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Logist. Res. (2016) 9:24 DOI 10.1007/s12159-016-0149-4 ORIGINAL PAPER Extension of multi-commodity closed-loop supply chain network design by aggregate production planning 1 1 Leena Steinke Kathrin Fischer Received: 30 June 2015 / Accepted: 17 October 2016 / Published online: 14 November 2016 The Author(s) 2016. This article is published with open access at Springerlink.com Abstract In this work the inﬂuence of production and capacity equipment at facilities and decisions regarding the capacity planning on decisions regarding facility location, production and distribution system are interdependent; distribution quantities and component remanufacturing therefore, they have to be managed jointly. Furthermore, it (and vice versa) in a closed-loop supply chain network is shown that the decision to process returned products and (CLSCN) with multiple make-to-order products is studied. use remanufactured components in the production does A mathematical model, the facility location, capacity and depend not only on the costs, but also on the quantity of aggregate production planning with remanufacturing returned products and the length of the planning horizon. (FLCAPPR) model, for designing the CLSCN, for planning capacities at the facilities and for structuring the production Keywords Closed-loop supply chain management and distribution system of the network cost-optimally, is Network design Remanufacturing Reverse logistics formulated. It consists of a facility location model with Aggregate production planning Capacity planning component remanufacturing over multiple time periods, which is extended by capacity and production planning on an aggregate level. The problem is solved for an example 1 Introduction set of data which is based on previous CLSC research in the copier industry. In a numerical study the effect of the Supply chains with product recovery differ, depending on extended planning approach on the decision to process the characteristics of the product, the recovery activity returned products is determined. Furthermore, the which is used and whether this activity is done by the FLCAPPR model is solved for different returned product original equipment manufacturer or a third party . In quantities and numbers of periods in the planning horizon general, supply chains with product recovery can be dis- to study the inﬂuence on the network design and on the tinguished into open-loop and closed-loop supply chains procuring, production and distribution quantities. It turns (CLSC). If there is hardly any connection of the forward out that decisions regarding the locations of and the and return product ﬂows, the supply chain is open-loop and the forward and reverse product ﬂows are managed sepa- rately. The forward product ﬂow can be described by the This article is part of a focus collection on ‘‘Robust Manufacturing traditional supply chain management theory, and the Control: Robustness and Resilience in Global Manufacturing reverse product ﬂow is planned independently by reverse Networks’’. supply chain management . If the forward and return & Leena Steinke product ﬂows are related, e.g. customers supply their used email@example.com products as production inputs, the supply chain is closed- Kathrin Fischer loop. In this case, often an integrated management of both kathrin.ﬁscher@tuhh.de ﬂows is necessary to achieve an optimized CLSC; for further details see [8, 9]. Institute of Operations Research and Information Systems, In this work, a supply chain is studied which is closed by Hamburg University of Technology, Schwarzenbergstr. 95, component remanufacturing. Remanufacturing is also 21073 Hamburg, Germany 123 24 Page 2 of 23 Logist. Res. (2016) 9:24 called value-added recovery, since it describes a series of these models support the procuring decision, i.e. when to operations which restore the value of a product after usage recover returned products and use them as production . A supply chain with remanufacturing is extended by inputs, as well, e.g. in [8, 9]. the following activities: collecting, cleaning and testing In the literature so far, location/allocation models in a returned products. Then, remanufacturable products are CLSCN consider opening costs of product recovery facil- disassembled into components, which are remanufactured, ities, but costs for volume capacity and costs for installing e.g. repaired or refurbished. After testing these compo- technology or hiring workforce for the operations at the nents, they are reassembled and sold in secondary markets respective facilities of the network, especially for product as remanufactured items or reintegrated to the original recovery operations, are neglected. However, to determine supply chain and used as as-new items , as in the a cost-optimal procurement policy, i.e. to decide when to supply chain studied in this work. High-value products, e.g. recover returned products and use the resulting items as copiers and automobiles, are suitable for component production inputs instead of new items procured from remanufacturing. A further discussion of product charac- suppliers, these costs have to be included. teristics that enable remanufacturing can be found in . Since remanufacturing is a labour-intensive operation Whether the supply chain is open- or closed-loop, pro- (see  for an extended discussion), labour hour costs are duct recovery forces supply chain management (SCM) to relevant for the decision to process returned products. The consider a reverse product