftree tree age age. . 111 Figure 3. Typical dragon fruit yield as a function of tree age. There are three varieties of dragon fruit planted in Vietnam: the red-skin white-flesh, the 112 There are three varieties of dragon fruit planted in Vietnam: the red-skin white-flesh, the red- 112 red-skin There red-flesh are three and var the ietiyellow-skin es of dragon white-flesh fruit planted (Figur in V e ietnam: 4). The rth ed-skin e red-s varieties kin whitar e-e fles very h, th popular e red- , 113 skin red-flesh and the yellow-skin white-flesh (Figure 4). The red-skin varieties are very popular, the the white-flesh variety being the most sold. The red-skin red-flesh variety has a high demand during 113 skin red-flesh and the yellow-skin white-flesh (Figure 4). The red-skin varieties are very popular, the 114 white-flesh variety being the most sold. The red-skin red-flesh variety has a high demand during the 114 whit the lunar e-flesh New variety Year be and ing is thalso e moexported st sold. Th ext e red ensively -skin red to China. -flesh vThe ariety yellow has a peel highwhite demand flesh du variety ring the is 115 lunar New Year and is also exported extensively to China. The yellow peel white flesh variety is relatively new in Vietnam and is available only in major metropolitan areas. 115 lunar New Year and is also exported extensively to China. The yellow peel white flesh variety is 116 relatively new in Vietnam and is available only in major metropolitan areas. 116 relatively new in Vietnam and is available only in major metropolitan areas. Red-skin white-flesh Red-skin red-flesh Yellow-skin white-flesh Red-skin white-flesh Red-skin red-flesh Yellow-skin white-flesh 117 Figure 4. Species of dragon fruit planted in Vietnam [41]. Figure 4. Species of dragon fruit planted in Vietnam [41]. 117 Figure 4. Species of dragon fruit planted in Vietnam [41]. The dragon fruit blooms from May to August and is ready a month later for harvesting in 118 The dragon fruit blooms from May to August and is ready a month later for harvesting in 118 The dragon fruit blooms from May to August and is ready a month later for harvesting in 119 Septem September ber an and d Oct October ober. . H However owever, ,dr dragon agon fruit fruitprice prices s are areu usually sually llow ow in inth the e ma main in season season ((due due to to th the e 119 September and October. However, dragon fruit prices are usually low in the main season (due to the availability of the fruit). Due to its high economic value in January and February, dragon fruit growers 120 availability of the fruit). Due to its high economic value in January and February, dragon fruit 120 availability of the fruit). Due to its high economic value in January and February, dragon fruit 121 growers install lighting install light systems ing sy to s sti tem mulate s to stimu treesla to te bloom trees to and bloom haveand fruits hav toe impr fruits ove to pr im oductivity prove produc in the tivity dry 121 growers install lighting systems to stimulate trees to bloom and have fruits to improve productivity season which lasts from November to April [40]. Therefore, there are two times for harvesting, either 122 in the dry season which lasts from November to April [40]. Therefore, there are two times for 122 in the dry season which lasts from November to April [40]. Therefore, there are two times for 123 harvestin from May g,to eith October er from (rainy May season to Octob or er season (rainy1) seor ason from or November season 1) or tofrom AprilNove (drymb season er toor Apri season l (dry 2) 123 harvesting, either from May to October (rainy season or season 1) or from November to April (dry (Figure 5). 124 season or season 2) (Figure 5). 124 season or season 2) (Figure 5). May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr Rainy season (season 1) Dry season (season 2) Rainy season (season 1) Dry season (season 2) 125 Figure 5. Dragon fruit production calendar in Vietnam. 125 Figure 5. Dragon fruit production calendar in Vietnam. Kg/pole Kg/pole AgriEngineering 2019, 2 FOR PEER REVIEW 4 0 2 4 6 8 10 12 14 Year 111 Figure 3. Typical dragon fruit yield as a function of tree age. 112 There are three varieties of dragon fruit planted in Vietnam: the red-skin white-flesh, the red- 113 skin red-flesh and the yellow-skin white-flesh (Figure 4). The red-skin varieties are very popular, the 114 white-flesh variety being the most sold. The red-skin red-flesh variety has a high demand during the 115 lunar New Year and is also exported extensively to China. The yellow peel white flesh variety is 116 relatively new in Vietnam and is available only in major metropolitan areas. Red-skin white-flesh Red-skin red-flesh Yellow-skin white-flesh 117 Figure 4. Species of dragon fruit planted in Vietnam [41]. 118 The dragon fruit blooms from May to August and is ready a month later for harvesting in 119 September and October. However, dragon fruit prices are usually low in the main season (due to the 120 availability of the fruit). Due to its high economic value in January and February, dragon fruit 121 growers install lighting systems to stimulate trees to bloom and have fruits to improve productivity 122 in the dry season which lasts from November to April [40]. Therefore, there are two times for AgriEngineering 2020, 2, 1 4 of 25 123 harvesting, either from May to October (rainy season or season 1) or from November to April (dry 124 season or season 2) (Figure 5). May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr AgriEngineering 2019, 2 FOR PEER REVIEW 5 Rainy season (season 1) Dry season (season 2) 126 Dragon fruit trees are commercially viable for 10–12 years, but because they grow quickly, the 125 Figure 5. Dragon fruit production calendar in Vietnam. Figure 5. Dragon fruit production calendar in Vietnam. 127 plantations can continue to harvest existing crops below that age or cut them down for investment in Dragon fruit trees are commercially viable for 10–12 years, but because they grow quickly, 128 other varieties based on demand and price. the plantations can continue to harvest existing crops below that age or cut them down for investment in other varieties based on demand and price. 129 2.2. Methodology 130 The methodology in this paper is aligned with the hierarchical planning approach which 2.2. Methodology 131 separates the decision-making process into tactical and operational phases [42]. In hierarchical The methodology in this paper is aligned with the hierarchical planning approach which separates 132 planning, decisions are first made at the tactical level and then at the operational level. Figure 6, the decision-making process into tactical and operational phases [42]. In hierarchical planning, 133 which is adapted from Ahumada et al. [31], shows how the hierarchical approach may be applied to decisions are first made at the tactical level and then at the operational level. Figure 6, which is 134 the dragon fruit chain. adapted from Ahumada et al. [31], shows how the hierarchical approach may be applied to the dragon 135 In this paper, a quantitative modeling approach for decision making for dragon fruit plantation fruit chain. 136 and harvesting in Vietnam is presented. As previously mentioned, this approach looks at planting In this paper, a quantitative modeling approach for decision making for dragon fruit plantation 137 and cutting (which are tactical decisions) taken over a multi-year planning horizon. The potential and harvesting in Vietnam is presented. As previously mentioned, this approach looks at planting 138 benefit from the hierarchical planning is that growers can be involved in making decisions about the and cutting (which are tactical decisions) taken over a multi-year planning horizon. The potential 139 market and production. In other words, coordinating tactical and operational decisions is beneficial benefit from the hierarchical planning is that growers can be involved in making decisions about the 140 for multiple parties: growers, producers, distributors, and vendors. market and production. In other words, coordinating tactical and operational decisions is beneficial for multiple parties: growers, producers, distributors, and vendors. Inputs Season demand Outputs Available resources Planting /Cutting Crops to plant Tactical Crop requirements Plan Seasonal production phase Expected price Cost Information Inputs Seasonal prices Operational Outputs Seasonal demand phase Harvesting Plan Seasonal harvesting Seasonal development of Seasonal shipments plants Production capacity Figure 6. Example of a hierarchical planning schematic. 143 Figure 6. Example of a hierarchical planning schematic. In Figure 6, the first phase deals with tactical decisions that are only made at the start of the season 144 In Figure 6, the first phase deals with tactical decisions that are only made at the start of the such as what crop to plant or truncate, and when and how much to plant or truncate. While in the 145 season such as what crop to plant or truncate, and when and how much to plant or truncate. While second phase, farmers must decide how much to sell to customers in each season according to the 146 in the second phase, farmers must decide how much to sell to customers in each season according to market conditions. 147 the market conditions. To execute the hierarchical planning schematic, a deterministic optimization model is developed 148 To execute the hierarchical planning schematic, a deterministic optimization model is developed in this paper for the dragon fruit production in Vietnam. Although dragon fruit is used as the main 149 in this paper for the dragon fruit production in Vietnam. Although dragon fruit is used as the main target the current study, our model can certainly be adapted to other fresh fruit production chains. 150 target the current study, our model can certainly be adapted to other fresh fruit production chains. 151 3. Linear Programming Optimization Model 152 3.1. Hypotheses and Assumptions 153 For this model, it is assumed that: 154 1. The facilities (farms) are already operational since the model does not deal with network 155 decisions. Kg/pole AgriEngineering 2020, 2, 1 5 of 25 3. Linear Programming Optimization Model 3.1. Hypotheses and Assumptions For this model, it is assumed that: 1. The facilities (farms) are already operational since the model does not deal with network decisions. 2. The time horizon for tactical planning is 10 years and two harvesting seasons (rainy season and dry season) for each year are considered. 3. Fruit trees are cut down when they are 10 years of age or earlier, if the model chooses to (e.g., when the future prices of other crops are much higher than the planted crop). It is assumed that cutting down or replanting decisions are only carried out in season 1. 4. The distribution of yield, demand, and market prices are represented by their expected values. 5. Storage is not allowed for fresh dragon fruit. However, the fruit may be used for by-products such as dry snacks and wine. 6. The amounts of each crop to cut and plant are decision variables which cannot exceed the maximum amount of land that is already determined. 7. Decision variables of the model are the new plantation and truncating areas of each crop, and the amount of fruit sent to customers (traders, wholesalers, and by-product producers) in every year. 8. Other decisions include the quantity of fruit to sell to customers and the amount of labor (fixed and part-time) is required to cover all the activities in the model. 3.2. Objective Function XXXX XXXX Max O = p ST + q SWM jist jist jmst jmst s m s t t j i j XXX XX X + r SB cp Y ch X jst jst jt jt t jkt1 s t t j j j X X X cr Z F cLab f Hire cLabp t t t j,k=10,t (1) t t X XXX cbp SB cPNT st jst jist i jst t s j j XX XX cwater w clighting v ks ks js js k j s=2 The objective of the proposed model is to determine the planting and harvesting decisions that maximize expected profit for the farmers; this is the di erence between the total revenue expected from selling to traders (ST), wholesale markets (SWM), and by-product suppliers (SB), and the total costs of planting, truncating, by-product processing, penalty for missing demand, labor, lighting cost, and watering. The notation is presented in Appendix A. 3.3. Constraints The first category of constraints (2, 3, and 4) is related to resources (land, water, and lighting). - Land availability XX X  L 8t (2) jkt j k Total of area of each crop j at age k cannot exceed the available land (L). - Water restriction AgriEngineering 2020, 2, 1 6 of 25 XX X w  W 8t, s (3) st jkst jkst At each tree age k, the amount of water w required per hectare for each crop j is di erent in season s of year t; this cannot exceed the availability of water. Also, yield decreases if the trees are watered too much. - Lighting restrictions X v  V 8s (4) s s js Due to lack of sunlight in the dry seasons (s = 2), a light supplementing method is applied at night. At each tree age k, the requirement of light per hectare for each crop j is di erent but limited. Constraints (5) and (6) are for plantation area and yield. - Minimum plantation size X  u 8t (5) jt jtk Constraint (5) is the lower bound for the planting area for each crop in a given period, which may come from forward contracts. The minimum planting area of each crop u is defined by the planner depending on commitments to customers. The parameter u could be 0 but should be less than the available land L. - Yield X X X ST + SWM + SB  X 8 j, s, t (6) jist jmst jst jkst jkst i k Constraint (6) ensures that the total harvest is less than the yield (metric tons per hectare) times plantation area (in hectares). - Plantation age class balance The third category of constraints (7–15) is related to the planning structure for agriculture models. The cutting down and replanting of new varieties has been modeled in Catalá [10] for a case study on apple and pear trees. X = X 8 j, k, t (7) j,k,s=1,t j,k,s=2,t Constraint (7) ensures that there is no change in the planted area of each crop within a year (i.e., between season 1 and season 2). This is because plantation or truncation decisions are only made at the start of season 1. The plantation decisions are decided by Y . The age of a newly planted fruit tree is always 0. jt 1 2 There are two types of truncations: Z , which is optional for a tree of age k = 1::: 9 and Z jkt j,k=10,t which is mandatory for all trees that have reached an age of 10. X = Y 8 j, k = 1, t = 1 (8) jkst jt Constraint (8) states that in year 1 only new crops (age class 1) can be planted. X = I Z 8 j, k = [2::: 9], t = 1 (9) jkst j,k1 jkt AgriEngineering 2020, 2, 1 7 of 25 Constraint (9) is similar to constraint 8 and applies only to year 1 but for other age classes (k = 2. . . 9). It states that the plantation area is the inventory of trees of age class k-1 in year 0 less what can be cut down in year 1 after they have aged by 1 year. X = I Z 8 j, k = 10, t = 1 (10) jkst j,k1 jkt Constraint (10) states that age-10-crops that have to be cut down in year 1 while determining the initial plantation area. X X X X = Y Z 8 j, k = 1, t > 1 (11) jkst j,t1 jkt Constraint (11) states that for periods t > 1 in the planning horizon, the plantation area for age class k = 1 is determined by new crop planted the year before less whatever is cut from that new plantation the next year. X = X Z 8 j, 10 > k > 1, t > 1 (12) jkst j,k1,s,t1 jkt Constraint (12) is for crop ageing for age classes 10 > k > 1. The plantation size in a given year depends on what it was the previous year, less the area cut down optionally. Z = X 8 j, k = 10, t > 1 (13) jkt j,k1,s,t1 Constraint (13) states that all crops of age 9 in a given year t-1 should be cut the next year. - Labor constraints X X X F + Hire P  Y H  X R  Z = 0 8t (14) t t t jt t jt t jkt j j j Constraints (14) models workforce requirements to plant, cut, and harvest in given year. F = M 8t (15) The number of fulltime workers is sometimes a fixed number. If that is the case, the full time complement of workers should be set to that number. Hire  N 8t (16) The number of part time workers hired based on requirements of cultivating or harvesting or truncating. However, the number is limited due to budget, as seen in constraint (16). The last set of constraints, (17) to (19), is for demand satisfaction: ST = d  8t, s (17) jist jist jist Constraint (17) is a soft constraint on trader demands, given that under-shipping to them is allowed. SWM = e 8t, s (18) jmst jmst Constraint (18) states that the demand of wholesalers should be satisfied. SB = f 8t (19) jt j AgriEngineering 2020, 2, 1 8 of 25 Constraint (19) states that the demand of by-products should be satisfied. 