ﬂow. In addition to the planning, well-established aggregate production planning (APP)- realization and control of all operations, production, framework is used to plan the production and workforce at inventory and distribution quantities and information ﬂows facilities cost-optimally in this work. In APP, the length of from the product origin to the point of consumption, all the planning horizon is usually between 6 and 24 months problems concerning the way back through the supply  and quantities are planned on an aggregate level. In the chain, i.e. after consumption, have to be considered in a following this APP-approach is described and a multi-pe- SCM with product recovery. These decision problems can riod facility location problem extended by capacity and be differentiated regarding their planning horizon: some aggregate production planning is developed. are made on a yearly basis and determine the framework The consideration of different product compositions, for decisions, which are made on a weekly or monthly basis component remanufacturing and component commonality . Then again, these decisions constrain the operational is possible with this modelling approach, and the inﬂuence decisions, which occur every day . of different return rates can be investigated. Hence, dif- The network design, decisions regarding the product and ferent realistic SC settings can be captured. material programme, supplier selection, collection strategy, The rest of the paper is organized as follows: relevant take-back arrangements and supply chain coordination are selected literature regarding network design and aggregate strategic decision problems and belong to long-term plan- production planning is presented and discussed in the next ning. Decision problems regarding inventory management section. Here, the differences between other contributions and production planning are tactical and have a mid-term and the approach taken in this work are also discussed. The planning horizon. Operative decision problems, as disas- CLSCN and the production planning problem are presented sembly planning, material requirement plans, scheduling in detail in Sect. 3. Afterwards the planning problem is and routing in the remanufacturing shop have a short-term described mathematically in Sect. 4. In Sect. 5, it is solved planning horizon [4, 5, 7, 28]. for an example data set and the results are presented. In order to achieve an optimized CLSC the tactical Furthermore, a sensitivity analysis is performed and planning has to be considered by strategic management selected results are discussed in Sect. 5, too. Finally, con- [14, 21, 26]. Long-range forecasts of aggregate product clusions and possibilities for further research are stated. demand are the input for strategic planning . They are used by the mathematical model developed in this work to derive a cost-optimally network design, i.e. cost-optimal 2 Literature review facility locations and capacity equipment, with cost-opti- mal procuring, transportation, production and storage Networks with product recovery are mathematically opti- quantities. The quantities are planned on an aggregate mized by extending the classical Warehouse Location level; therefore, ﬂuctuations of data are neglected and the Problem (WLP) to capture reverse product ﬂows. Mostly modelling approach is deterministic. these problems are described by Mixed Integer Program- In the facility location problem (FLP), facilities are ming (MIP) and Mixed Integer Linear Programming located and quantities of goods are allocated and dis- (MILP) models. In the following, selected papers are dis- tributed in the network a cost-optimal way, e.g. in . In cussed, which present the state of research, and have the special case of a CLSN with reverse product ﬂows inﬂuenced this study. A more detailed review of network 123 Logist. Res. (2016) 9:24 Page 3 of 23 24 design literature concerning supply chains with product Salema et al.  extend the model from  to study recovery is offered in . multiple product types. Furthermore, in  the product As one of the ﬁrst, Marin and Pelegrin  study a ﬂow capacity at facilities is limited by maximum and network with reverse product ﬂows: customers get products minimum capacity bounds for the facilities. at plants and return them to plants. The objective is to ﬁnd As in [9, 23], the CLSCN studied in this work has three the optimal plant location and shipping quantities, such that facility levels. Here, the three facility levels of the CLSCN the costs for opening facilities and for transportation are are DCCs, plants and suppliers and remanufacturing cen- minimized. Marin and Pelegrin’s  model is an unca- tres, both delivering components to plants. The production pacitated Facility Location Problem (FLP), whereas the system of the CLSCN consists of two stages: at the ﬁrst other models discussed in the following are capacitated stage components are delivered from remanufacturing FLP. centres or from suppliers to plants, where they are assem- Following , in this work it is assumed that customers bled to products. This way, component remanufacturing, return their products to those facilities from which the unlike product remanufacturing as in [9, 15, 19, 23], with products are distributed. Unlike , in the network stud- different product and component types and component ied here, these facilities are not plants, but facilities for commonality in the assembly of different product types can distribution and collection of products, called distribution be modelled. and collection centres (DCCs). Furthermore, in a In contrast to [9, 15, 23], the capacity for storage and single product type is considered, whereas in this work product and component ﬂows at facilities are decision multiple product types are studied. variables, i.e. have to be determined out of a parameter A remanufacturing network with multiple product types range and induce costs. In addition, capacity for the oper- is examined by Jayaraman et al. . Used products are ations at facilities is determined by the model stated in this shipped from collection zones to remanufacturing centres, work. Hence, the inﬂuence of different capacity types on where they can be remanufactured or stored. Remanufac- the facility location decisions and on the decision to pro- tured products are distributed, i.e. are used to fulﬁl cus- duce, remanufacture, store or distribute is studied. tomer demand, or stored. The shipping quantities between All studies discussed above have a single time period collection zones, customers and remanufacturing/distribu- planning horizon. Following [15, 21] consider inventory in tion locations are to be determined optimally; the objective a single time period planning facility location problem and is cost minimization. study the trade-off between storing and distributing prod- In this work, following , it is assumed that returned ucts. Further discussions of inventory in distribution net- products can be stored at remanufacturing centres. As in works and the interdependence of inventory, transportation , the storage capacity at remanufacturing facilities is and facility location can be found in  and different assumed to be limited. Additional to storage capacities, approaches to extend facility location problems by inven- capacities for operations at facilities are planned in this tory management can be found in . work, too. In this work, the planning horizon of the CLSCN design Operative capacity equipment is studied by Schultmann problem is modiﬁed to a multi-period setting, as in  and et al. . The model by  allocates the optimal operative . Pishvaee and Torabi  use a multi-objective capacity equipment to open facilities of an existing reverse approach to combine cost minimization of the CLSCN with supply chain. The capacity at facilities is needed for opera- the minimization of delivery tardiness for the single pro- tions, as e.g. inspection and sorting, of multiple product duct case. In this work, the objective is to minimize costs types. The objective is to minimize costs, caused by capacity and the production and capacity planning problem at open equipment, production and distribution quantities. facilities in a network with multiple commodities is con- Unlike in , in this work a closed-loop system is sidered in a MILP-approach. studied, i.e. in addition to reverse product ﬂows, forward In this work, a FLP for a closed-loop supply chain with product ﬂows are considered. Fleischmann et al.  and component remanufacturing is extended by production Fleischmann et al.  study such a closed-loop system as a planning on an aggregate level, using the idea of APP, as in three echelon network, consisting of warehouses, plants Steinke and Fischer . In APPs, the different products and test centres, where products are recovered. These are aggregated to product types and the capacities are not facilities have to be located optimally, and the quantities of product speciﬁc, but are summarized and stated in common the forward and reverse product ﬂows of the network are to units, e.g. labour hours. APP is used to determine cost- be determined such that costs for opening, transport and for optimal manufacturing and storage plans, which match the unsatisﬁed demand and not-collected returned products are limited means in terms of workforce or working stations, minimized under capacity limitations for the product ﬂows respectively, and production input with forecasted demand between facilities of different network echelons. . The planning horizon of an APP can vary; usually it 123 24 Page 4 of 23 Logist. Res. (2016) 9:24 consists of 6–24 months, . In particular, when adjust- returned not only in a speciﬁc period following the buying, ments of capacities are allowed in each period, the periods but in all subsequent periods of the planning horizon. In have to be sufﬁciently long. this work, the model in  is extended to capture these Jayaraman  studies the production planning problem aspects. of a company, which offers recovered mobile phones for a Moreover, the FLCAPPR model developed in this work secondary market. He states the Remanufacturing APP determines cost-optimal volume capacities and optimal (RAPP) model, which minimizes costs by determining the workforce size at the facilities for every period. In contrast, optimal disassembly, disposal, remanufacturing, procure- in  the capacity planning is integrated in a more sim- ment and storage quantities under ﬁxed workforce pliﬁed way, such that overcapacities can occur: whenever a capacities. facility is opened, its volume capacity and workforce are In this work, the approach of  is followed to model set to their respective upper limits and adjusted to the the production system. While in  the reverse product actual required levels only in the last period. Furthermore, ﬂow is managed, here, a closed-loop system is studied, and while in  total costs are minimized, here discounting is the model is extended accordingly, i.e. the remanufactured considered in the objective function, too. components are reintegrated into the original