4. Case Study The model for dragon fruit cultivation presented in the previous section was applied using the conditions of an actual dragon fruit plantation in Vietnam. The authors of this study contacted a small growing operation covering an area of about 20 hectares. Data were obtained on dragon fruit prices and demands, planting, replanting, and harvesting costs, labor availability, water and light requirements, species yields, etc. The important issue facing such operations is land management, where farmers need to make decisions on land allocation for di erent species of dragon fruit over a period of 10 years. The model is intended to allow farming communities to evaluate alternative land allocation and commitment scenarios based on di erent prices. As mentioned, farmers are planting two kinds of dragon fruit (white-flesh and red-flesh) on their lands. The price of each crop is di erent and depends on market demands. The price of the red-skin white-flesh dragon fruit (Crop 1) is stable in season 1 (favorite season) and increases a bit in season 2 (o -season). The price of the red-skin red-flesh dragon fruit (Crop 2) is double because Crop 2 is planted for export to China, where the demand is always good. However, the price of this crop fluctuates highly, relying heavily on Chinese traders. Verbal agreements are usually made between farmers and traders; however farmers could be ruled by the prices set by the traders [40]. In the case of traders cancelling deals, the price drops down dramatically. The yellow-skin white-flesh dragon fruit (Crop 3) (currently imported from Malaysia) has only recently appeared in the market and has had an extremely high price for the last three years. It is still in great demand because of its sweetness and the curiosity of consumers. Farmers intend to grow Crop 3 trees to cover that demand but have some disadvantages: the plants are novel and disease prone, and yields are just one-third of Crop 1 or Crop 2 (according to the experience of many farmers). However, farmers like to grow all three kinds of dragon fruit, to cover all market demands and hedge their risks against demand and price. In the baseline scenario, the Crop 1 is the traditional chain for both domestic and export markets with a stable demand, while Crop 2 is only planted for export to China. Crop 3 is cultivated only for the purpose of testing its viability in the consumer market. The model assumes that the demands and selling prices of all crops increase steadily over 10 years. The land proportion for each type of dragon fruit is proposed to help farmers managing their costs and benefits in planning the combination framework to install various dragon fruits, and also to decide thereafter which dragon fruit category they have to grow within 10 years. The mean values for one year are based on the previous year ’s data. Using recent pricing in the Vietnamese market it was found that: (a) the price of Crop 3 is around 10 times higher than the price of Crop 1, and (b) the price of Crop 2 is three times as high as for Crop 1. After the baseline scenario is completed and analyzed by the proposed model, other scenarios are developed, based on the minimum limit of area for each crop of dragon fruit to plant, and the fluctuations of the prices and market demands. To test how the model adapts to any changes or requirements of dragon fruit production, groups of di erent expansion scenarios are developed with various assumptions. The model is implemented using open source LP/MIP solver GLPK/GUSEK, that was developed by Free Software Foundation, Inc., Boston, USA, and it is computationally tractable. 4.1. Baseline Scenario In this scenario, approximately 15 hectares of Crop 1 and Crop 2 have been planted on 20 hectares of land to meet orders in year 0 (the start of the planning horizon). All initial input values such as yields, prices, demands, labor costs, and resource costs were collected from farmers, market reports, and dragon fruit cultivating guidelines in 2017. Figure 7 shows the typical yield curve of three dragon fruit varieties as a function of tree age [41,43]. Total planted area (ha) AgriEngineering 2020, 2, 1 9 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 10 Crop Yield 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Year Crop 1 Crop 2 Crop 3 278 Figure Figure 7. 7. Yie Yields lds of of thr three ee drag dragon on fruit fruit varie varieties ties [ [41 41,,43 43]. ]. It is assumed that all dragon fruits are sold to five traders and five wholesalers. After meeting the 279 It is assumed that all dragon fruits are sold to five traders and five wholesalers. After meeting needs of all traders and wholesalers, if any amount of Crop 1 is left over, it is sold as a by-product to 280 the needs of all traders and wholesalers, if any amount of Crop 1 is left over, it is sold as a by-product produce wine and snacks. General information of average yields, demand, and prices of each crop in 281 to produce wine and snacks. General information of average yields, demand, and prices of each crop the current market is show in Table 1: 282 in the current market is show in Table 1: Table 1. General information for the model [43]. 283 Table 1. General information for the model [43]. Average Yield Average Demand Average Price Average Yield Average Demand Average Price Crop 1 15 30 0.5 US$ Crop 1 15 30 0.5 US$ Crop 2 14 30 1.5 US$ Crop 2 14 30 1.5 US$ Crop 3 5 5 5 US$ Crop 3 5 5 5 US$ 284 The results of the baseline scenario are show below: The results of the baseline scenario are show below: Figure 8 shows the recommended dragon fruit cultivation allocation to crops on 20 hectares of land over 10 years. Crop 3 is planted primarily to meet demand; the land area allocation of Crop 1 and Crop 2 are relatively constant through the 10 years. We can see that growing new trees and cutting old ones occur on a large area of land from year 3 to year 6; this also a ects to the profitability of the farmers. The profit increases rapidly in the first three years due to income from Crop 3. However, it goes down in year 4 because many older Crop 1 and 2 plants are truncated and replaced by new ones. The variations of revenues, profits, and costs are shown in Figure 9. Figure 10 shows the profit of 10 10 each crop over 10 years. 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting Cutting area area 286 Figure 8. Baseline model result. 287 Figure 8 shows the recommended dragon fruit cultivation allocation to crops on 20 hectares of 288 land over 10 years. Crop 3 is planted primarily to meet demand; the land area allocation of Crop 1 289 and Crop 2 are relatively constant through the 10 years. We can see that growing new trees and Planted area of each crop (ha) Kg/pole Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 10 Crop Yield 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Year Crop 1 Crop 2 Crop 3 278 Figure 7. Yields of three dragon fruit varieties [41,43]. 279 It is assumed that all dragon fruits are sold to five traders and five wholesalers. After meeting 280 the needs of all traders and wholesalers, if any amount of Crop 1 is left over, it is sold as a by-product 281 to produce wine and snacks. General information of average yields, demand, and prices of each crop 282 in the current market is show in Table 1: 283 Table 1. General information for the model [43]. Average Yield Average Demand Average Price Crop 1 15 30 0.5 US$ Crop 2 14 30 1.5 US$ Crop 3 5 5 5 US$ AgriEngineering 2020, 2, 1 10 of 25 284 The results of the baseline scenario are show below: 10 10 AgriEngineering 2019, 2 FOR PEER REVIEW 11 AgriEngineering 2019, 2 FOR PEER REVIEW 11 290 cutting old ones occur on a large area of land from year 3 to year 6; this also affects to the profitability 291 of the farmers. The profit increases rapidly in the first three years due to income from Crop 3. 290 cutting old ones occur on a large area of land from year 3 to year 6; this also affects to the profitability 292 However, it goes down in year 4 because many older Crop 1 and 2 plants are truncated and replaced 0 1 2 3 4 5 6 7 8 9 10 291 of the farmers. The profit increases rapidly in the first three years due to income from Crop 3. Year 293 by new ones. The variations of revenues, profits, and costs are shown in Figure 9. Figure 10 shows Crop 1 area Crop 2 area Crop 3 area Total used area 292 However, it goes down in year 4 because many older Crop 1 and 2 plants are truncated and replaced 294 the profit of each crop over 10 years. New planting 293 by new ones. The variations of revenues, profits, and cost Cuttis ngar aree a shown in Figure 9. Figure 10 shows area 294 the profit of each crop over 10 years. 286 Figure 8. Baseline model result. Figure 8. Baseline model result. 2000000.00 2000000.00 1500000.00 287 Figure 8 shows the recommended dragon fruit cultivation allocation to crops on 20 hectares of 288 land over 10 years. Crop 3 is planted primarily to meet demand; the land area allocation of Crop 1 1500000.00 1000000.00 289 and Crop 2 are relatively constant through the 10 years. We can see that growing new trees and 1000000.00 500000.00 500000.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 0.00 Year 0 1 2 3 4 5 6 7 8 9 10 11 Year Revenue Cost Profit Revenue Cost Profit 296 Figure 9. Revenue, profit, and cost of the baseline scenario for the 10-year horizon. Figure 9. Revenue, profit, and cost of the baseline scenario for the 10-year horizon. 296 Figure 9. Revenue, profit, and cost of the baseline scenario for the 10-year horizon. 1000000.00 800000.00 1000000.00 600000.00 800000.00 400000.00 600000.00 200000.00 400000.00 0.00 200000.00 0 1 2 3 4 5 6 7 8 9 10 11 -200000.00 0.00 Year 0 1 2 3 4 5 6 7 8 9 10 11 -200000.00 Year Crop 1 Crop 2 Crop 3 297 . Cro Figure p 1 10. Profit Cro of p 2 each crop.Crop 3 298 Figure 10. Profit of each crop. 297 . Building upon the baseline scenario, four di erent expansion scenarios are proposed with 298 Figure 10. Profit of each crop. 299 assumptions Building about upon changes the basto elin prices e scen or ardemands, io, four dprice ifferent fluctuation expansion with scenar a probability ios are pro factor posed , and with the 300 as initial sump plantation. tions about All chang scenarios es to pr ar ice e described s or demands briefly , pri in ce Appendix fluctuation B with (Table a pro A1). bability factor, and the 299 Building upon the baseline scenario, four different expansion scenarios are proposed with 301 initial plantation. All scenarios are described briefly in Appendix B (Table B1). 300 assumptions about changes to prices or demands, price fluctuation with a probability factor, and the 301 initial plantation. All scenarios are described briefly in Appendix B (Table B1). 302 4.2. Changes to Price of Crop 2 303 In this scenario, the price of Crop 2 is considered increasing or decreasing linearly within the 302 4.2. Changes to Price of Crop 2 304 range of 0.5 US$ (Crop 1 price) and 5 US$ (Crop 3 price). The other information is the same as in the 303 In this scenario, the price of Crop 2 is considered increasing or decreasing linearly within the 305 baseline scenario. The cultivation changes for each crop when the price of Crop 2 changes in two 304 range of 0.5 US$ (Crop 1 price) and 5 US$ (Crop 3 price). The other information is the same as in the 306 cases are shown below: 305 baseline scenario. The cultivation changes for each crop when the price of Crop 2 changes in two 306 cases are shown below: Planted area of each crop (ha) Kg/pole ProfiProfi t (USt D) (USD) US do US do llars llars Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2020, 2, 1 11 of 25 4.2. Changes to Price of Crop 2 In this scenario, the price of Crop 2 is considered increasing or decreasing linearly within the range of 0.5 US$ (Crop 1 price) and 5 US$ (Crop 3 price). The other information is the same as in the baseline scenario. The cultivation changes for each crop when the price of Crop 2 changes in two cases AgriEngineering 2019, 2 FOR PEER REVIEW 12 are shown below: We can see e ect the price of Crop 2 price in Figures 11 and 12. The total profits are also a ected AgriEngineering 2019, 2 FOR PEER REVIEW 12 when the prices are changed (Figure 13). 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year New planting area Cutting area Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 308 Figure 11. Plantation allocation when Crop 2 price increases. Figure 11. Plantation allocation when Crop 2 price increases. 308 Figure 11. Plantation allocation when Crop 2 price increases. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year New planting area Cutting area Crop 1 area Crop 2 area Crop 3 area Total used area Figure 12. Ne Plantation w planting are allocation a whenC Cr uttop ing 2 are price a decreases. 310 Figure 12. Plantation allocation when Crop 2 price decreases. 310 Figure 12. Plantation allocation when Crop 2 price decreases. 311 We can see effect the price of Crop 2 price in Figures 11 and 12. The total profits are also affected 312 when the prices are changed (Figure 13). 311 We can see effect the price of Crop 2 price in Figures 11 and 12. The total profits are also affected 312 when the prices are changed (Figure 13). Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2020, 2, 1 12 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 13 AgriEngineering 2019, 2 FOR PEER REVIEW 13 Yearly profit as a result change in price of Crop 2 4000000.00 Yearly profit as a result change in price of Crop 2 3000000.00 4000000.00 2000000.00 3000000.00 1000000.00 2000000.00 0.00 1000000.00 0 2 4 6 8 10 12 0.00 Year 0 2 4 6 8 10 12 Profit when Crop 2 price increases Year Profit when Crop 2 price decreases Profit when Crop 2 price increases 314 Figure 13. Effect of changes in Crop 2 price on profit. Figure 13. E ect of changes in Crop 2 price on profit. Profit when Crop 2 price decreases 4.3. Changing Demands 315 4.3. Changing Demands 314 Figure 13. Effect of changes in Crop 2 price on profit. In this scenario, market demand variations are considered. It is assumed that the need of the 316 In this scenario, market demand variations are considered. It is assumed that the need of the 315 4.3. market Changin risesgfor Deman all cr ds ops. The following cases are considered: Crop 3 demand increases four-fold and 317 market rises for all crops. The following cases are considered: Crop 3 demand increases four-fold and the demand for all crops required increases by 20%, 40%, and 80%, respectively, based on the baseline 318 the demand for all crops required increases by 20%, 40%, and 80%, respectively, based on the baseline 316 In this scenario, market demand variations are considered. It is assumed that the need of the scenario demand. Other information is unchanged. 319 scenario demand. Other information is unchanged. 317 market rises for all crops. The following cases are considered: Crop 3 demand increases four-fold and 318 the demand for all crops required increases by 20%, 40%, and 80%, respectively, based on the baseline 4.3.1. Crop 3 Demand Increases Four-Fold 320 4.3.1. Crop 3 Demand Increases Four-Fold 319 scenario demand. Other information is unchanged. In this case, it is supposed that the yellow-skin white-flesh dragon fruit is popular, so that the 321 In this case, it is supposed that the yellow-skin white-flesh dragon fruit is popular, so that the farmers have more orders from traders and wholesalers. The areas of new planting or cutting of the 320 4.3.1. Crop 3 Demand Increases Four-Fold 322 farmers have more orders from traders and wholesalers. The areas of new planting or cutting of the dragon fruit trees are shown below: 323 dragon fruit trees are shown below: 321 In this case, it is supposed that the yellow-skin white-flesh dragon fruit is popular, so that the Figure 14 shows us that with the rising demand along with its high selling price, Crop 3 is 322 farmers have more orders from traders and wholesalers. The areas of new planting or cutting of the produced on most of the current planting area. On the other hand, Crop 2 is grown on the small 323 dragon fruit trees are shown below: remaining land and Crop 1 is cut o completely in year 2. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 2 Year Crop 1 area Crop 2 area Crop 3 area Total used area 0 1 2 3 4 5 6 7 8 9 10 New planting area Cutting area Year Crop 1 area Crop 2 area Crop 3 area Total used area 325 Figure 14. Plantation allocation when Crop 3 demand increases four-fold. New planting area Cutting area 326 Figure 14 shows us that with the rising demand along with its high selling price, Crop 3 is Figure 14. Plantation allocation when Crop 3 demand increases four-fold. 325 Figure 14. Plantation allocation when Crop 3 demand increases four-fold. 327 produced on most of the current planting area. On the other hand, Crop 2 is grown on the small 328 remaining land and Crop 1 is cut off completely in year 2. 326 Figure 14 shows us that with the rising demand along with its high selling price, Crop 3 is 327 produced on most of the current planting area. On the other hand, Crop 2 is grown on the small 328 remaining land and Crop 1 is cut off completely in year 2. Planted area P lo afn e te ad ch a c rr eo ap o f ( h ea a)ch crop (ha) US Dollars US Dollars TotalT p olta an l tp eld a n at re ed a a (h re aa ) (ha) TotalT p olta an l tp eld a n at re ed a a (h re aa ) (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 14 AgriEngineering 2020, 2, 1 13 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 14 329 4.3.2. All Crop Demands Increasing by a Fixed Percentage 329 4.3.2. All Crop Demands Increasing by a Fixed Percentage 4.3.2. All Crop Demands Increasing by a Fixed Percentage 330 This case is slightly different from the case 2.3.1, and all crop demands increase by 20%, 40%, 330 This case is slightly different from the case 2.3.1, and all crop demands increase by 20%, 40%, 331 and 80% respectively over the baseline scenario demand. Other data are the same. The changes in This case is slightly di erent from the case 2.3.1, and all crop demands increase by 20%, 40%, 331 and 80% respectively over the baseline scenario demand. Other data are the same. The changes in 332 plantation allocation for each case is shown in Figures 15–17 below: and 80% respectively over the baseline scenario demand. Other data are the same. The changes in 332 plantation allocation for each case is shown in Figures 15–17 below: plantation allocation for each case is shown in Figures 15–17 below: 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area 334 Figure 15. Plantation allocation when all crop demands increase by 20%. Figure 15. Plantation allocation when all crop demands increase by 20%. 334 Figure 15. Plantation allocation when all crop demands increase by 20%. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Figure 16. Plantation allocation when all crop demands increase by 40%. 336 Figure 16. Plantation allocation when all crop demands increase by 40%. 336 Figure 16. Plantation allocation when all crop demands increase by 40%. PlantP eld a n at re ed a a or fe e aa o ch f e ca rc oh p c (r ho ap ) (ha) PlantP eld a n at re ed a a or fe e aa o ch f e ca rc oh p c (r ho ap ) (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2020, 2, 1 14 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 15 AgriEngineering 2019, 2 FOR PEER REVIEW 15 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Year Year Crop 1 area Crop 2 area Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Figure 17. Plantation allocation when all crop demands increase by 80%. 338 Figure 17. Plantation allocation when all crop demands increase by 80%. 