supply chain instead of being shipped to secondary markets. Moreover, in contrast to , capacities in volume units and labour 3 Problem description hours at facilities are not ﬁxed but can be adjusted over the planning horizon. In this section the network structure of the CLSCN with In the RAPP proposed by  only one site for component remanufacturing is introduced and the respec- remanufacturing is considered, whereas in this work, tive planning problem is described in detail. multiple possible facility locations exist. Hence, the APP The CLSCN consists of nodes, which represent cus- for a closed-loop system is integrated into a FLP. tomers and facilities with their operations, and arrows, Extending a yearly FLP for a CLSCN with component which show the ﬂows of multiple commodities through the recovery by an APP on a monthly basis leads to a model network, see Fig. 1. There are ﬁve different types of nodes: with extensive solution times. Furthermore, the considered costumers, DCCs, remanufacturing centres, plants and capacities cannot be adjusted within one month; especially, suppliers. Customers demand different product quantities decisions regarding the volume capacity are made on a in each period, and they return their products to DCCs in a strategic level. Therefore, also the APP is extended and the later period, i.e. it is assumed that a known fraction of APP is modelled for a strategic, yearly, planning horizon. products shipped to customers in one period is returned in a With such an extended strategic planning model, deci- later period of the planning horizon. The residence time of sions regarding the location of facilities and their capacity products can be different, but there is a given number of equipment for operations and storage can be studied periods the product has to stay with a customer before it is jointly. Furthermore, different product and component returned and considered as remanufacturable. The mini- types are considered and the interdependence of process- mum residence time can be interpreted as the minimum ing, storing and distributing them is examined. Moreover, number of periods a product is in full working condition. by considering capacity costs and operative capacity in Demand quantities are assumed as deterministic and addition to storage capacity, the cost effects of the deci- known; therefore, the returned product quantities are sions regarding the returned products, i.e. if they are deterministic and known, too. Demand is lost whenever it remanufactured, stored or disposed, are captured com- is not met, i.e. it cannot be backlogged. pletely unlike in facility location problems without The CLSCN consists of three facility levels: DCCs, capacity and production planning. plants, remanufacturing centres and suppliers. The latter Following [9, 19, 23, 30], a ﬁxed relation between are summarized to one level since both provide compo- demand and returned products is assumed in this work; the nents. Supplier locations are given, whereas the locations returned product quantity is determined as a fraction of the of DCCs, remanufacturing centres and plants have to be sold product quantity. As in , the CLSCN is studied determined. These facilities can be opened in one period over multiple time periods, and hence, there is a time lag and then remain open or are closed in a later period. It is between the selling and the returning of a product. In it assumed that once a facility is closed, it cannot be opened is assumed that products are returned by customers after again. one period of usage. However, products can stay longer Capacities at facilities are determined in volume and with the customers, i.e. the residence time of a product, labour hours. The volume capacity restricts the volume of deﬁned as the number of periods a product is used by a commodity ﬂows passing a facility and, if existent, the customer, can be longer. Furthermore, products are volume of stocked products and components, respectively. 123 Logist. Res. (2016) 9:24 Page 5 of 23 24 Fig. 1 Closed-loop supply chain network The labour hour capacity limits the available hours of the remanufacturing centres it is possible to store returned workforce needed for remanufacturing and assembly at products, instead of remanufacturing them immediately. remanufacturing centres and plants, and for handling At plants, components are assembled to products of products at DCCs. different types. Product types differ regarding their com- Capacity levels at facilities are determined once a bination of components, i.e. at least one component in the facility is opened and can be adjusted in a later period, i.e. product composition has to be different in different prod- they can be expanded or reduced in ﬁxed steps in every ucts. Components can be product type-speciﬁcally or period. commonly used among different product types. They are The product and component ﬂows through the network shipped from suppliers or remanufacturing centres to plants are described by three different types of arrows, see Fig. 1. and can be held on inventory at plants. No ﬁnal products The solid arrows show the forward product ﬂows, which are stored in the studied network and products are assem- are shipped from plants to DCCs and further to the cus- bled only if an order exists (MTO). Since the planning tomer locations. The dotted arrows describe the component horizon is strategic, no lead-times for operations or trans- ﬂows leaving suppliers or remanufacturing centres, port are considered. respectively, to plants. The dashed