338 Figure 17. Plantation allocation when all crop demands increase by 80%. We can see that if the needs of all crops are increased, only crops that are more profitable are 339 We can see that if the needs of all crops are increased, only crops that are more profitable are 339 We can see that if the needs of all crops are increased, only crops that are more profitable are grown. Therefore, Crop 2 and 3 are prioritized for planting. The profit of each case is summarized in 340 grown. Therefore, Crop 2 and 3 are prioritized for planting. The profit of each case is summarized in 340 grown. Therefore, Crop 2 and 3 are prioritized for planting. The profit of each case is summarized in Figure 18. In general, the higher the demand is, the more the dragon fruit grower ’s revenue is. 341 Figure 18. In general, the higher the demand is, the more the dragon fruit grower’s revenue is. 341 Figure 18. In general, the higher the demand is, the more the dragon fruit grower’s revenue is. 2200000.00 2200000.00 1700000.00 1700000.00 1200000.00 1200000.00 700000.00 700000.00 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 Year Year 20% 40% 80% 20% 40% 80% 343 Figure 18. Profit for each case of increasing demand. 343 Figure 18. Profit for each case of increasing demand. Figure 18. Profit for each case of increasing demand. 4.4. Crop 3 Selling Price with a Probability Factor 344 4.4. Crop 3 Selling Price with a Probability Factor 344 4.4. Crop 3 Selling Price with a Probability Factor Currently, the bulk of Crop 3 in the market is imported. If it could be produced domestically, 345 Currently, the bulk of Crop 3 in the market is imported. If it could be produced domestically, 345 Currently, the bulk of Crop 3 in the market is imported. If it could be produced domestically, this demand would be less dependent on imports and could relieve price fluctuations. For this case, 346 this demand would be less dependent on imports and could relieve price fluctuations. For this case, 346 this demand would be less dependent on imports and could relieve price fluctuations. For this case, a probability factor is considered in the selling price. It is assumed three Crop 3 price scenarios of $1, 347 a probability factor is considered in the selling price. It is assumed three Crop 3 price scenarios of $1, 347 a probability factor is considered in the selling price. It is assumed three Crop 3 price scenarios of $1, $5, or $10 occurs in each year of the planning period of 10 years. The probability for each price is 348 $5, or $10 occurs in each year of the planning period of 10 years. The probability for each price is 348 $5, or $10 occurs in each year of the planning period of 10 years. The probability for each price is assumed be a discrete combination of 0.2, 0.2, and 0.6 for a total of 1.0 for the three price scenarios. 349 assumed be a discrete combination of 0.2, 0.2, and 0.6 for a total of 1.0 for the three price scenarios. 349 assumed be a discrete combination of 0.2, 0.2, and 0.6 for a total of 1.0 for the three price scenarios. The changes to the plantation for each case is presented below: 350 The changes to the plantation for each case is presented below: 350 The changes to the plantation for each case is presented below: Figures 19–21 show that the higher the most probable price of Crop 3, the greater the land allocated to it in the first year. The area of Crop 3 for each case is 5 ha, 4.7 ha, and 4 ha, respectively. In addition, the change in area of cultivating land is also a ected: the lower the most probable price, the higher the changeover to other crops. This can be observed in the 10-year profit projections (Figure 22). P Plla an ntte ed d a arre ea a o off e ea acch h ccrro op p ((h ha a)) Profi Profit t (US (USD) D) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 16 AgriEngineering 2020, 2, 1 15 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 16 16 15 10 10 10 10 4 5 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Year Year Crop 1 area Crop 2 area Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area New planting Cutting area New a p rle aa nting Cutting area area 352 Figure 19. Plantation allocation with probability combinationof prices$1 (0.2)–$5 (0.2)–$10 (0.6). 352 Figure 19. Plantation allocation with probability combinationof prices$1 (0.2)–$5 (0.2)–$10 (0.6). Figure 19. Plantation allocation with probability combinationof prices$1 (0.2)–$5 (0.2)–$10 (0.6). 16 15 14 15 10 10 10 10 6 5 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Year Total used Year Crop 1 area Crop 2 area Crop 3 area Tota ar l e u ased Crop 1 area Crop 2 area Crop 3 area area New planting area Cutting area AgriEngineering 2019, 2 FOR PEER REVIEW 17 New planting area Cutting area Figure 20. Plantation allocation with probability combination of prices $1 (0.2)–$5 (0.6)–$10 (0.2). 354 Figure 20. Plantation allocation with probability combination of prices $1 (0.2)–$5 (0.6)–$10 (0.2). 354 Figure 20. Plantation allocation with probability combination of prices $1 (0.2)–$5 (0.6)–$10 (0.2). 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area Figure 21. Plantation allocation with probability combinationof prices $1 (0.6)–$5 (0.2)–$10 (0.2). 356 Figure 21. Plantation allocation with probability combinationof prices $1 (0.6)–$5 (0.2)–$10 (0.2). 357 Figures 19–21 show that the higher the most probable price of Crop 3, the greater the land 358 allocated to it in the first year. The area of Crop 3 for each case is 5 ha, 4.7 ha, and 4 ha, respectively. 359 In addition, the change in area of cultivating land is also affected: the lower the most probable price, 360 the higher the changeover to other crops. This can be observed in the 10-year profit projections 361 (Figure 22). 1900000.00 1400000.00 900000.00 0 1 2 3 4 5 6 7 8 9 10 11 Year P20-20-60 P20-60-20 P60-20-20 363 Figure 22. Profit for each case in scenario 2.4. 364 4.5. Land Restriction 365 This scenario was suggested by the farmers who want to not only have a stable plantation size 366 for each crop, but also supply all three varieties of dragon fruits to the market. They would like to 367 use 50%, 35%, and 15% of their land to produce Crop 1, Crop 2, and Crop 3, respectively, and this is 368 in some sense a risk-hedging strategy. The cultivation activities (Figure 23) and the profit–cost 369 relationship (Figure 24) for a 10-year horizon are shown below: Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Profit ($US) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 17 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 356 Figure 21. Plantation allocation with probability combinationof prices $1 (0.6)–$5 (0.2)–$10 (0.2). 357 Figures 19–21 show that the higher the most probable price of Crop 3, the greater the land 358 allocated to it in the first year. The area of Crop 3 for each case is 5 ha, 4.7 ha, and 4 ha, respectively. 359 In addition, the change in area of cultivating land is also affected: the lower the most probable price, 360 AgriEngineering the higher 2020 the , chang 2, 1 eover to other crops. This can be observed in the 10-year profit projections 16 of 25 361 (Figure 22). 1900000.00 1400000.00 900000.00 0 1 2 3 4 5 6 7 8 9 10 11 Year P20-20-60 P20-60-20 P60-20-20 363 Figure 22. Profit for each case in scenario 2.4. Figure 22. Profit for each case in scenario 2.4. 4.5. Land Restriction 364 4.5. Land Restriction 365 This This scenario scenario was wasuggested s suggested by by the thfarmers e farmers who who want want to to not not only only have have aa stable stableplantation plantation size sizefor 366 for each crop, but also supply all three varieties of dragon fruits to the market. They would like to each crop, but also supply all three varieties of dragon fruits to the market. They would like to use 50%, 367 use 50%, 35%, and 15% of their land to produce Crop 1, Crop 2, and Crop 3, respectively, and this is 35%, and 15% of their land to produce Crop 1, Crop 2, and Crop 3, respectively, and this is in some 368 in some sense a risk-hedging strategy. The cultivation activities (Figure 23) and the profit–cost sense a risk-hedging strategy. The cultivation activities (Figure 23) and the profit–cost relationship AgriEngineering 2019, 2 FOR PEER REVIEW 18 369 relationship (Figure 24) for a 10-year horizon are shown below: (Figure 24) for a 10-year horizon are shown below: AgriEngineering 2019, 2 FOR PEER REVIEW 18 14 15 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Year Year Crop 1 area Crop 2 area Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area NN ew ew p p laln an titn in gg a a rr ee aa C Cu uttttiin n g g a a rr ee aa 370 370 Figure 23. Plantation allocation for land restriction scenario. 371 371 Figure Figure 23. 23. Pl Pl an an tati tati on alloc on allocati atio on n for for lland and restr restr ic ic ti ti on on scenar scenar io io . . 2000000.00 2000000.00 1500000.00 1500000.00 1000000.00 1000000.00 500000.00 500000.00 0.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 Year Year Revenue Cost Profit Revenue Cost Profit 373 Figure 24. Revenue, profit, and cost in 10 years. Figure 24. Revenue, profit, and cost in 10 years. 373 Figure 24. Revenue, profit, and cost in 10 years. 374 To ensure both the stability of area for each crop and the amount supplied to the market, farmers 374 To ensure both the stability of area for each crop and the amount supplied to the market, farmers 375 should re-vitalize the trees every few years (cutting old plants and planting new ones), especially in th 375 should re-vitalize the trees every few years (cutting old plants and planting new ones), especially in 376 the 4 year. th 376 the 4 year. 377 4.6. Influence of the Initial Plantation Conditions 377 4.6. Influence of the Initial Plantation Conditions 378 In addition to the mentioned variables above, such as customer demand and selling prices, the 379 initial crop status of the arable land is also considered to determine its influence on the changes in 378 In addition to the mentioned variables above, such as customer demand and selling prices, the 380 planting area. Based on the result of the baseline scenario, two sub-scenarios are proposed to look at 379 initial crop status of the arable land is also considered to determine its influence on the changes in 381 the effect of the variety of the initial crop and the age of the initial crop. In the first sub-scenario set, 380 planting area. Based on the result of the baseline scenario, two sub-scenarios are proposed to look at 382 it is supposed that all initial area has been allocated to only one of the three crops (Crop 1 or Crop 2 381 the effect of the variety of the initial crop and the age of the initial crop. In the first sub-scenario set, 383 or Crop 3). In the second sub-scenario set, only the initial land for Crop 1 is considered, with different 382 it is supposed that all initial area has been allocated to only one of the three crops (Crop 1 or Crop 2 384 ages (age 1, age 3, and age 5) in year 0. Other data is the same as in the baseline scenario. 383 or Crop 3). In the second sub-scenario set, only the initial land for Crop 1 is considered, with different 384 ages (age 1, age 3, and age 5) in year 0. Other data is the same as in the baseline scenario. 385 4.6.1. Initial Plantation with Only One Kind of Crop 386 According to results of the baseline scenario, the initial area that is used in year 0 is 15.3 hectares. 385 4.6.1. Initial Plantation with Only One Kind of Crop 387 It is assumed that only one crop has been planted on that area in year 0. Figures 25–27 show the 386 According to results of the baseline scenario, the initial area that is used in year 0 is 15.3 hectares. 388 cultivation activities for each case. 387 It is assumed that only one crop has been planted on that area in year 0. Figures 25–27 show the 388 cultivation activities for each case. Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) USD USD Profit ($US) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2020, 2, 1 17 of 25 To ensure both the stability of area for each crop and the amount supplied to the market, farmers should re-vitalize the trees every few years (cutting old plants and planting new ones), especially in the 4th year. 4.6. Influence of the Initial Plantation Conditions In addition to the mentioned variables above, such as customer demand and selling prices, the initial crop status of the arable land is also considered to determine its influence on the changes in planting area. Based on the result of the baseline scenario, two sub-scenarios are proposed to look at the e ect of the variety of the initial crop and the age of the initial crop. In the first sub-scenario set, it is supposed that all initial area has been allocated to only one of the three crops (Crop 1 or Crop 2 or Crop 3). In the second sub-scenario set, only the initial land for Crop 1 is considered, with di erent ages (age 1, age 3, and age 5) in year 0. Other data is the same as in the baseline scenario. 4.6.1. Initial Plantation with Only One Kind of Crop According to results of the baseline scenario, the initial area that is used in year 0 is 15.3 hectares. AgriEngineering 2019, 2 FOR PEER REVIEW 19 It is assumed that only one crop has been planted on that area in year 0. Figures 25–27 show the AgriEngineering 2019, 2 FOR PEER REVIEW 19 cultivation activities for each case. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Year Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area 390 Figure 25. Plantation allocation if the initial plantation only has Crop 1. Figure 25. Plantation allocation if the initial plantation only has Crop 1. 390 Figure 25. Plantation allocation if the initial plantation only has Crop 1. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Figure 26. Plantation allocation if the initial plantation only has Crop 2. 392 Figure 26. Plantation allocation if the initial plantation only has Crop 2. 392 Figure 26. Plantation allocation if the initial plantation only has Crop 2. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Year Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 19 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 390 Figure 25. Plantation allocation if the initial plantation only has Crop 1. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area AgriEngineering 2020, 2, 1 18 of 25 392 Figure 26. Plantation allocation if the initial plantation only has Crop 2. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area AgriEngineering 2019, 2 FOR PEER REVIEW 20 New planting area Cutting area Figure 27. Plantation allocation if the initial plantation only has Crop 3. 394 Figure 27. Plantation allocation if the initial plantation only has Crop 3. Although the initial land varies across these sub scenarios, Crop 2 is still the most planted over the 395 Although the initial land varies across these sub scenarios, Crop 2 is still the most planted over next 10 years. The profit for the case where the entire plantation consists of Crop 2 is also the highest, 396 the next 10 years. The profit for the case where the entire plantation consists of Crop 2 is also the as shown in Figure 28 below: 397 highest, as shown in Figure 28 below: 1600000.00 1400000.00 1200000.00 1000000.00 800000.00 600000.00 400000.00 200000.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 -200000.00 Year Crop 1 initial Crop 2 Initial Crop 3 Initial 399 Figure 28. The profit of the three cases of the initial land allocation. Figure 28. The profit of the three cases of the initial land allocation. 4.6.2. The Initial Crop Allocation with Di erent Crop 1 Ages 400 4.6.2. The Initial Crop Allocation With Different Crop 1 Ages In this case, it is assumed that the initial crop allocation is only for Crop 1. However, it is assumed 401 In this case, it is assumed that the initial crop allocation is only for Crop 1. However, it is assumed that the age is 1, 3, or 5 in year 0. The optimal crop allocation over the next 10 years is shown in 402 that the age is 1, 3, or 5 in year 0. The optimal crop allocation over the next 10 years is shown in Figures 29–31. 403 Figures 29–31. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 405 Figure 29. Plantation allocation if the initial land is only for Crop 1 at age 1. Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Profit (USD) Total planted area (ha) Total planted area (ha) Total T p ol ta an l t p eld an atreed a a (h re aa ) (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 20 394 Figure 27. Plantation allocation if the initial plantation only has Crop 3. 395 Although the initial land varies across these sub scenarios, Crop 2 is still the most planted over 396 the next 10 years. The profit for the case where the entire plantation consists of Crop 2 is also the 397 highest, as shown in Figure 28 below: 1600000.00 1400000.00 1200000.00 1000000.00 800000.00 600000.00 400000.00 200000.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 -200000.00 Year Crop 1 initial Crop 2 Initial Crop 3 Initial 399 Figure 28. The profit of the three cases of the initial land allocation. 400 4.6.2. The Initial Crop Allocation With Different Crop 1 Ages 401 In this case, it is assumed that the initial crop allocation is only for Crop 1. However, it is assumed 402 that the age is 1, 3, or 5 in year 0. The optimal crop allocation over the next 10 years is shown in AgriEngineering 2020, 2, 1 19 of 25 403 Figures 29–31. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area AgriEngineering 2019, 2 FOR PEER REVIEW 21 New planting area Cutting area AgriEngineering 2019, 2 FOR PEER REVIEW 21 Figure 29. Plantation allocation if the initial land is only for Crop 1 at age 1. 405 Figure 29. Plantation allocation if the initial land is only for Crop 1 at age 1. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area 407 Figure 30. Plantation allocation if the initial land is only for Crop 1 at age 3. Figure 30. Plantation allocation if the initial land is only for Crop 1 at age 3. 407 Figure 30. Plantation allocation if the initial land is only for Crop 1 at age 3. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Figure 31. Plantation allocation if the initial land is only for Crop 1 at age 5. 409 Figure 31. Plantation allocation if the initial land is only for Crop 1 at age 5. 409 Figure 31. Plantation allocation if the initial land is only for Crop 1 at age 5. 410 We can see that the young Crop 1 (age 1) is truncated more than the grown one (age 3 or age 5). 410 We can see that the young Crop 1 (age 1) is truncated more than the grown one (age 3 or age 5). 411 Similar to trends observed earlier, after Crop 1 area is reduced, most of the remaining land is 411 Similar to trends observed earlier, after Crop 1 area is reduced, most of the remaining land is 412 prioritized for Crop 2, which has the most revenue because of its high demand. The profits for all 412 prioritized for Crop 2, which has the most revenue because of its high demand. The profits for all 413 three cases are shown in Figure 32. 413 three cases are shown in Figure 32. 2500000.00 2500000.00 1500000.00 1500000.00 500000.00 500000.00 -500000.00 0 1 2 3 4 5 6 7 8 9 10 11 -500000.00 0 1 2 3 4 5 Year 6 7 8 9 10 11 Year Age 1 Age 3 Age 5 Age 1 Age 3 Age 5 Plant P eld an atreed a a orfe e aa o cf h e ca rc oh p c(r h oa p ) (ha) Plant P eld an atreed a a orfe e aa o cf h e ca rc oh p c(r h oa p ) (ha) Planted area of each crop (ha) Profit (USD) Profi Profi t (US t (US D) D) Total planted area (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 21 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 407 Figure 30. Plantation allocation if the initial land is only for Crop 1 at age 3. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area AgriEngineering 2020, 2, 1 20 of 25 409 Figure 31. Plantation allocation if the initial land is only for Crop 1 at age 5. We can see that the young Crop 1 (age 1) is truncated more than the grown one (age 3 or age 5). 410 We can see that the young Crop 1 (age 1) is truncated more than the grown one (age 3 or age 5). Similar to trends observed earlier, after Crop 1 area is reduced, most of the remaining land is prioritized 411 Similar to trends observed earlier, after Crop 1 area is reduced, most of the remaining land is for Crop 2, which has the most revenue because of its high demand. The profits for all three cases are 412 prioritized for Crop 2, which has the most revenue because of its high demand. The profits for all shown in Figure 32. 413 three cases are shown in Figure 32. 2500000.00 1500000.00 500000.00 -500000.00 0 1 2 3 4 5 6 7 8 9 10 11 Year Age 1 Age 3 Age 5 Figure 32. The profits for the three cases of initial land allocation to Crop 1 for di erent ages. 4.7. Discussion Throughout scenarios and cases above, summarized in Table 2, we can see that the dragon fruit growers earn more profit if they prioritize planting the varieties for which both demand and selling price are high. This is the case for Crop 2 which has a very high demand and its price is only lower than the price of Crop 3. In contrast, although the price of Crop 3 is the highest, due to lower demand and yield, it is not prioritized in the solutions. Finally, the selling price of Crop 1 is the lowest; therefore, it is replaced by other varieties when the demands or prices of the other two crops increase. Table 2 summarizes the profits for each of the scenarios. Table 2. Summary of the profitability of the various scenarios. Scenario Sub-Scenario Limit on Plantation Area for Each Crop Profit Baseline scenario No limit for each crop USD 12,576,086.80 1 No limit for each crop USD 20,089,622.07 Changes in price of Crop 2 2 No limit for each crop USD 20,116,237.86 1 No limit for each crop USD 16,815,478.39 Changes in demands 2 No limit for each crop USD 13,932,145.96 3 No limit for each crop USD 15,166,044.33 4 No limit for each crop USD 15,740,093.18 1 No limit for each crop USD 14,438,789.39 Crop 3 selling price with probability factor 2 No limit for each crop USD 12,745,440.97 3 No limit for each crop USD 11,415,607.18 50% for Crop 1, 35% for Crop 2, 15% for Land restriction USD 9,963,130.32 Crop 3 Crop 1 No limit for each crop USD 10,921,697.80 Crop 2 No limit for each crop USD 12,182,762.60 Influence of initial land Crop 3 No limit for each crop USD 11,630,711.50 Crop 1—Age 1 No limit for each crop USD 10,763,932.06 Crop 1—Age 3 No limit for each crop USD 10,907,367.04 Crop 1—Age 5 No limit for each crop USD 10,879,376.28 Planted area of each crop (ha) Planted area of each crop (ha) Profit (USD) AgriEngineering 2020, 2, 1 21 of 25 5. Conclusions A deterministic model is proposed in this paper to assist dragon fruit farmers with their decision making on crop allocation for di erent species of dragon fruits. Consequently, it can provide them a long-term overview through groups of production scenarios that could occur, such as (1) price changes (e.g., price of the red-skin red-flesh dragon fruit—Crop 2); (2) changes in demand (e.g., demand of the yellow-skin white-flesh dragon fruit—Crop 3); (3) requirements for land restrictions for each type of crop, and (4) the influence of the initial state. All scenarios are variants from a baseline scenario of the actual dragon fruit production conditions in Vietnam intended to provide insights. Results obtained from this model confirmed that the Crop 2 should be prioritized for planting. The model presented in this paper represents a first step towards a comprehensive quantitative approach for decision making in dragon fruit cultivation in Vietnam. The model works well with some scenarios showing relationships of input factors (demands, prices, and costs) and output decisions (plantation area of crops) over a 10-year period. This is evident in the cases of “no limit plantation area” of all scenarios: the crop is grown if its demand and price increase, or it is cut down when its demand is low and its price drops. For a specific crop, the old plants are replaced by new ones if its yield is too low due to age. The proposed model is a meaningful tool for managers and farmers to have a holistic view for long term planning with the goal of maximizing profits. It helps decide which varieties to plant proactively based on demand and price scenarios. As with other fresh fruit supply chains, the dragon fruit chain faces challenges due to inherent uncertainties such as demands, price, and yield. This is the main limitation of the deterministic approach. Therefore, future research to deal with randomness and uncertainty for dragon fruit cultivation could involve stochastic programming [44–46] or robust optimization [47]. The approach can be generalized to other similar fresh fruit supply chains. Author Contributions: Conceptualization: T.-D.N., U.V., T.N.-Q.; Data curation: T.-D.N., T.N.-Q.; Format analysis: T.-D.N., U.V., T.N.-Q.; Funding acquisition: T.N.-Q.; Investigation: T.-D.N., U.V.; Methodology: T.-D.N., U.V., T.N.-Q.; Supervision: U.V., T.N.-Q., C.D., M.A.; Validation: T.-D.N., U.V., T.N.-Q., C.D., M.A.; Visualization: C.D., M.A.; Writing—original draft: T.-D.N., U.V., T.N.-Q.; Writing—review & editing: T.-D.N., U.V., T.N.-Q., C.D., M.A. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Vietnam International Education Development (VIED). Acknowledgments: The first author acknowledges the Vietnam International Education Development (VIED) via the 911 research scholarship program as well as Vietnamese colleagues, collaborators, and the farmers from Binh Thuan, Vietnam for the data collection. Conflicts of Interest: The authors have no conflicting financial or other interests. Nomenclature DC Distribution Centers DF Dragon fruit FFSC Fresh Fruit Supply Chain FSC Fruit Supply Chain GLPK GNU Linear Programming Kit GUSEK GLPK Under Scite Extended Kit LP Linear Programming MIP Mixed Integer Programming VIED The Vietnam International Education Development AgriEngineering 2020, 2, 1 22 of 25 Appendix A Indices: t Time periods k Age classes in the plantation, each representing a two-year period s Harvesting season (1 for wet, 2 for dry) j Di erent species of dragon fruit i Traders m Wholesale markets (WM) b By-product Parameters: L Amount of land available w Water required per hectare for crop j of age class k in season s ks v Lighting required per hectare for crop j in season s js W Water restriction in season V Lighting restriction in season u Minimum planting area per crop j in period t jt Yield in kgs per hectare of crop j belonging to age class k in season s jkst p Price per kg of crop j for trader i in season s of period t jist q Price per kg of crop j for wholesaler m in season s of period t jmst r Price per kg of byproducts (e.g., wine) in period t st d Demand of trader i for crop j in season s of period t i jst e Demand of wholesale market m for crop j in season s of period t m jst f Demand for byproducts (e.g., wine) in period t P Number of workers needed to plant one hectare H Number of workers needed to harvest one hectare R Number of workers needed to cut one hectare M Maximum number of fixed workers in a period N Maximum number of part-time workers in a period I Initial area of crop j of age class k jk Cost parameters: cp Cost per hectare of planting in period t ch Cost per hectare of harvesting in period t cr Cost per hectare of cut in period t cbp Cost per kg of processing (e.g. wine) cLab f Cost of fixed workers per period cLabp Labor cost of part-time workers per period cPNT Penalty for not meeting demand per kg of crop j for trader i jist in season s of period t Cost of required water per hectare for crop j of age class k cwater ks in season s clighting Cost of required light per hectare for crop j in season s js Variables: X Plantation area of crop j in period t of age class k jkt ST Quantity of crop j shipped to trader i in season s of period t jist Quantity of crop j under shipped to trader i in season s of period t i jst SWM Quantity of crop j shipped to WM m in season s of period t jmst AgriEngineering 2020, 2, 1 23 of 25 SB Quantity of crop j harvested for by-products (e.g. wine) in season s of jst period t F Number of fixed workers in t Hire Part-time workers hired in period t Y Area of crop j planted in period t jt Z Area of crop j of age class k cut optionally in period t jkt Z Area of crop j of age class k = 10 that must be cut in period t jkt Z Area of crop j of age class k cut in period t in total jt Appendix B Table A1. Summary of scenarios with their characteristics. Situation (Sub-Scenario Limit of Planting Area Scenario Descriptions or Case) for Each Crop Demands and prices unchanged Baseline scenario No limit for each crop within 10 years The price increasing gradually 1 No limit for each crop within 10 years Changes in price of Crop 2 The price decreasing gradually 2 No limit for each crop within 10 years Demand of Crop 3 increasing 1 No limit for each crop 4 times 2 No limit for each crop Demands of all crops increasing 20% Changes in demands 3 No limit for each crop Demands of all crops increasing 40% 4 No limit for each crop Demands of all crops increasing 80% 1 No limit for each crop 0.2 for $1, 0.2 for $5, and 0.6 for $10 Crop 3 selling price with probability factor 2 No limit for each crop 0.2 for $1, 0.6 for $5, and 0.2 for $10 3 No limit for each crop 0.6 for $1, 0.2 for $5, and 0.2 for $10 50% for Crop 1, 35% for Demands and prices unchanged Land restriction Crop 2, 15% for Crop 3 within 10 years All initial land used for Crop 1. Crop 1 No limit for each crop Demands and prices unchanged within 10 years All initial land used for Crop 2. Crop 2 No limit for each crop Demands and prices unchanged within 10 years All initial land used for Crop 2. Crop 3 No limit for each crop Demands and prices unchanged within 10 years Influence of initial land All initial land used for Crop 1 at Crop 1—Age 1 No limit for each crop age 1. Demands and prices unchanged within 10 years All initial land used for Crop 1 at Crop 1—Age 3 No limit for each crop age 3. Demands and prices unchanged within 10 years All initial land used for Crop 1 at Crop 1—Age 5 No limit for each crop age 5. Demands and prices unchanged within 10 years References 1. Ahumada, O.; Villalobos, J.R. Application of planning models in the agri-food supply chain: A review. Eur. J. Oper. Res. 2009, 196, 1–20. [CrossRef] 2. Hamer, P.J. A decision support system for the provision of planting plans for Brussels sprouts. Comput. Electron. Agric. 1994, 11, 97–115. 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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png AgriEngineering Multidisciplinary Digital Publishing Institute

Optimization Model for Fresh Fruit Supply Chains: Case-Study of Dragon Fruit in Vietnam

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AgriEngineering Article Optimization Model for Fresh Fruit Supply Chains: Case-Study of Dragon Fruit in Vietnam 1 , 2 1 2 , 1 Tri-Dung Nguyen , Uday Venkatadri , Tri Nguyen-Quang *, Claver Diallo and Michelle Adams Department of Industrial Engineering, Dalhousie University, PO BOX 15000, Halifax, NS B3H 4R2, Canada; TD.Nguyen@dal.ca (T.-D.N.); uday.venkatadri@dal.ca (U.V.); claver.diallo@dal.ca (C.D.) Biofluids and Biosystems Modeling Lab. (BBML), Department of Engineering, Faculty of Agriculture, Dalhousie University, 39 Cox Road, Truro, NS B2N 5E3, Canada School for Resource and Environmental Studies, Dalhousie University, 6100 University Ave, PO BOX 15000, Halifax, NS B3H 4R2, Canada; Michelle.Adams@dal.ca * Correspondence: tri.nguyen-quang@dal.ca Received: 4 November 2019; Accepted: 16 December 2019; Published: 20 December 2019 Abstract: We present an optimization model for dragon fruit plantations in Vietnam. The timing of cultivating and harvesting decisions are taken into account as the dragon fruit plant has an approximately ten-year life cycle with maximum average yield in the fourth year. Another consideration also included is the prevalence of forward-buying contracts with locked-in prices. The dragon fruit supply chain faces several diculties as yield, price, and demand are highly sensitive to weather conditions and global uncertainty factors. The risk factors in the dragon fruit supply chain also depend on species—for example, the red varieties, while more profitable than the white varieties, also have higher export risk because they are subject to global prices and adverse geopolitical conditions. Keywords: dragon fruit (DF); optimization model; fresh fruit supply chain; Vietnam 1. Introduction In recent years, along with the development of the supply chain management and logistics industry, the agri-food supply chain in general and the fresh fruit chain in particular have been recognized as strategic components of the national economy of many developing countries such as Vietnam. Compared to staple crops, fruit production brings greater economic benefits. However, the fruit and vegetable production sector also faces particular risks such as climate change, water scarcity, increase in land-use for industrial and urban development, and consumer behavior and price volatility. Moreover, the planning and managing of production, distribution, and pricing of fresh fruits are more complicated because of their very short shelf-life. The value can be increased if the value chain of fruit and vegetable production and distribution is better organized from farmers to retailers. Countries where agriculture is in development, i.e., Vietnam, are still facing challenges such as: The influence of traditional trade practices—there are many intermediate nodes involved in the network, making the food supply chain longer and more complex than in other developed countries. The high cost of storage after harvesting and transportation—this is due to the tropical climate with high temperature and humidity. AgriEngineering 2020, 2, 1; doi:10.3390/agriengineering2010001 www.mdpi.com/journal/agriengineering AgriEngineering 2020, 2, 1 1 of 25 The continued use of low paid labor. Though labor is cheap, there is a high workforce turnaround. The workforce shortages are acute at the beginning and end of the harvest season when labor demand is high due to competition. During these periods, workers often change employers for better pay. The poor availability of information within the value chain from growers to collectors/traders, wholesalers, retailers, and supermarkets about the harvest, preliminary processing, packing, labeling, preserving, and transportation. The inability of farmers to set produce prices—farmers play the most important role in the food supply chain but most of them are small, with little influence on price. They must sell their products at prices determined by traders due to lack of market information and experience. Due to the lack of long-term orientation at the macro-level of management, farmers target profits based on market demand. In the dragon fruit case, this may imply cutting existing varieties of the fruit and changing over to other varieties, based on anticipated demand. Since dragon fruit is a perennial plant, the impact of these decisions can last several years. It can be said that making decisions for a fresh fruit supply chain management is a more dicult and complex problem than with other supply chains [1]. This is a great challenge for fresh fruit supply chain (FFSC) managers over the past 40 years, given the increasing globalization and rapidly increasing demand. They need a tool to support modern and accurate decision-making for long-term production. There are several articles in the literature related to FFSCs with many di erent approaches or methods that could support optimization of a part or the whole chain. The deterministic approach is a very common and often used in the FFSC research; formulations are based on both linear programming [2–7] and mixed integer programming [8–17]. There are two essential types of fruit used for case studies: perennial crops such as apples [18–21], oranges [6,12], pome fruit [10], pears [16,22,23], cherries [24] and grapes [4,25,26] or annual crops such as pineapple [27], strawberries [28], melon [29], and tomato [13,30,31]. Dragon fruit is a tropical fast-growing perennial crop, other examples being asparagus [32], Persian lime [33], Thai soursop, Taiwan pear-shaped guava, etc. During the last several years, the fresh produce cold chain has received attention from researchers around the world to enhance the quality and freshness of fruits and vegetables delivered to customers. The cold chain issues considered by most researchers have to do with controlling the temperature and gas flow in containers [34–36], minimizing the energy used to refrigerate containers [37], and optimizing the transport system in the chain [38]. The dragon fruit (Figure 1) is a tropical fruit grown extensively in Vietnam. With 36.5 thousand hectares of cultivated land and 630 thousand tons of total yield, Vietnam is the world’s leading exporter of dragon fruit [39]. However, dragon fruit production and processing are still in a nascent stage of development and face issues around severe price fluctuations due to conditions such as: a. Product development is still nascent; b. Market price fluctuations; c. Chinese imports are subject to price and currency exchange risks; d. High competition with other exporting countries (such as Thailand, Malaysia, etc.) driving down value despite increased export volumes; e. Export has been increasing both in volume and value but the increase in value has been declining. This paper presents an optimization model for dragon fruit crop planning to support farmers make decisions on the allocation of land to crop varieties. The objective of the model is to maximize profit, while satisfying customer demand. Given that dragon fruit is perennial but fast growing, there is an opportunity to change the crop mix based on anticipated future prices. However, there could be a loss in yield depending on the maturity of the crops in a plantation mix. The remainder of this paper is organized as follows: Section 2 introduces dragon fruit plantation and crop planning. Section 3 AgriEngineering 2020, 2, 1 2 of 25 presents a linear programming optimization model for crop harvesting and replantation decisions. Section 4 presents the results and discussions from example scenarios. Section 5 concludes the paper AgriEngineering 2019, 2 FOR PEER REVIEW 3 and outlines areas for further study. AgriEngineering 2019, 2 FOR PEER REVIEW 3 95 Figure 1. Dragon fruit trees blossoming (left) and fruiting (right) in June–July. Photos taken in 2016 in 95 Figure 1. Dragon fruit trees blossoming (left) and fruiting (right) in June–July. Photos taken in 2016 in Figure 1. Dragon fruit trees blossoming (left) and fruiting (right) in June–July. Photos taken in 2016 in 96 Binh Thuan province, Vietnam. 