arrows represent the For each planning period the demand and return product reverse product ﬂows, i.e. the ﬂows from customers to quantities are known, while facility locations and capacity DCCs and from DCCs to remanufacturing centres. In this equipment at the facilities, as well as procurement, trans- CLSCN redistribution is possible, i.e. products and com- portation, production and inventory quantities, have to be ponents can be shipped between facilities of the same type. determined with the objective of total cost minimization. DCCs are bi-directional facilities, because products ﬂow To support these decisions, the planning problem is for- through DCCs to customers and customers return used mulated as a MILP, presented in the next section. products to DCCs. At DCCs returned products are col- lected, visually inspected and, afterwards, they are shipped either to remanufacturing centres or to the disposal unit. 4 The facility location, capacity and aggregate The decomposition of returned products into compo- production planning with remanufacturing nents and the remanufacturing of those components to an problem as-new condition is performed at remanufacturing centres. It is assumed that components can be remanufactured In this section, the planning problem described above, the repeatedly in the planning horizon, i.e. the limited number Facility Location, Capacity and Aggregate Production of possible remanufacturing cycles for components is not Planning with Remanufacturing (FLCAPPR) Problem, is reached. However, there is a known and constant fraction stated and explained using the notation listed in Tables 1, 2 of components that cannot be remanufactured to the quality and 3, presented below. The model presented here is an standards of as-new components with a reasonable given extension of the model given in , as described in Sect. 2 effort and therefore has to be disposed. Moreover, at above. 123 24 Page 6 of 23 Logist. Res. (2016) 9:24 Table 1 Deﬁnition of relevant Set Deﬁnition sets C Set of components, c 2 C F Set of potential plants, f 2 F FD F [fg D , set of potential plants and the disposal unit D K Set of customer locations, k 2 K P Set of products, p 2 P R Set of potential remanufacturing centres, r 2 R RD R [fg D , set of potential remanufacturing centres and the disposal unit D T Set of time periods, t 2 T V Set of potential DCCs, v 2 V Z Set of suppliers for components, z 2 Z Table 2 Deﬁnition of relevant variables Variable Deﬁnition Cap Number of capacity steps at open facility y in period t (in m ), 8y 2 F [ V [ R; t 2 T CCap Expansion or reduction of capacity steps at facility y in period t (in m ), 8y 2 F [ V [ R; t 2 T CCapD Reduction of capacity steps at facility y in period t (in m ), 8y 2 F [ V [ R; t 2 T CCapU Expansion of capacity steps at facility y in period t (in m ), 8y 2 F [ V [ R; t 2 T Quantity of c remaining in the inventory of plant f at the end of the last planning period, 8f 2 F; c 2 C EI EI Quantity of x remaining in the inventory of remanufacturing centre r at the end of the last planning period, 8r 2 R; x 2 C [ P yw Quantity of x transported from facility y to facility w of the same echelon in period t, EXI xt 8y; w 2 F [ V [ R : y 6¼ w; x 2 C [ P; t 2 T < 1; if facility y is closed in period t 8y 2 F [ V [ R; t 2 T 0; otherwise Quantity of c remaining at plant f at the end of period t, 8f 2 F; c 2 C; t 2 T ct I Quantity of x remaining at remanufacturing centre r at the end of period t, 8r 2 R; x 2 C [ P; t 2 T xt LCap Workforce available at facility y in period t, 8y 2 F [ V [ R; t 2 T Number of unmet demand for product p of customer k in period t, 8k 2 K; p 2 P; t 2 T pt X Quantity of x processed in facility y in period t, 8y 2 F [ R; x 2 C [ P; t 2 T xt yw Quantity of x transported from facility y to facility w in period t, 8y; w 2 FD; V; RD; Z : y 6¼ w; x 2 C [ P; t 2 T xt Y 1; if facility y is opened in period t; Et 8y 2 F [ V [ R; t 2 T 0; otherwise < 1; if facility y is open in period t; 8y 2 F [ V [ R; t 2 T 0; otherwise YCCapU 1; if capacity of facility y is increased in t < period t; 8y 2 F [ V [ R; t 2 T 0; otherwise The objective function of the FLCAPPR problem mini- and closing facilities, for the volume capacity equipment and mizes the discounted total costs of the CLSCN over multiple the labour force at open facilities, for processing and storing time periods. As the model combines multi-period facility goods at facilities, for procuring components at suppliers, for location, capacity and aggregate production planning, the transporting goods in the network and for disposing returned objective function consists of cost terms for opening, running products and components. 123 Logist. Res. (2016) 9:24 Page 7 of 23 24 Table 3 Deﬁnition of relevant parameters Parameters Deﬁnition a Discount rate a Number of component c yielded by the remanufacturing of one product unit of p, 8p 2 P; c 2 C cp b Number of component c needed for producing one unit of product p, 8p 2 P; c 2 C cp O 3 Cap Maximum capacity at facility y in period t (in m ), 8y 2 F [ V [ R; t 2 T yt U 3 Cap Minimum capacity at facility y (in m ), 8y 2 F [ V [ R c Unit cost for procuring component c from supplier z, 8z 2 Z; c 2 C DEnt Disposal cost (per unit) c Unit penalty cost for unmet demand k, 8k 2 K c Cost for transportation of a unit x from y to w (per km), 8y; w 2 F; V; R; K : y 6¼ w; x 2 C [ P yw c Unit cost for processing at facility y, 8y 2 F [ R dy Time required for processing a unit of x at facility y, 8y 2 F [ V [ R; x 2 C [ P Size of capacity step