96 Binh Thuan province, Vietnam. Binh Thuan province, Vietnam. 97 2. Dragon Fruit Plantation Characteristics 2. Dragon Fruit Plantation Characteristics 97 2. Dragon Fruit Plantation Characteristics 98 2.1. Fruit Distribution Context 2.1. Fruit Distribution Context 98 2.1. Fruit Distribution Context 99 The dragon fruit supply chain starts with farmers who make plantation decisions based on The dragon fruit supply chain starts with farmers who make plantation decisions based on 99 The dragon fruit supply chain starts with farmers who make plantation decisions based on 100 forward buy-in contracts with traders. The traders sell fruit to by-products and wholesalers who in forward buy-in contracts with traders. The traders sell fruit to by-products and wholesalers who in 100 forward buy-in contracts with traders. The traders sell fruit to by-products and wholesalers who in 101 turn distribute the fruit and by-products to retail, export, and by-product producers. The dragon fruit turn distribute the fruit and by-products to retail, export, and by-product producers. The dragon fruit 101 turn distribute the fruit and by-products to retail, export, and by-product producers. The dragon fruit 102 supply chain is depicted in Figure 2. Typical dragon fruit by-products are wine and packaged dried supply chain is depicted in Figure 2. Typical dragon fruit by-products are wine and packaged dried 102 supply chain is depicted in Figure 2. Typical dragon fruit by-products are wine and packaged dried 103 fruit snacks. fruit snacks. 103 fruit snacks. Export markets Export markets Collectors/ Farmers Wholesalers Retailers Collectors/ Traders Farmers Wholesalers Retailers Traders By-product By-product producers producers Figure 2. Simplified dragon fruit supply chain [40]. 105 Figure 2. Simplified dragon fruit supply chain [40]. 105 Figure 2. Simplified dragon fruit supply chain [40]. Dragon fruit is typically planted twice a year in Vietnam. Harvesting starts one year after 106 Dragon fruit is typically planted twice a year in Vietnam. Harvesting starts one year after 106 Dragon fruit is typically planted twice a year in Vietnam. Harvesting starts one year after plantation, but the fruit is at the quality required for commercial purposes 2–10 years after harvest. 107 plantation, but the fruit is at the quality required for commercial purposes 2–10 years after harvest. 107 plantation, but the fruit is at the quality required for commercial purposes 2–10 years after harvest. 108 Dragon fruit yield typically depends on age and a tree is usually only considered productive until 108 Dragon fruit yield typically depends on age and a tree is usually only considered productive until 109 the age of 12 years. Figure 3 shows the typical yield curve as a function of tree age (based on [41]). 109 the age of 12 years. Figure 3 shows the typical yield curve as a function of tree age (based on [41]). AgriEngineering 2020, 2, 1 3 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 4 Dragon fruit yield typically depends on age and a tree is usually only considered productive until the AgriEngineering 2019, 2 FOR PEER REVIEW 4 age of 12 years. Figure 3 shows the typical yield curve as a function of tree age (based on [41]). 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Year Year 111 Figure Figure3. 3. Typ Typical ical dragon dragon fru fruit it yield yield aas s aa fun function ction of oftree tree age age. . 111 Figure 3. Typical dragon fruit yield as a function of tree age. There are three varieties of dragon fruit planted in Vietnam: the red-skin white-flesh, the 112 There are three varieties of dragon fruit planted in Vietnam: the red-skin white-flesh, the red- 112 red-skin There red-flesh are three and var the ietiyellow-skin es of dragon white-flesh fruit planted (Figur in V e ietnam: 4). The rth ed-skin e red-s varieties kin whitar e-e fles very h, th popular e red- , 113 skin red-flesh and the yellow-skin white-flesh (Figure 4). The red-skin varieties are very popular, the the white-flesh variety being the most sold. The red-skin red-flesh variety has a high demand during 113 skin red-flesh and the yellow-skin white-flesh (Figure 4). The red-skin varieties are very popular, the 114 white-flesh variety being the most sold. The red-skin red-flesh variety has a high demand during the 114 whit the lunar e-flesh New variety Year be and ing is thalso e moexported st sold. Th ext e red ensively -skin red to China. -flesh vThe ariety yellow has a peel highwhite demand flesh du variety ring the is 115 lunar New Year and is also exported extensively to China. The yellow peel white flesh variety is relatively new in Vietnam and is available only in major metropolitan areas. 115 lunar New Year and is also exported extensively to China. The yellow peel white flesh variety is 116 relatively new in Vietnam and is available only in major metropolitan areas. 116 relatively new in Vietnam and is available only in major metropolitan areas. Red-skin white-flesh Red-skin red-flesh Yellow-skin white-flesh Red-skin white-flesh Red-skin red-flesh Yellow-skin white-flesh 117 Figure 4. Species of dragon fruit planted in Vietnam [41]. Figure 4. Species of dragon fruit planted in Vietnam [41]. 117 Figure 4. Species of dragon fruit planted in Vietnam [41]. The dragon fruit blooms from May to August and is ready a month later for harvesting in 118 The dragon fruit blooms from May to August and is ready a month later for harvesting in 118 The dragon fruit blooms from May to August and is ready a month later for harvesting in 119 Septem September ber an and d Oct October ober. . H However owever, ,dr dragon agon fruit fruitprice prices s are areu usually sually llow ow in inth the e ma main in season season ((due due to to th the e 119 September and October. However, dragon fruit prices are usually low in the main season (due to the availability of the fruit). Due to its high economic value in January and February, dragon fruit growers 120 availability of the fruit). Due to its high economic value in January and February, dragon fruit 120 availability of the fruit). Due to its high economic value in January and February, dragon fruit 121 growers install lighting install light systems ing sy to s sti tem mulate s to stimu treesla to te bloom trees to and bloom haveand fruits hav toe impr fruits ove to pr im oductivity prove produc in the tivity dry 121 growers install lighting systems to stimulate trees to bloom and have fruits to improve productivity season which lasts from November to April [40]. Therefore, there are two times for harvesting, either 122 in the dry season which lasts from November to April [40]. Therefore, there are two times for 122 in the dry season which lasts from November to April [40]. Therefore, there are two times for 123 harvestin from May g,to eith October er from (rainy May season to Octob or er season (rainy1) seor ason from or November season 1) or tofrom AprilNove (drymb season er toor Apri season l (dry 2) 123 harvesting, either from May to October (rainy season or season 1) or from November to April (dry (Figure 5). 124 season or season 2) (Figure 5). 124 season or season 2) (Figure 5). May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr Rainy season (season 1) Dry season (season 2) Rainy season (season 1) Dry season (season 2) 125 Figure 5. Dragon fruit production calendar in Vietnam. 125 Figure 5. Dragon fruit production calendar in Vietnam. Kg/pole Kg/pole AgriEngineering 2019, 2 FOR PEER REVIEW 4 0 2 4 6 8 10 12 14 Year 111 Figure 3. Typical dragon fruit yield as a function of tree age. 112 There are three varieties of dragon fruit planted in Vietnam: the red-skin white-flesh, the red- 113 skin red-flesh and the yellow-skin white-flesh (Figure 4). The red-skin varieties are very popular, the 114 white-flesh variety being the most sold. The red-skin red-flesh variety has a high demand during the 115 lunar New Year and is also exported extensively to China. The yellow peel white flesh variety is 116 relatively new in Vietnam and is available only in major metropolitan areas. Red-skin white-flesh Red-skin red-flesh Yellow-skin white-flesh 117 Figure 4. Species of dragon fruit planted in Vietnam [41]. 118 The dragon fruit blooms from May to August and is ready a month later for harvesting in 119 September and October. However, dragon fruit prices are usually low in the main season (due to the 120 availability of the fruit). Due to its high economic value in January and February, dragon fruit 121 growers install lighting systems to stimulate trees to bloom and have fruits to improve productivity 122 in the dry season which lasts from November to April [40]. Therefore, there are two times for AgriEngineering 2020, 2, 1 4 of 25 123 harvesting, either from May to October (rainy season or season 1) or from November to April (dry 124 season or season 2) (Figure 5). May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr AgriEngineering 2019, 2 FOR PEER REVIEW 5 Rainy season (season 1) Dry season (season 2) 126 Dragon fruit trees are commercially viable for 10–12 years, but because they grow quickly, the 125 Figure 5. Dragon fruit production calendar in Vietnam. Figure 5. Dragon fruit production calendar in Vietnam. 127 plantations can continue to harvest existing crops below that age or cut them down for investment in Dragon fruit trees are commercially viable for 10–12 years, but because they grow quickly, 128 other varieties based on demand and price. the plantations can continue to harvest existing crops below that age or cut them down for investment in other varieties based on demand and price. 129 2.2. Methodology 130 The methodology in this paper is aligned with the hierarchical planning approach which 2.2. Methodology 131 separates the decision-making process into tactical and operational phases [42]. In hierarchical The methodology in this paper is aligned with the hierarchical planning approach which separates 132 planning, decisions are first made at the tactical level and then at the operational level. Figure 6, the decision-making process into tactical and operational phases [42]. In hierarchical planning, 133 which is adapted from Ahumada et al. [31], shows how the hierarchical approach may be applied to decisions are first made at the tactical level and then at the operational level. Figure 6, which is 134 the dragon fruit chain. adapted from Ahumada et al. [31], shows how the hierarchical approach may be applied to the dragon 135 In this paper, a quantitative modeling approach for decision making for dragon fruit plantation fruit chain. 136 and harvesting in Vietnam is presented. As previously mentioned, this approach looks at planting In this paper, a quantitative modeling approach for decision making for dragon fruit plantation 137 and cutting (which are tactical decisions) taken over a multi-year planning horizon. The potential and harvesting in Vietnam is presented. As previously mentioned, this approach looks at planting 138 benefit from the hierarchical planning is that growers can be involved in making decisions about the and cutting (which are tactical decisions) taken over a multi-year planning horizon. The potential 139 market and production. In other words, coordinating tactical and operational decisions is beneficial benefit from the hierarchical planning is that growers can be involved in making decisions about the 140 for multiple parties: growers, producers, distributors, and vendors. market and production. In other words, coordinating tactical and operational decisions is beneficial for multiple parties: growers, producers, distributors, and vendors. Inputs Season demand Outputs Available resources Planting /Cutting Crops to plant Tactical Crop requirements Plan Seasonal production phase Expected price Cost Information Inputs Seasonal prices Operational Outputs Seasonal demand phase Harvesting Plan Seasonal harvesting Seasonal development of Seasonal shipments plants Production capacity Figure 6. Example of a hierarchical planning schematic. 143 Figure 6. Example of a hierarchical planning schematic. In Figure 6, the first phase deals with tactical decisions that are only made at the start of the season 144 In Figure 6, the first phase deals with tactical decisions that are only made at the start of the such as what crop to plant or truncate, and when and how much to plant or truncate. While in the 145 season such as what crop to plant or truncate, and when and how much to plant or truncate. While second phase, farmers must decide how much to sell to customers in each season according to the 146 in the second phase, farmers must decide how much to sell to customers in each season according to market conditions. 147 the market conditions. To execute the hierarchical planning schematic, a deterministic optimization model is developed 148 To execute the hierarchical planning schematic, a deterministic optimization model is developed in this paper for the dragon fruit production in Vietnam. Although dragon fruit is used as the main 149 in this paper for the dragon fruit production in Vietnam. Although dragon fruit is used as the main target the current study, our model can certainly be adapted to other fresh fruit production chains. 150 target the current study, our model can certainly be adapted to other fresh fruit production chains. 151 3. Linear Programming Optimization Model 152 3.1. Hypotheses and Assumptions 153 For this model, it is assumed that: 154 1. The facilities (farms) are already operational since the model does not deal with network 155 decisions. Kg/pole AgriEngineering 2020, 2, 1 5 of 25 3. Linear Programming Optimization Model 3.1. Hypotheses and Assumptions For this model, it is assumed that: 1. The facilities (farms) are already operational since the model does not deal with network decisions. 2. The time horizon for tactical planning is 10 years and two harvesting seasons (rainy season and dry season) for each year are considered. 3. Fruit trees are cut down when they are 10 years of age or earlier, if the model chooses to (e.g., when the future prices of other crops are much higher than the planted crop). It is assumed that cutting down or replanting decisions are only carried out in season 1. 4. The distribution of yield, demand, and market prices are represented by their expected values. 5. Storage is not allowed for fresh dragon fruit. However, the fruit may be used for by-products such as dry snacks and wine. 6. The amounts of each crop to cut and plant are decision variables which cannot exceed the maximum amount of land that is already determined. 7. Decision variables of the model are the new plantation and truncating areas of each crop, and the amount of fruit sent to customers (traders, wholesalers, and by-product producers) in every year. 8. Other decisions include the quantity of fruit to sell to customers and the amount of labor (fixed and part-time) is required to cover all the activities in the model. 