by which the locations can be extended within one period (in m ) Cost fcap Cost for capacity increase at facility y by one step, 8y 2 F [ V [ R Rev fcap Revenue for capacity reduction at facility y by one step, 8y 2 F [ V [ R f Cost for opening facility y, 8y 2 F [ V [ R Cost for open facility y in period t, 8y 2 F [ V [ R; t 2 T Volume of one unit of x (in m ), 8x 2 C [ P h Cost per period for holding a unit of c in inventory at plant f, 8f 2 F; c 2 C h Cost per period for holding a unit of x in inventory at remanufacturing centre r, 8r 2 R; x 2 C [ P Maximum labour hours available at facility y in period t, 8y 2 F [ V [ R; t 2 T LabCap yt LabCap Minimum labour hours at facility y, 8y 2 F [ V [ R labcc Hourly cost for workforce at facility y, 8y 2 F [ V [ R le Labour hours per worker per period LT Last planning time period, LT 2 T M Sufﬁciently large number md Minimum proportion of returned products that has to be disposed after visual inspection at the DCCs in period t, 8t 2 T md Minimum proportion of component c that has to be disposed after disassembly, remanufacturing and testing in period t, 8c 2 C; t 2 T mr Minimum number of periods before products are returned for remanufacturing N Demand of customer k for product p in period t, 8k 2 K; p 2 P; t 2 T kpt q Return rate in period t of customer k for product p, sold in period o, 8k 2 K; p 2 P; ðo; tÞ2 T; where o t kpo sf Cost for closing facility y, 8y 2 F [ V [ R sh Cost for disposing a stored unit of x at remanufacturing centre r at the end of the last planning, period LT, 8r 2 R; x 2 C [ P sh Cost for disposing a stored unit of c at facility f at the end of the last planning period LT, 8f 2 F; c 2 C t Distance of y to w (in km), 8y; w 2 F; V; R; K : y 6¼ w; x 2 C [ P yw 123 24 Page 8 of 23 Logist. Res. (2016) 9:24 induces costs; these costs are captured by the terms in line The discounted total costs are described by the follow- ing objective function (1). For the sake of clarity the three. In line four the costs for closing a facility are stated. The cost terms in the next line are for procuring and objective function is split up into three different cost functions. The ﬁrst cost function presents the costs induced shipping components from suppliers to plants. Costs for transporting components from remanufacturing centres to by multi-period facility location, the second function includes the costs resulting from capacity planning, and the plants are listed in line six. The transportation costs of the forward product ﬂow, the costs of aggregate production planning are described by the third function. Below the functions are introduced followed ﬂow of products from plants to DCCs and from DCCs to customers, and the penalty costs for unsatisﬁed demand are by the respective explanations. stated in line seven and eight. min OF ¼ OF þ OF þ OF ð1Þ 1 2 3 The cost terms in line nine and ten are the shipping costs of the reverse product ﬂow, i.e. the ﬂow of products which are with returned by customers to DCCs and ﬂow further in the net- X X work to remanufacturing centres or to the disposal unit. In the OF ¼ 1=ð1 þ aÞ f Y 1 r Et t2T r2R latter case, costs for disposing occur. The disposal costs for X X returned products and remanufactured components are listed þ f Y þ f Y v f Et Et v2V f2F in line eleven. The costs for distributing products or com- X X X r r v v f f ponents, respectively, on the same facility level are listed in þ f Y þ f Y þ f Y t t t t t t r2R v2V line 12–15. f 2F X X X r v f þ sf H þ sf H þ sf H r v f t t t X X r2R v2V f 2F Cost r OF ¼ 1=ð1 þ aÞ fcap CCapU X r t c c c zf t2T r2R þ ðc t þ c Þ X zf zf z ct X X Cost f Cost v z2Z; c2C; f 2F þ fcap CCapU þ fcap CCapU f t v t c c rf f 2F v2V þ c t X rf rf ct X X Rev r Rev f r2R; c2C; f 2F þ fcap CCapD þ fcap CCapD r t f t p p fv r2R f 2F þ c t X fv fv pt f2F; v2V; p2P Rev v X X þ fcap CCapD p p v t vk U k þ c t X þ c U v2V vk vk pt k pt v2V; k2K; p2P k2K; p2P p p kv At facilities, certain volume capacities in m are available and þ c t X pt kv vk v2V; k2K; p2P they can be increased or decreased within one period. These p p vr adjustments induce costs or revenues, as reﬂected by the cost þ c t X vr vr pt v2V; r2R; p2P terms in line 1 and 2 or revenues in line 3 and 4, respectively. X X X X DEnt vD rD þ c X þ X pt ct OF ¼ 1=ð1 þ aÞ c X 3 r ct v2V; p2P r2R; c2C t2T r2R; c2C c c rs X X þ c t EXI rs rs ct f Cost r þ c X þ le labcc LCap pt r t c2C;ðr;sÞ2R:r6¼s f2F; p2P r2R p p rs þ c t EXI rs rs pt X X Cost f Cost v p2P;ðr;sÞ2R:r6¼s þ labcc LCap þ labcc LCap f t v t f2F v2V c c fi þ c t EXI X X fi fi ct p r c r þ h I þ h I c2C;ðf ;iÞ2F:f6¼i r pt r ct r2R; p2P r2R; c2C p p vj þ c t EXI X vj vj pt c f þ h I p2P;ðv;jÞ2V:v6¼j f ct f2F; c2C In the multi-period FLP studied in this work, the facilities can LT c f þð1=ð1 þ aÞ Þ sh EI be opened in one period and in the later periods they can stay f c y y y f2F; c2C open or are closed. The variables Y , Y and H describe the Et t t X X respective state of a facility. The costs for opening, i.e. p r c r þ sh EI þ sh EI r p r c building, a facility, occur just once and are listed in line one r2R; p2P r2R; c2C and two. For every period in which a facility remains open it 123 Logist. Res. (2016) 9:24 Page 9 of 23 24 H 1 8y 2 F [ R [ V Remanufacturing components at remanufacturing centres ð6Þ t2T and assembling products at plants induces costs, see lines one and two. Labour hours of the workforce are needed for Closing of facilities is allowed to happen once within the performing the respective operations at the facilities. The planning horizon. respective costs occur in every period and are stated in line The next set of constraints, constraints (7)–(19), describes 2 and 3. the forward and reverse product ﬂows in the network and the Holding products and components at remanufacturing inventory balance at plants and remanufacturing centres. centres and holding components at plants induces costs, vk k X þ U ¼ N 8k 2 K; p 2 P; t 2 T kpt pt pt ð7Þ which are captured by the cost terms in lines 4 and 5. v2V The costs stated in lines 1–5 occur in every period, Products are shipped from DCCs to satisfy demand of and hence, these costs have to summed up over the customer k for product p in period t. Unsatisﬁed demand is planning horizon. At the end of the planning horizon the remaining items on stock at the facilities are disposed, captured by U . pt and the respective cost terms are stated in the last two kv X ¼ 0 8t 2fg 1; ...; mr 1 ; k 2 K; p 2 P pt lines. ð8Þ v2V In the following, the constraints of the problem are X X X presented, but before that, important variables are kv t vk X ¼ q X pt kpo po explained. ð9Þ v2V v2V o¼1 y y y The variables Y , Y and H are interrelated. If a facility t t Et 8t 2fg mr; ...; T ; k 2 K; p 2 P is opened in one period, then it is running in this period; y y y therefore, both variables Y and Y take value 1 and H is After mr periods, products can be returned for the ﬁrst t t Et zero. time. In period t a proportion of products sold in period o, In the next period this facility can be still open, then q , is returned to DCCs. Every returned product is col- kpo y y Y ¼ 1 and Y ¼ 0, because the facility is already lected in DCCs. tþ1 Etþ1 X X opened, and H ¼ 0. However, the open facility can be tþ1 f f zf rf I ¼ I þ X þ X ct ct1 ct ct closed in t þ 1, then H takes value 1, and tþ1 z2Z r2R y y X X Y ¼ Y ¼ 0. if fi f tþ1 Etþ1 ð10Þ þ EXI EXI X ct ct ct It is assumed that a facility cannot be opened again after i2F:i6¼f i2F:i6¼f it is closed. The constraints (2)–(6) deﬁne these 8f 2 F; c 2 C; t 2 T : t [ 1 interrelations. These constraints represent the inventory balance equations Y 1 8y 2 F [ R [ V Et ð2Þ for components at plants. t2T X X r r vr sr I ¼ I þ X þ EXI A facility can be opened just once in the planning horizon. pt pt1 pt pt v2V s2R:s6¼r y y Y ¼ Y 8y 2 F [ R [ V ð3Þ E1 1 rs r ð11Þ EXI X pt pt s2R:s6¼r If a facility is opened in the ﬁrst planing period, it is open in period 1. 8r 2 R; p 2 P; t 2 T : t [ 1 y y ðY H Þ¼ Y The inventory balance equations for returned products at Et t s t2T:t s ð4Þ remanufacturing centres are stated in (11). 8y 2 F [ R [ V; s 2 T : s [ 1 r r r sr I ¼ I þ X þ EXI ct ct1 ct ct s2R:s6¼r If a facility is opened and not closed in one of the periods X X rs rf t s, where ðs; tÞ2 T, then the facility is open in period s. ð12Þ EXI X ct ct s2R:s6¼r f 2F y y y Y Y H 8y 2 F [ R [ V; t 2 T : t [ 1 ð5Þ t1 t t 8r 2 R; c 2 C; t 2 T : t [ 1 These constraints indicate the closing of facilities by Components can be stocked at remanufacturing centres, too. comparing the opening indicator variables of two succes- The inventory balance is determined by the equations (12). sive periods. 123 24 Page 10 of 23 Logist. Res. (2016) 9:24 X X X f zf rf if The following constraint sets, the constraints (22) I ¼ X þ X þ EXI c1 c1 c1 c1 and (23), describe the disassembly and assembly z2Z r2R i2F:i6¼f X ð13Þ fi f operations at the remanufacturing centres and plants, EXI X 8f 2 F; c 2 C c1 c1 respectively. i2F:i6¼f X X r r X ¼ a X 8r 2 R; t 2 T; c 2 C r r sr rs cp ct pt ð22Þ I ¼ X þ EXI EXI x1 x1 x1 x1 p2P s2R:s6¼r s2R:s6¼r ð14Þ rf The number of as-new components, derived by disassem- X 8r 2 R; x 2 C [ P x1 bling returned products and remanufacturing the respective f 2F components, is deﬁned by the equations above. The constraints (13) and (14) deﬁne the balance of the f f respective inventory at the end of the ﬁrst period. X ¼ b X 8f 2 F; t 2 T; c 2 C cp ct pt ð23Þ p2P I ¼ EI 8f 2 F; c 2 C ð15Þ cLT c The number of components required for product assembly r r I ¼ EI 8r 2 R; x 2 C [ P ð16Þ xLT x at plants is deﬁned by these equations. At facilities capacity in labour hours and volume are Products and components remaining in the respective considered and have to be planned over the planning inventories at the end of the last planning period, LT, are horizon. The next sets of constraints, the constraints (24)– captured by (15) and (16). (43), describe the capacity planning. X X X fv jv vj X þ EXI EXI pt pt pt X X kv vk v f2F j2V:j6¼v j2V:j6¼v dV ðX þ X Þ le LCap pt pt t X ð17Þ ð24Þ vk p2P k2K ¼ X 8v 2 V; t 2 T; p 2 P pt k2K 8v 2 V; t 2 T Since no inventory at DCCs is allowed, every product The capacity level in terms of labour hours at facilities is entering a DCC in period t also has to leave it in period t. the product of one worker’s labour hours per period, le, fv f multiplied by the workforce available in t, determined by X ¼ X 8f 2 F; t 2 T; p 2 P pt pt ð18Þ LCap for DCCs. The constraints above adhere that the v2V labour hours needed for handling products at DCCs do not There is no product inventory at plants, i.e. every assem- exceed the available capacity level. bled product in a plant in period t is shipped to DCCs in the r r same period. dR X le LCap 8r 2 R; t 2 T ct t ð25Þ X X c2C vr kv X ¼ X 8v 2 V; t 2 T; p 2 P pt pt ð19Þ The labour hours used for remanufacturing at a remanufac- r2RD k2K turing centre cannot exceed the respective available capacity. Every returned product is shipped from DCCs either to f f remanufacturing centres or to the disposal unit D. dF X