3.2. Objective Function XXXX XXXX Max O = p ST + q SWM jist jist jmst jmst s m s t t j i j XXX XX X + r SB cp Y ch X jst jst jt jt t jkt1 s t t j j j X X X cr Z F cLab f Hire cLabp t t t j,k=10,t (1) t t X XXX cbp SB cPNT st jst jist i jst t s j j XX XX cwater w clighting v ks ks js js k j s=2 The objective of the proposed model is to determine the planting and harvesting decisions that maximize expected profit for the farmers; this is the di erence between the total revenue expected from selling to traders (ST), wholesale markets (SWM), and by-product suppliers (SB), and the total costs of planting, truncating, by-product processing, penalty for missing demand, labor, lighting cost, and watering. The notation is presented in Appendix A. 3.3. Constraints The first category of constraints (2, 3, and 4) is related to resources (land, water, and lighting). - Land availability XX X  L 8t (2) jkt j k Total of area of each crop j at age k cannot exceed the available land (L). - Water restriction AgriEngineering 2020, 2, 1 6 of 25 XX X w  W 8t, s (3) st jkst jkst At each tree age k, the amount of water w required per hectare for each crop j is di erent in season s of year t; this cannot exceed the availability of water. Also, yield decreases if the trees are watered too much. - Lighting restrictions X v  V 8s (4) s s js Due to lack of sunlight in the dry seasons (s = 2), a light supplementing method is applied at night. At each tree age k, the requirement of light per hectare for each crop j is di erent but limited. Constraints (5) and (6) are for plantation area and yield. - Minimum plantation size X  u 8t (5) jt jtk Constraint (5) is the lower bound for the planting area for each crop in a given period, which may come from forward contracts. The minimum planting area of each crop u is defined by the planner depending on commitments to customers. The parameter u could be 0 but should be less than the available land L. - Yield X X X ST + SWM + SB  X 8 j, s, t (6) jist jmst jst jkst jkst i k Constraint (6) ensures that the total harvest is less than the yield (metric tons per hectare) times plantation area (in hectares). - Plantation age class balance The third category of constraints (7–15) is related to the planning structure for agriculture models. The cutting down and replanting of new varieties has been modeled in Catalá [10] for a case study on apple and pear trees. X = X 8 j, k, t (7) j,k,s=1,t j,k,s=2,t Constraint (7) ensures that there is no change in the planted area of each crop within a year (i.e., between season 1 and season 2). This is because plantation or truncation decisions are only made at the start of season 1. The plantation decisions are decided by Y . The age of a newly planted fruit tree is always 0. jt 1 2 There are two types of truncations: Z , which is optional for a tree of age k = 1::: 9 and Z jkt j,k=10,t which is mandatory for all trees that have reached an age of 10. X = Y 8 j, k = 1, t = 1 (8) jkst jt Constraint (8) states that in year 1 only new crops (age class 1) can be planted. X = I Z 8 j, k = [2::: 9], t = 1 (9) jkst j,k1 jkt AgriEngineering 2020, 2, 1 7 of 25 Constraint (9) is similar to constraint 8 and applies only to year 1 but for other age classes (k = 2. . . 9). It states that the plantation area is the inventory of trees of age class k-1 in year 0 less what can be cut down in year 1 after they have aged by 1 year. X = I Z 8 j, k = 10, t = 1 (10) jkst j,k1 jkt Constraint (10) states that age-10-crops that have to be cut down in year 1 while determining the initial plantation area. X X X X = Y Z 8 j, k = 1, t > 1 (11) jkst j,t1 jkt Constraint (11) states that for periods t > 1 in the planning horizon, the plantation area for age class k = 1 is determined by new crop planted the year before less whatever is cut from that new plantation the next year. X = X Z 8 j, 10 > k > 1, t > 1 (12) jkst j,k1,s,t1 jkt Constraint (12) is for crop ageing for age classes 10 > k > 1. The plantation size in a given year depends on what it was the previous year, less the area cut down optionally. Z = X 8 j, k = 10, t > 1 (13) jkt j,k1,s,t1 Constraint (13) states that all crops of age 9 in a given year t-1 should be cut the next year. - Labor constraints X X X F + Hire P  Y H  X R  Z = 0 8t (14) t t t jt t jt t jkt j j j Constraints (14) models workforce requirements to plant, cut, and harvest in given year. F = M 8t (15) The number of fulltime workers is sometimes a fixed number. If that is the case, the full time complement of workers should be set to that number. Hire  N 8t (16) The number of part time workers hired based on requirements of cultivating or harvesting or truncating. However, the number is limited due to budget, as seen in constraint (16). The last set of constraints, (17) to (19), is for demand satisfaction: ST = d  8t, s (17) jist jist jist Constraint (17) is a soft constraint on trader demands, given that under-shipping to them is allowed. SWM = e 8t, s (18) jmst jmst Constraint (18) states that the demand of wholesalers should be satisfied. SB = f 8t (19) jt j AgriEngineering 2020, 2, 1 8 of 25 Constraint (19) states that the demand of by-products should be satisfied. 4. Case Study The model for dragon fruit cultivation presented in the previous section was applied using the conditions of an actual dragon fruit plantation in Vietnam. The authors of this study contacted a small growing operation covering an area of about 20 hectares. Data were obtained on dragon fruit prices and demands, planting, replanting, and harvesting costs, labor availability, water and light requirements, species yields, etc. The important issue facing such operations is land management, where farmers need to make decisions on land allocation for di erent species of dragon fruit over a period of 10 years. The model is intended to allow farming communities to evaluate alternative land allocation and commitment scenarios based on di erent prices. As mentioned, farmers are planting two kinds of dragon fruit (white-flesh and red-flesh) on their lands. The price of each crop is di erent and depends on market demands. The price of the red-skin white-flesh dragon fruit (Crop 1) is stable in season 1 (favorite season) and increases a bit in season 2 (o -season). The price of the red-skin red-flesh dragon fruit (Crop 2) is double because Crop 2 is planted for export to China, where the demand is always good. However, the price of this crop fluctuates highly, relying heavily on Chinese traders. Verbal agreements are usually made between farmers and traders; however farmers could be ruled by the prices set by the traders [40]. In the case of traders cancelling deals, the price drops down dramatically. The yellow-skin white-flesh dragon fruit (Crop 3) (currently imported from Malaysia) has only recently appeared in the market and has had an extremely high price for the last three years. It is still in great demand because of its sweetness and the curiosity of consumers. Farmers intend to grow Crop 3 trees to cover that demand but have some disadvantages: the plants are novel and disease prone, and yields are just one-third of Crop 1 or Crop 2 (according to the experience of many farmers). However, farmers like to grow all three kinds of dragon fruit, to cover all market demands and hedge their risks against demand and price. In the baseline scenario, the Crop 1 is the traditional chain for both domestic and export markets with a stable demand, while Crop 2 is only planted for export to China. Crop 3 is cultivated only for the purpose of testing its viability in the consumer market. The model assumes that the demands and selling prices of all crops increase steadily over 10 years. The land proportion for each type of dragon fruit is proposed to help farmers managing their costs and benefits in planning the combination framework to install various dragon fruits, and also to decide thereafter which dragon fruit category they have to grow within 10 years. The mean values for one year are based on the previous year ’s data. Using recent pricing in the Vietnamese market it was found that: (a) the price of Crop 3 is around 10 times higher than the price of Crop 1, and (b) the price of Crop 2 is three times as high as for Crop 1. After the baseline scenario is completed and analyzed by the proposed model, other scenarios are developed, based on the minimum limit of area for each crop of dragon fruit to plant, and the fluctuations of the prices and market demands. To test how the model adapts to any changes or requirements of dragon fruit production, groups of di erent expansion scenarios are developed with various assumptions. The model is implemented using open source LP/MIP solver GLPK/GUSEK, that was developed by Free Software Foundation, Inc., Boston, USA, and it is computationally tractable. 4.1. Baseline Scenario In this scenario, approximately 15 hectares of Crop 1 and Crop 2 have been planted on 20 hectares of land to meet orders in year 0 (the start of the planning horizon). All initial input values such as yields, prices, demands, labor costs, and resource costs were collected from farmers, market reports, and dragon fruit cultivating guidelines in 2017. Figure 7 shows the typical yield curve of three dragon fruit varieties as a function of tree age [41,43]. Total planted area (ha) AgriEngineering 2020, 2, 1 9 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 10 Crop Yield 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Year Crop 1 Crop 2 Crop 3 278 Figure Figure 7. 7. Yie Yields lds of of thr three ee drag dragon on fruit fruit varie varieties ties [ [41 41,,43 43]. ]. It is assumed that all dragon fruits are sold to five traders and five wholesalers. After meeting the 279 It is assumed that all dragon fruits are sold to five traders and five wholesalers. After meeting needs of all traders and wholesalers, if any amount of Crop 1 is left over, it is sold as a by-product to 280 the needs of all traders and wholesalers, if any amount of Crop 1 is left over, it is sold as a by-product produce wine and snacks. General information of average yields, demand, and prices of each crop in 281 to produce wine and snacks. General information of average yields, demand, and prices of each crop the current market is show in Table 1: 282 in the current market is show in Table 1: Table 1. General information for the model [43]. 283 Table 1. General information for the model [43]. Average Yield Average Demand Average Price Average Yield Average Demand Average Price Crop 1 15 30 0.5 US$ Crop 1 15 30 0.5 US$ Crop 2 14 30 1.5 US$ Crop 2 14 30 1.5 US$ Crop 3 5 5 5 US$ Crop 3 5 5 5 US$ 284 The results of the baseline scenario are show below: The results of the baseline scenario are show below: Figure 8 shows the recommended dragon fruit cultivation allocation to crops on 20 hectares of land over 10 years. Crop 3 is planted primarily to meet demand; the land area allocation of Crop 1 and Crop 2 are relatively constant through the 10 years. We can see that growing new trees and cutting old ones occur on a large area of land from year 3 to year 6; this also a ects to the profitability of the farmers. The profit increases rapidly in the first three years due to income from Crop 3. However, it goes down in year 4 because many older Crop 1 and 2 plants are truncated and replaced by new ones. The variations of revenues, profits, and costs are shown in Figure 9. Figure 10 shows the profit of 10 10 each crop over 10 years. 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting Cutting area area 286 Figure 8. Baseline model result. 287 Figure 8 shows the recommended dragon fruit cultivation allocation to crops on 20 hectares of 288 land over 10 years. Crop 3 is planted primarily to meet demand; the land area allocation of Crop 1 289 and Crop 2 are relatively constant through the 10 years. We can see that growing new trees and Planted area of each crop (ha) Kg/pole Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 10 Crop Yield 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Year Crop 1 Crop 2 Crop 3 278 Figure 7. Yields of three dragon fruit varieties [41,43]. 279 It is assumed that all dragon fruits are sold to five traders and five wholesalers. After meeting 280 the needs of all traders and wholesalers, if any amount of Crop 1 is left over, it is sold as a by-product 281 to produce wine and snacks. General information of average yields, demand, and prices of each crop 282 in the current market is show in Table 1: 283 Table 1. General information for the model [43]. Average Yield Average Demand Average Price Crop 1 15 30 0.5 US$ Crop 2 14 30 1.5 US$ Crop 3 5 5 5 US$ AgriEngineering 2020, 2, 1 10 of 25 284 The results of the baseline scenario are show below: 10 10 AgriEngineering 2019, 2 FOR PEER REVIEW 11 AgriEngineering 2019, 2 FOR PEER REVIEW 11 290 cutting old ones occur on a large area of land from year 3 to year 6; this also affects to the profitability 291 of the farmers. The profit increases rapidly in the first three years due to income from Crop 3. 290 cutting old ones occur on a large area of land from year 3 to year 6; this also affects to the profitability 292 However, it goes down in year 4 because many older Crop 1 and 2 plants are truncated and replaced 0 1 2 3 4 5 6 7 8 9 10 291 of the farmers. The profit increases rapidly in the first three years due to income from Crop 3. Year 293 by new ones. The variations of revenues, profits, and costs are shown in Figure 9. Figure 10 shows Crop 1 area Crop 2 area Crop 3 area Total used area 292 However, it goes down in year 4 because many older Crop 1 and 2 plants are truncated and replaced 294 the profit of each crop over 10 years. New planting 293 by new ones. The variations of revenues, profits, and cost Cuttis ngar aree a shown in Figure 9. Figure 10 shows area 294 the profit of each crop over 10 years. 286 Figure 8. Baseline model result. Figure 8. Baseline model result. 2000000.00 2000000.00 1500000.00 287 Figure 8 shows the recommended dragon fruit cultivation allocation to crops on 20 hectares of 288 land over 10 years. Crop 3 is planted primarily to meet demand; the land area allocation of Crop 1 1500000.00 1000000.00 289 and Crop 2 are relatively constant through the 10 years. We can see that growing new trees and 1000000.00 500000.00 500000.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 0.00 Year 0 1 2 3 4 5 6 7 8 9 10 11 Year Revenue Cost Profit Revenue Cost Profit 296 Figure 9. Revenue, profit, and cost of the baseline scenario for the 10-year horizon. Figure 9. Revenue, profit, and cost of the baseline scenario for the 10-year horizon. 296 Figure 9. Revenue, profit, and cost of the baseline scenario for the 10-year horizon. 1000000.00 800000.00 1000000.00 600000.00 800000.00 400000.00 600000.00 200000.00 400000.00 0.00 200000.00 0 1 2 3 4 5 6 7 8 9 10 11 -200000.00 0.00 Year 0 1 2 3 4 5 6 7 8 9 10 11 -200000.00 Year Crop 1 Crop 2 Crop 3 297 . Cro Figure p 1 10. Profit Cro of p 2 each crop.Crop 3 298 Figure 10. Profit of each crop. 297 . Building upon the baseline scenario, four di erent expansion scenarios are proposed with 298 Figure 10. Profit of each crop. 299 assumptions Building about upon changes the basto elin prices e scen or ardemands, io, four dprice ifferent fluctuation expansion with scenar a probability ios are pro factor posed , and with the 300 as initial sump plantation. tions about All chang scenarios es to pr ar ice e described s or demands briefly , pri in ce Appendix fluctuation B with (Table a pro A1). bability factor, and the 299 Building upon the baseline scenario, four different expansion scenarios are proposed with 301 initial plantation. All scenarios are described briefly in Appendix B (Table B1). 300 assumptions about changes to prices or demands, price fluctuation with a probability factor, and the 301 initial plantation. All scenarios are described briefly in Appendix B (Table B1). 302 4.2. Changes to Price of Crop 2 303 In this scenario, the price of Crop 2 is considered increasing or decreasing linearly within the 302 4.2. Changes to Price of Crop 2 304 range of 0.5 US$ (Crop 1 price) and 5 US$ (Crop 3 price). The other information is the same as in the 303 In this scenario, the price of Crop 2 is considered increasing or decreasing linearly within the 305 baseline scenario. The cultivation changes for each crop when the price of Crop 2 changes in two 304 range of 0.5 US$ (Crop 1 price) and 5 US$ (Crop 3 price). The other information is the same as in the 306 cases are shown below: 305 baseline scenario. The cultivation changes for each crop when the price of Crop 2 changes in two 306 cases are shown below: Planted area of each crop (ha) Kg/pole ProfiProfi t (USt D) (USD) US do US do llars llars Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2020, 2, 1 11 of 25 4.2. Changes to Price of Crop 2 In this scenario, the price of Crop 2 is considered increasing or decreasing linearly within the range of 0.5 US$ (Crop 1 price) and 5 US$ (Crop 3 price). The other information is the same as in the baseline scenario. The cultivation changes for each crop when the price of Crop 2 changes in two cases AgriEngineering 2019, 2 FOR PEER REVIEW 12 are shown below: We can see e ect the price of Crop 2 price in Figures 11 and 12. The total profits are also a ected AgriEngineering 2019, 2 FOR PEER REVIEW 12 when the prices are changed (Figure 13). 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year New planting area Cutting area Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 308 Figure 11. Plantation allocation when Crop 2 price increases. Figure 11. Plantation allocation when Crop 2 price increases. 308 Figure 11. Plantation allocation when Crop 2 price increases. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year New planting area Cutting area Crop 1 area Crop 2 area Crop 3 area Total used area Figure 12. Ne Plantation w planting are allocation a whenC Cr uttop ing 2 are price a decreases. 310 Figure 12. Plantation allocation when Crop 2 price decreases. 310 Figure 12. Plantation allocation when Crop 2 price decreases. 311 We can see effect the price of Crop 2 price in Figures 11 and 12. The total profits are also affected 312 when the prices are changed (Figure 13). 311 We can see effect the price of Crop 2 price in Figures 11 and 12. The total profits are also affected 312 when the prices are changed (Figure 13). Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2020, 2, 1 12 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 13 AgriEngineering 2019, 2 FOR PEER REVIEW 13 Yearly profit as a result change in price of Crop 2 4000000.00 Yearly profit as a result change in price of Crop 2 3000000.00 4000000.00 2000000.00 3000000.00 1000000.00 2000000.00 0.00 1000000.00 0 2 4 6 8 10 12 0.00 Year 0 2 4 6 8 10 12 Profit when Crop 2 price increases Year Profit when Crop 2 price decreases Profit when Crop 2 price increases 314 Figure 13. Effect of changes in Crop 2 price on profit. Figure 13. E ect of changes in Crop 2 price on profit. Profit when Crop 2 price decreases 4.3. Changing Demands 315 4.3. Changing Demands 314 Figure 13. Effect of changes in Crop 2 price on profit. In this scenario, market demand variations are considered. It is assumed that the need of the 316 In this scenario, market demand variations are considered. It is assumed that the need of the 315 4.3. market Changin risesgfor Deman all cr ds ops. The following cases are considered: Crop 3 demand increases four-fold and 317 market rises for all crops. The following cases are considered: Crop 3 demand increases four-fold and the demand for all crops required increases by 20%, 40%, and 80%, respectively, based on the baseline 318 the demand for all crops required increases by 20%, 40%, and 80%, respectively, based on the baseline 316 In this scenario, market demand variations are considered. It is assumed that the need of the scenario demand. Other information is unchanged. 319 scenario demand. Other information is unchanged. 317 market rises for all crops. The following cases are considered: Crop 3 demand increases four-fold and 318 the demand for all crops required increases by 20%, 40%, and 80%, respectively, based on the baseline 4.3.1. Crop 3 Demand Increases Four-Fold 320 4.3.1. Crop 3 Demand Increases Four-Fold 319 scenario demand. Other information is unchanged. In this case, it is supposed that the yellow-skin white-flesh dragon fruit is popular, so that the 321 In this case, it is supposed that the yellow-skin white-flesh dragon fruit is popular, so that the farmers have more orders from traders and wholesalers. The areas of new planting or cutting of the 320 4.3.1. Crop 3 Demand Increases Four-Fold 322 farmers have more orders from traders and wholesalers. The areas of new planting or cutting of the dragon fruit trees are shown below: 323 dragon fruit trees are shown below: 321 In this case, it is supposed that the yellow-skin white-flesh dragon fruit is popular, so that the Figure 14 shows us that with the rising demand along with its high selling price, Crop 3 is 322 farmers have more orders from traders and wholesalers. The areas of new planting or cutting of the produced on most of the current planting area. On the other hand, Crop 2 is grown on the small 323 dragon fruit trees are shown below: remaining land and Crop 1 is cut o completely in year 2. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 2 Year Crop 1 area Crop 2 area Crop 3 area Total used area 0 1 2 3 4 5 6 7 8 9 10 New planting area Cutting area Year Crop 1 area Crop 2 area Crop 3 area Total used area 325 Figure 14. Plantation allocation when Crop 3 demand increases four-fold. New planting area Cutting area 326 Figure 14 shows us that with the rising demand along with its high selling price, Crop 3 is Figure 14. Plantation allocation when Crop 3 demand increases four-fold. 325 Figure 14. Plantation allocation when Crop 3 demand increases four-fold. 327 produced on most of the current planting area. On the other hand, Crop 2 is grown on the small 328 remaining land and Crop 1 is cut off completely in year 2. 326 Figure 14 shows us that with the rising demand along with its high selling price, Crop 3 is 327 produced on most of the current planting area. On the other hand, Crop 2 is grown on the small 328 remaining land and Crop 1 is cut off completely in year 2. Planted area P lo afn e te ad ch a c rr eo ap o f ( h ea a)ch crop (ha) US Dollars US Dollars TotalT p olta an l tp eld a n at re ed a a (h re aa ) (ha) TotalT p olta an l tp eld a n at re ed a a (h re aa ) (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 14 AgriEngineering 2020, 2, 1 13 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 14 329 4.3.2. All Crop Demands Increasing by a Fixed Percentage 329 4.3.2. All Crop Demands Increasing by a Fixed Percentage 4.3.2. All Crop Demands Increasing by a Fixed Percentage 330 This case is slightly different from the case 2.3.1, and all crop demands increase by 20%, 40%, 330 This case is slightly different from the case 2.3.1, and all crop demands increase by 20%, 40%, 331 and 80% respectively over the baseline scenario demand. Other data are the same. The changes in This case is slightly di erent from the case 2.3.1, and all crop demands increase by 20%, 40%, 331 and 80% respectively over the baseline scenario demand. Other data are the same. The changes in 332 plantation allocation for each case is shown in Figures 15–17 below: and 80% respectively over the baseline scenario demand. Other data are the same. The changes in 332 plantation allocation for each case is shown in Figures 15–17 below: plantation allocation for each case is shown in Figures 15–17 below: 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area 334 Figure 15. Plantation allocation when all crop demands increase by 20%. Figure 15. Plantation allocation when all crop demands increase by 20%. 334 Figure 15. Plantation allocation when all crop demands increase by 20%. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Figure 16. Plantation allocation when all crop demands increase by 40%. 336 Figure 16. Plantation allocation when all crop demands increase by 40%. 336 Figure 16. Plantation allocation when all crop demands increase by 40%. PlantP eld a n at re ed a a or fe e aa o ch f e ca rc oh p c (r ho ap ) (ha) PlantP eld a n at re ed a a or fe e aa o ch f e ca rc oh p c (r ho ap ) (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2020, 2, 1 14 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 15 AgriEngineering 2019, 2 FOR PEER REVIEW 15 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Year Year Crop 1 area Crop 2 area Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Figure 17. Plantation allocation when all crop demands increase by 80%. 338 Figure 17. Plantation allocation when all crop demands increase by 80%. 338 Figure 17. Plantation allocation when all crop demands increase by 80%. We can see that if the needs of all crops are increased, only crops that are more profitable are 339 We can see that if the needs of all crops are increased, only crops that are more profitable are 339 We can see that if the needs of all crops are increased, only crops that are more profitable are grown. Therefore, Crop 2 and 3 are prioritized for planting. The profit of each case is summarized in 340 grown. Therefore, Crop 2 and 3 are prioritized for planting. The profit of each case is summarized in 340 grown. Therefore, Crop 2 and 3 are prioritized for planting. The profit of each case is summarized in Figure 18. In general, the higher the demand is, the more the dragon fruit grower ’s revenue is. 341 Figure 18. In general, the higher the demand is, the more the dragon fruit grower’s revenue is. 341 Figure 18. In general, the higher the demand is, the more the dragon fruit grower’s revenue is. 2200000.00 2200000.00 1700000.00 1700000.00 1200000.00 1200000.00 700000.00 700000.00 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 Year Year 20% 40% 80% 20% 40% 80% 343 Figure 18. Profit for each case of increasing demand. 343 Figure 18. Profit for each case of increasing demand. Figure 18. Profit for each case of increasing demand. 4.4. Crop 3 Selling Price with a Probability Factor 344 4.4. Crop 3 Selling Price with a Probability Factor 344 4.4. Crop 3 Selling Price with a Probability Factor Currently, the bulk of Crop 3 in the market is imported. If it could be produced domestically, 345 Currently, the bulk of Crop 3 in the market is imported. If it could be produced domestically, 345 Currently, the bulk of Crop 3 in the market is imported. If it could be produced domestically, this demand would be less dependent on imports and could relieve price fluctuations. For this case, 346 this demand would be less dependent on imports and could relieve price fluctuations. For this case, 346 this demand would be less dependent on imports and could relieve price fluctuations. For this case, a probability factor is considered in the selling price. It is assumed three Crop 3 price scenarios of $1, 347 a probability factor is considered in the selling price. It is assumed three Crop 3 price scenarios of $1, 347 a probability factor is considered in the selling price. It is assumed three Crop 3 price scenarios of $1, $5, or $10 occurs in each year of the planning period of 10 years. The probability for each price is 348 $5, or $10 occurs in each year of the planning period of 10 years. The probability for each price is 348 $5, or $10 occurs in each year of the planning period of 10 years. The probability for each price is assumed be a discrete combination of 0.2, 0.2, and 0.6 for a total of 1.0 for the three price scenarios. 349 assumed be a discrete combination of 0.2, 0.2, and 0.6 for a total of 1.0 for the three price scenarios. 349 assumed be a discrete combination of 0.2, 0.2, and 0.6 for a total of 1.0 for the three price scenarios. The changes to the plantation for each case is presented below: 350 The changes to the plantation for each case is presented below: 350 The changes to the plantation for each case is presented below: Figures 19–21 show that the higher the most probable price of Crop 3, the greater the land allocated to it in the first year. The area of Crop 3 for each case is 5 ha, 4.7 ha, and 4 ha, respectively. In addition, the change in area of cultivating land is also a ected: the lower the most probable price, the higher the changeover to other crops. This can be observed in the 10-year profit projections (Figure 22). P Plla an ntte ed d a arre ea a o off e ea acch h ccrro op p ((h ha a)) Profi Profit t (US (USD) D) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 16 AgriEngineering 2020, 2, 1 15 of 25 AgriEngineering 2019, 2 FOR PEER REVIEW 16 16 15 10 10 10 10 4 5 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Year Year Crop 1 area Crop 2 area Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area New planting Cutting area New a p rle aa nting Cutting area area 352 Figure 19. Plantation allocation with probability combinationof prices$1 (0.2)–$5 (0.2)–$10 (0.6). 352 Figure 19. Plantation allocation with probability combinationof prices$1 (0.2)–$5 (0.2)–$10 (0.6). Figure 19. Plantation allocation with probability combinationof prices$1 (0.2)–$5 (0.2)–$10 (0.6). 16 15 14 15 10 10 10 10 6 5 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Year Total used Year Crop 1 area Crop 2 area Crop 3 area Tota ar l e u ased Crop 1 area Crop 2 area Crop 3 area area New planting area Cutting area AgriEngineering 2019, 2 FOR PEER REVIEW 17 New planting area Cutting area Figure 20. Plantation allocation with probability combination of prices $1 (0.2)–$5 (0.6)–$10 (0.2). 354 Figure 20. Plantation allocation with probability combination of prices $1 (0.2)–$5 (0.6)–$10 (0.2). 354 Figure 20. Plantation allocation with probability combination of prices $1 (0.2)–$5 (0.6)–$10 (0.2). 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area Figure 21. Plantation allocation with probability combinationof prices $1 (0.6)–$5 (0.2)–$10 (0.2). 356 Figure 21. Plantation allocation with probability combinationof prices $1 (0.6)–$5 (0.2)–$10 (0.2). 357 Figures 19–21 show that the higher the most probable price of Crop 3, the greater the land 358 allocated to it in the first year. The area of Crop 3 for each case is 5 ha, 4.7 ha, and 4 ha, respectively. 359 In addition, the change in area of cultivating land is also affected: the lower the most probable price, 360 the higher the changeover to other crops. This can be observed in the 10-year profit projections 361 (Figure 22). 1900000.00 1400000.00 900000.00 0 1 2 3 4 5 6 7 8 9 10 11 Year P20-20-60 P20-60-20 P60-20-20 363 Figure 22. Profit for each case in scenario 2.4. 364 4.5. Land Restriction 365 This scenario was suggested by the farmers who want to not only have a stable plantation size 366 for each crop, but also supply all three varieties of dragon fruits to the market. They would like to 367 use 50%, 35%, and 15% of their land to produce Crop 1, Crop 2, and Crop 3, respectively, and this is 368 in some sense a risk-hedging strategy. The cultivation activities (Figure 23) and the profit–cost 369 relationship (Figure 24) for a 10-year horizon are shown below: Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Profit ($US) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 17 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 356 Figure 21. Plantation allocation with probability combinationof prices $1 (0.6)–$5 (0.2)–$10 (0.2). 357 Figures 19–21 show that the higher the most probable price of Crop 3, the greater the land 358 allocated to it in the first year. The area of Crop 3 for each case is 5 ha, 4.7 ha, and 4 ha, respectively. 359 In addition, the change in area of cultivating land is also affected: the lower the most probable price, 360 AgriEngineering the higher 2020 the , chang 2, 1 eover to other crops. This can be observed in the 10-year profit projections 16 of 25 361 (Figure 22). 1900000.00 1400000.00 900000.00 0 1 2 3 4 5 6 7 8 9 10 11 Year P20-20-60 P20-60-20 P60-20-20 363 Figure 22. Profit for each case in scenario 2.4. Figure 22. Profit for each case in scenario 2.4. 4.5. Land Restriction 364 4.5. Land Restriction 365 This This scenario scenario was wasuggested s suggested by by the thfarmers e farmers who who want want to to not not only only have have aa stable stableplantation plantation size sizefor 366 for each crop, but also supply all three varieties of dragon fruits to the market. They would like to each crop, but also supply all three varieties of dragon fruits to the market. They would like to use 50%, 367 use 50%, 35%, and 15% of their land to produce Crop 1, Crop 2, and Crop 3, respectively, and this is 35%, and 15% of their land to produce Crop 1, Crop 2, and Crop 3, respectively, and this is in some 368 in some sense a risk-hedging strategy. The cultivation activities (Figure 23) and the profit–cost sense a risk-hedging strategy. The cultivation activities (Figure 23) and the profit–cost relationship AgriEngineering 2019, 2 FOR PEER REVIEW 18 369 relationship (Figure 24) for a 10-year horizon are shown below: (Figure 24) for a 10-year horizon are shown below: AgriEngineering 2019, 2 FOR PEER REVIEW 18 14 15 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Year Year Crop 1 area Crop 2 area Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area NN ew ew p p laln an titn in gg a a rr ee aa C Cu uttttiin n g g a a rr ee aa 370 370 Figure 23. Plantation allocation for land restriction scenario. 371 371 Figure Figure 23. 23. Pl Pl an an tati tati on alloc on allocati atio on n for for lland and restr restr ic ic ti ti on on scenar scenar io io . . 2000000.00 2000000.00 1500000.00 1500000.00 1000000.00 1000000.00 500000.00 500000.00 0.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 Year Year Revenue Cost Profit Revenue Cost Profit 373 Figure 24. Revenue, profit, and cost in 10 years. Figure 24. Revenue, profit, and cost in 10 years. 373 Figure 24. Revenue, profit, and cost in 10 years. 374 To ensure both the stability of area for each crop and the amount supplied to the market, farmers 374 To ensure both the stability of area for each crop and the amount supplied to the market, farmers 375 should re-vitalize the trees every few years (cutting old plants and planting new ones), especially in th 375 should re-vitalize the trees every few years (cutting old plants and planting new ones), especially in 376 the 4 year. th 376 the 4 year. 377 4.6. Influence of the Initial Plantation Conditions 377 4.6. Influence of the Initial Plantation Conditions 378 In addition to the mentioned variables above, such as customer demand and selling prices, the 379 initial crop status of the arable land is also considered to determine its influence on the changes in 378 In addition to the mentioned variables above, such as customer demand and selling prices, the 380 planting area. Based on the result of the baseline scenario, two sub-scenarios are proposed to look at 379 initial crop status of the arable land is also considered to determine its influence on the changes in 381 the effect of the variety of the initial crop and the age of the initial crop. In the first sub-scenario set, 380 planting area. Based on the result of the baseline scenario, two sub-scenarios are proposed to look at 382 it is supposed that all initial area has been allocated to only one of the three crops (Crop 1 or Crop 2 381 the effect of the variety of the initial crop and the age of the initial crop. In the first sub-scenario set, 383 or Crop 3). In the second sub-scenario set, only the initial land for Crop 1 is considered, with different 382 it is supposed that all initial area has been allocated to only one of the three crops (Crop 1 or Crop 2 384 ages (age 1, age 3, and age 5) in year 0. Other data is the same as in the baseline scenario. 383 or Crop 3). In the second sub-scenario set, only the initial land for Crop 1 is considered, with different 384 ages (age 1, age 3, and age 5) in year 0. Other data is the same as in the baseline scenario. 385 4.6.1. Initial Plantation with Only One Kind of Crop 386 According to results of the baseline scenario, the initial area that is used in year 0 is 15.3 hectares. 385 4.6.1. Initial Plantation with Only One Kind of Crop 387 It is assumed that only one crop has been planted on that area in year 0. Figures 25–27 show the 386 According to results of the baseline scenario, the initial area that is used in year 0 is 15.3 hectares. 388 cultivation activities for each case. 387 It is assumed that only one crop has been planted on that area in year 0. Figures 25–27 show the 388 cultivation activities for each case. Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) USD USD Profit ($US) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2020, 2, 1 17 of 25 To ensure both the stability of area for each crop and the amount supplied to the market, farmers should re-vitalize the trees every few years (cutting old plants and planting new ones), especially in the 4th year. 4.6. Influence of the Initial Plantation Conditions In addition to the mentioned variables above, such as customer demand and selling prices, the initial crop status of the arable land is also considered to determine its influence on the changes in planting area. Based on the result of the baseline scenario, two sub-scenarios are proposed to look at the e ect of the variety of the initial crop and the age of the initial crop. In the first sub-scenario set, it is supposed that all initial area has been allocated to only one of the three crops (Crop 1 or Crop 2 or Crop 3). In the second sub-scenario set, only the initial land for Crop 1 is considered, with di erent ages (age 1, age 3, and age 5) in year 0. Other data is the same as in the baseline scenario. 4.6.1. Initial Plantation with Only One Kind of Crop According to results of the baseline scenario, the initial area that is used in year 0 is 15.3 hectares. AgriEngineering 2019, 2 FOR PEER REVIEW 19 It is assumed that only one crop has been planted on that area in year 0. Figures 25–27 show the AgriEngineering 2019, 2 FOR PEER REVIEW 19 cultivation activities for each case. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Year Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area 390 Figure 25. Plantation allocation if the initial plantation only has Crop 1. Figure 25. Plantation allocation if the initial plantation only has Crop 1. 390 Figure 25. Plantation allocation if the initial plantation only has Crop 1. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Figure 26. Plantation allocation if the initial plantation only has Crop 2. 392 Figure 26. Plantation allocation if the initial plantation only has Crop 2. 392 Figure 26. Plantation allocation if the initial plantation only has Crop 2. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Year Crop 3 area Total used area Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 19 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 390 Figure 25. Plantation allocation if the initial plantation only has Crop 1. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area AgriEngineering 2020, 2, 1 18 of 25 392 Figure 26. Plantation allocation if the initial plantation only has Crop 2. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area AgriEngineering 2019, 2 FOR PEER REVIEW 20 New planting area Cutting area Figure 27. Plantation allocation if the initial plantation only has Crop 3. 394 Figure 27. Plantation allocation if the initial plantation only has Crop 3. Although the initial land varies across these sub scenarios, Crop 2 is still the most planted over the 395 Although the initial land varies across these sub scenarios, Crop 2 is still the most planted over next 10 years. The profit for the case where the entire plantation consists of Crop 2 is also the highest, 396 the next 10 years. The profit for the case where the entire plantation consists of Crop 2 is also the as shown in Figure 28 below: 397 highest, as shown in Figure 28 below: 1600000.00 1400000.00 1200000.00 1000000.00 800000.00 600000.00 400000.00 200000.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 -200000.00 Year Crop 1 initial Crop 2 Initial Crop 3 Initial 399 Figure 28. The profit of the three cases of the initial land allocation. Figure 28. The profit of the three cases of the initial land allocation. 4.6.2. The Initial Crop Allocation with Di erent Crop 1 Ages 400 4.6.2. The Initial Crop Allocation With Different Crop 1 Ages In this case, it is assumed that the initial crop allocation is only for Crop 1. However, it is assumed 401 In this case, it is assumed that the initial crop allocation is only for Crop 1. However, it is assumed that the age is 1, 3, or 5 in year 0. The optimal crop allocation over the next 10 years is shown in 402 that the age is 1, 3, or 5 in year 0. The optimal crop allocation over the next 10 years is shown in Figures 29–31. 403 Figures 29–31. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 405 Figure 29. Plantation allocation if the initial land is only for Crop 1 at age 1. Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Planted area of each crop (ha) Profit (USD) Total planted area (ha) Total planted area (ha) Total T p ol ta an l t p eld an atreed a a (h re aa ) (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 20 394 Figure 27. Plantation allocation if the initial plantation only has Crop 3. 395 Although the initial land varies across these sub scenarios, Crop 2 is still the most planted over 396 the next 10 years. The profit for the case where the entire plantation consists of Crop 2 is also the 397 highest, as shown in Figure 28 below: 1600000.00 1400000.00 1200000.00 1000000.00 800000.00 600000.00 400000.00 200000.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 -200000.00 Year Crop 1 initial Crop 2 Initial Crop 3 Initial 399 Figure 28. The profit of the three cases of the initial land allocation. 400 4.6.2. The Initial Crop Allocation With Different Crop 1 Ages 401 In this case, it is assumed that the initial crop allocation is only for Crop 1. However, it is assumed 402 that the age is 1, 3, or 5 in year 0. The optimal crop allocation over the next 10 years is shown in AgriEngineering 2020, 2, 1 19 of 25 403 Figures 29–31. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area AgriEngineering 2019, 2 FOR PEER REVIEW 21 New planting area Cutting area AgriEngineering 2019, 2 FOR PEER REVIEW 21 Figure 29. Plantation allocation if the initial land is only for Crop 1 at age 1. 405 Figure 29. Plantation allocation if the initial land is only for Crop 1 at age 1. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area 407 Figure 30. Plantation allocation if the initial land is only for Crop 1 at age 3. Figure 30. Plantation allocation if the initial land is only for Crop 1 at age 3. 407 Figure 30. Plantation allocation if the initial land is only for Crop 1 at age 3. 10 10 10 10 0 1 2 3 4 5 6 7 8 9 10 Year 0 1 2 3 4 5 6 7 8 9 10 Crop 1 area Crop 2 area Crop 3 area Total used area Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area New planting area Cutting area Figure 31. Plantation allocation if the initial land is only for Crop 1 at age 5. 409 Figure 31. Plantation allocation if the initial land is only for Crop 1 at age 5. 409 Figure 31. Plantation allocation if the initial land is only for Crop 1 at age 5. 410 We can see that the young Crop 1 (age 1) is truncated more than the grown one (age 3 or age 5). 410 We can see that the young Crop 1 (age 1) is truncated more than the grown one (age 3 or age 5). 411 Similar to trends observed earlier, after Crop 1 area is reduced, most of the remaining land is 411 Similar to trends observed earlier, after Crop 1 area is reduced, most of the remaining land is 412 prioritized for Crop 2, which has the most revenue because of its high demand. The profits for all 412 prioritized for Crop 2, which has the most revenue because of its high demand. The profits for all 413 three cases are shown in Figure 32. 413 three cases are shown in Figure 32. 2500000.00 2500000.00 1500000.00 1500000.00 500000.00 500000.00 -500000.00 0 1 2 3 4 5 6 7 8 9 10 11 -500000.00 0 1 2 3 4 5 Year 6 7 8 9 10 11 Year Age 1 Age 3 Age 5 Age 1 Age 3 Age 5 Plant P eld an atreed a a orfe e aa o cf h e ca rc oh p c(r h oa p ) (ha) Plant P eld an atreed a a orfe e aa o cf h e ca rc oh p c(r h oa p ) (ha) Planted area of each crop (ha) Profit (USD) Profi Profi t (US t (US D) D) Total planted area (ha) Total planted area (ha) AgriEngineering 2019, 2 FOR PEER REVIEW 21 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area 407 Figure 30. Plantation allocation if the initial land is only for Crop 1 at age 3. 10 10 0 1 2 3 4 5 6 7 8 9 10 Year Crop 1 area Crop 2 area Crop 3 area Total used area New planting area Cutting area AgriEngineering 2020, 2, 1 20 of 25 409 Figure 31. Plantation allocation if the initial land is only for Crop 1 at age 5. We can see that the young Crop 1 (age 1) is truncated more than the grown one (age 3 or age 5). 410 We can see that the young Crop 1 (age 1) is truncated more than the grown one (age 3 or age 5). Similar to trends observed earlier, after Crop 1 area is reduced, most of the remaining land is prioritized 411 Similar to trends observed earlier, after Crop 1 area is reduced, most of the remaining land is for Crop 2, which has the most revenue because of its high demand. The profits for all three cases are 412 prioritized for Crop 2, which has the most revenue because of its high demand. The profits for all shown in Figure 32. 413 three cases are shown in Figure 32. 2500000.00 1500000.00 500000.00 -500000.00 0 1 2 3 4 5 6 7 8 9 10 11 Year Age 1 Age 3 Age 5 Figure 32. The profits for the three cases of initial land allocation to Crop 1 for di erent ages. 4.7. Discussion Throughout scenarios and cases above, summarized in Table 2, we can see that the dragon fruit growers earn more profit if they prioritize planting the varieties for which both demand and selling price are high. This is the case for Crop 2 which has a very high demand and its price is only lower than the price of Crop 3. In contrast, although the price of Crop 3 is the highest, due to lower demand and yield, it is not prioritized in the solutions. Finally, the selling price of Crop 1 is the lowest; therefore, it is replaced by other varieties when the demands or prices of the other two crops increase. Table 2 summarizes the profits for each of the scenarios. Table 2. Summary of the profitability of the various scenarios. Scenario Sub-Scenario Limit on Plantation Area for Each Crop Profit Baseline scenario No limit for each crop USD 12,576,086.80 1 No limit for each crop USD 20,089,622.07 Changes in price of Crop 2 2 No limit for each crop USD 20,116,237.86 1 No limit for each crop USD 16,815,478.39 Changes in demands 2 No limit for each crop USD 13,932,145.96 3 No limit for each crop USD 15,166,044.33 4 No limit for each crop USD 15,740,093.18 1 No limit for each crop USD 14,438,789.39 Crop 3 selling price with probability factor 2 No limit for each crop USD 12,745,440.97 3 No limit for each crop USD 11,415,607.18 50% for Crop 1, 35% for Crop 2, 15% for Land restriction USD 9,963,130.32 Crop 3 Crop 1 No limit for each crop USD 10,921,697.80 Crop 2 No limit for each crop USD 12,182,762.60 Influence of initial land Crop 3 No limit for each crop USD 11,630,711.50 Crop 1—Age 1 No limit for each crop USD 10,763,932.06 Crop 1—Age 3 No limit for each crop USD 10,907,367.04 Crop 1—Age 5 No limit for each crop USD 10,879,376.28 Planted area of each crop (ha) Planted area of each crop (ha) Profit (USD) AgriEngineering 2020, 2, 1 21 of 25 5. Conclusions A deterministic model is proposed in this paper to assist dragon fruit farmers with their decision making on crop allocation for di erent species of dragon fruits. Consequently, it can provide them a long-term overview through groups of production scenarios that could occur, such as (1) price changes (e.g., price of the red-skin red-flesh dragon fruit—Crop 2); (2) changes in demand (e.g., demand of the yellow-skin white-flesh dragon fruit—Crop 3); (3) requirements for land restrictions for each type of crop, and (4) the influence of the initial state. All scenarios are variants from a baseline scenario of the actual dragon fruit production conditions in Vietnam intended to provide insights. Results obtained from this model confirmed that the Crop 2 should be prioritized for planting. The model presented in this paper represents a first step towards a comprehensive quantitative approach for decision making in dragon fruit cultivation in Vietnam. The model works well with some scenarios showing relationships of input factors (demands, prices, and costs) and output decisions (plantation area of crops) over a 10-year period. This is evident in the cases of “no limit plantation area” of all scenarios: the crop is grown if its demand and price increase, or it is cut down when its demand is low and its price drops. For a specific crop, the old plants are replaced by new ones if its yield is too low due to age. The proposed model is a meaningful tool for managers and farmers to have a holistic view for long term planning with the goal of maximizing profits. It helps decide which varieties to plant proactively based on demand and price scenarios. As with other fresh fruit supply chains, the dragon fruit chain faces challenges due to inherent uncertainties such as demands, price, and yield. This is the main limitation of the deterministic approach. Therefore, future research to deal with randomness and uncertainty for dragon fruit cultivation could involve stochastic programming [44–46] or robust optimization [47]. The approach can be generalized to other similar fresh fruit supply chains. Author Contributions: Conceptualization: T.-D.N., U.V., T.N.-Q.; Data curation: T.-D.N., T.N.-Q.; Format analysis: T.-D.N., U.V., T.N.-Q.; Funding acquisition: T.N.-Q.; Investigation: T.-D.N., U.V.; Methodology: T.-D.N., U.V., T.N.-Q.; Supervision: U.V., T.N.-Q., C.D., M.A.; Validation: T.-D.N., U.V., T.N.-Q., C.D., M.A.; Visualization: C.D., M.A.; Writing—original draft: T.-D.N., U.V., T.N.-Q.; Writing—review & editing: T.-D.N., U.V., T.N.-Q., C.D., M.A. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Vietnam International Education Development (VIED). Acknowledgments: The first author acknowledges the Vietnam International Education Development (VIED) via the 911 research scholarship program as well as Vietnamese colleagues, collaborators, and the farmers from Binh Thuan, Vietnam for the data collection. Conflicts of Interest: The authors have no conflicting financial or other interests. Nomenclature DC Distribution Centers DF Dragon fruit FFSC Fresh Fruit Supply Chain FSC Fruit Supply Chain GLPK GNU Linear Programming Kit GUSEK GLPK Under Scite Extended Kit LP Linear Programming MIP Mixed Integer Programming VIED The Vietnam International Education Development AgriEngineering 2020, 2, 1 22 of 25 Appendix A Indices: t Time periods k Age classes in the plantation, each representing a two-year period s Harvesting season (1 for wet, 2 for dry) j Di erent species of dragon fruit i Traders m Wholesale markets (WM) b By-product Parameters: L Amount of land available w Water required per hectare for crop j of age class k in season s ks v Lighting required per hectare for crop j in season s js W Water restriction in season V Lighting restriction in season u Minimum planting area per crop j in period t jt Yield in kgs per hectare of crop j belonging to age class k in season s jkst p Price per kg of crop j for trader i in season s of period t jist q Price per kg of crop j for wholesaler m in season s of period t jmst r Price per kg of byproducts (e.g., wine) in period t st d Demand of trader i for crop j in season s of period t i jst e Demand of wholesale market m for crop j in season s of period t m jst f Demand for byproducts (e.g., wine) in period t P Number of workers needed to plant one hectare H Number of workers needed to harvest one hectare R Number of workers needed to cut one hectare M Maximum number of fixed workers in a period N Maximum number of part-time workers in a period I Initial area of crop j of age class k jk Cost parameters: cp Cost per hectare of planting in period t ch Cost per hectare of harvesting in period t cr Cost per hectare of cut in period t cbp Cost per kg of processing (e.g. wine) cLab f Cost of fixed workers per period cLabp Labor cost of part-time workers per period cPNT Penalty for not meeting demand per kg of crop j for trader i jist in season s of period t Cost of required water per hectare for crop j of age class k cwater ks in season s clighting Cost of required light per hectare for crop j in season s js Variables: X Plantation area of crop j in period t of age class k jkt ST Quantity of crop j shipped to trader i in season s of period t jist Quantity of crop j under shipped to trader i in season s of period t i jst SWM Quantity of crop j shipped to WM m in season s of period t jmst AgriEngineering 2020, 2, 1 23 of 25 SB Quantity of crop j harvested for by-products (e.g. wine) in season s of jst period t F Number of fixed workers in t Hire Part-time workers hired in period t Y Area of crop j planted in period t jt Z Area of crop j of age class k cut optionally in period t jkt Z Area of crop j of age class k = 10 that must be cut in period t jkt Z Area of crop j of age class k cut in period t in total jt Appendix B Table A1. Summary of scenarios with their characteristics. Situation (Sub-Scenario Limit of Planting Area Scenario Descriptions or Case) for Each Crop Demands and prices unchanged Baseline scenario No limit for each crop within 10 years The price increasing gradually 1 No limit for each crop within 10 years Changes in price of Crop 2 The price decreasing gradually 2 No limit for each crop within 10 years Demand of Crop 3 increasing 1 No limit for each crop 4 times 2 No limit for each crop Demands of all crops increasing 20% Changes in demands 3 No limit for each crop Demands of all crops increasing 40% 4 No limit for each crop Demands of all crops increasing 80% 1 No limit for each crop 0.2 for $1, 0.2 for $5, and 0.6 for $10 Crop 3 selling price with probability factor 2 No limit for each crop 0.2 for $1, 0.6 for $5, and 0.2 for $10 3 No limit for each crop 0.6 for $1, 0.2 for $5, and 0.2 for $10 50% for Crop 1, 35% for Demands and prices unchanged Land restriction Crop 2, 15% for Crop 3 within 10 years All initial land used for Crop 1. Crop 1 No limit for each crop Demands and prices unchanged within 10 years All initial land used for Crop 2. Crop 2 No limit for each crop Demands and prices unchanged within 10 years All initial land used for Crop 2. Crop 3 No limit for each crop Demands and prices unchanged within 10 years Influence of initial land All initial land used for Crop 1 at Crop 1—Age 1 No limit for each crop age 1. Demands and prices unchanged within 10 years All initial land used for Crop 1 at Crop 1—Age 3 No limit for each crop age 3. Demands and prices unchanged within 10 years All initial land used for Crop 1 at Crop 1—Age 5 No limit for each crop age 5. Demands and prices unchanged within 10 years References 1. Ahumada, O.; Villalobos, J.R. Application of planning models in the agri-food supply chain: A review. Eur. J. Oper. Res. 2009, 196, 1–20. [CrossRef] 2. Hamer, P.J. A decision support system for the provision of planting plans for Brussels sprouts. Comput. Electron. Agric. 1994, 11, 97–115. 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