le LCap 8f 2 F; t 2 T pt t ð26Þ p2P The constraints (20) and (21) deﬁne the disposal quan- tities in the network. At plants, capacity in terms of labour hours is needed for vD kv assembling products. It is limited by the capacity level at a X md X 8v 2 V; t 2 T; p 2 P pt pt ð20Þ plant. k2K U y y O y LabCap Y le LCap LabCap Y At least a proportion of md of the returned products has to t y t t yt t ð27Þ be disposed in period t, because of failing the inspection at 8y 2 F [ V [ R; t 2 T the DCCs. The capacity in labour hours at an open facility is restricted c r rD md X X 8r 2 R; t 2 T; c 2 C ð21Þ t ct ct by upper and lower bounds, forced by operations and the availability of workers. After remanufacturing, at least a proportion of md of the f f components does not comply with the requirements for as- g I e Cap 8f 2 F; t 2 T ct t ð28Þ new components and is disposed. c2C 123 Logist. Res. (2016) 9:24 Page 11 of 23 24 The volume capacity at the facilities is a multiple of e. The The volume of products ﬂowing through a DCC has to volume of components stocked at an open plant cannot comply with its capacity. exceed its available volume capacity. U y y O y Cap Y e Cap Cap Y y t t yt t X X ð35Þ r r r g I þ g I e Cap 8r 2 R; t 2 T c p ct pt t 8y 2 F [ V [ R; t 2 T c2C p2P The volume capacity level of a facility is a multiple of ð29Þ e and is limited by given upper and lower bound. At an open remanufacturing centre, the volume of stored y y Cap Cap ¼ CCap products and components has to comply with the volume t t1 t ð36Þ capacity. 8y 2 F [ V [ R; t 2 T : t [ 1 X X X X Volume capacity at facilities can be expanded or reduced zf rf if g X þ X þ EXI ct ct ct within one period. ð30Þ c2C z2Z r2R i2F:i6¼f y y Cap ¼ CCap 8y 2 F [ V [ R ð37Þ e Cap 8f 2 F; t 2 T 1 1 In the ﬁrst planning period, the number of capacity steps at The volume of components ﬂowing into a plant is restricted a facility is identical to the capacity expansion carried out by the available volume capacity. X in period 1. fv f g X e Cap 8f 2 F; t 2 T pt t ð31Þ y O y CCap Cap YCCapU p2P t yt t ð38Þ 8y 2 F [ V [ R; t 2 T The product ﬂow through a plant adheres to the volume capacity restriction of a plant. y The variable YCCapU takes value 1, if the respective variable CCap is bigger than zero, i.e. the capacity of X X X r sr g X þ EXI þ g c p facility y is increased in period t. ct ct c2C s2R:s6¼r p2P y y O y CCap CCapU Cap ð1 YCCapU Þ t t yt t X X ð32Þ ð39Þ vr sr r X þ EXI e Cap pt pt t 8y 2 F [ V [ R; t 2 T v2V s2R:s6¼r Capacity increase is assigned to the variable CCapU . 8r 2 R; t 2 T y O y CCapU Cap YCCapU t yt t The volume of the components and products ﬂowing into a ð40Þ remanufacturing centre is limited by its volume capacity 8y 2 F [ V [ R; t 2 T restriction. The upper capacity bound of a facility limits the capacity X X X increase. rf rs g X þ EXI þ g c p ct ct y y O y c2C p2P s2R:s6¼r CCap CCapD Cap YCCapU t t yt t ð41Þ ð33Þ 8y 2 F [ V [ R; t 2 T rs r EXI e Cap pt t s2R:s6¼r The variable CCapD captures the capacity decrease. 8r 2 R; t 2 T y O y CCapD Cap ð1 YCCapU Þ t yt t ð42Þ The volume of the components and products leaving a 8y 2 F [ V [ R; t 2 T remanufacturing centre has to be less or equal than the Capacity decrease at a facility cannot be higher than the respective capacity level. respective upper capacity bound. X X X X fv kv jv y y g X þ X þ EXI pt pt pt YCCapU Y 8y 2 F [ V [ R; t 2 T ð43Þ t t ð34Þ p2P f 2F k2K j2V:j6¼v Capacity can just be increased at an open facility. e Cap 8v 2 V; t 2 T 123 24 Page 12 of 23 Logist. Res. (2016) 9:24 k kv vk vr zf r r rf fv the total product demand is assumed as 10 units per 1000 U ; X ; X ; X ; X ; X ; X ; X ; X ; pt pt pt pt ct ct pt ct pt inhabitants, where the number of inhabitants is taken from f f rs rs fi vj f r X ; X ; EXI ; EXI ; EXI ; EXI ; I ; I ; pt ct ct pt ct pt ct ct . Furthermore, it is assumed that demand occurs in r f r r r f v y ð44Þ I ; EI ; EI ; EI ; Cap ; Cap ; Cap ; CCapU ; every period of the planning horizon, since, as in , one pt c c p t t t t r f v þ planning period equates to one year. LCap ; LCap ; LCap 2 Z 8p 2 P; c 2 C; t t t Costumers demand two different product types, P1 and r 2 RD; k 2 K; v 2 V; f 2 FD; z 2 Z; t 2 T P2. Demand for P1 and P2 is assumed as equally high, i.e. 500 units of P1 and P2 are required, in every period. Unsatisﬁed demand, the ﬂows of products or components It is possible to open DCCs and remanufacturing centres between different echelons and between facilities of one at the demand locations. Suppliers and possible plant echelon, the produced units, the units on stock, the locations are to be found only in the ﬁve biggest German capacities at the facilities and the capacity increase are cities. In Fig. 2 the customer locations with their demand in described by positive integer variables. product units per planning period are given. Furthermore, CCap 2 Z 8y 2 F [ V [ R; t 2 T ð45Þ the suppliers and all possible locations for DCCs, reman- ufacturing centres and plants are shown. Variables describing the change of capacities at facilities In the initial example used in this work, it is assumed are integers and can be positive or negative. that demand for P1- and P2-products is known for ﬁve CCapD 2 Z 8y 2 F [ V [ R; t 2 T ð46Þ years and remains constant over the planning horizon. Later on, a sensitivity analysis is presented which includes The variables that determine the volume capacity decrease a study on the impact of varying the length of the planning are negative integer variables. horizon. y y y y Y ; Y ; H ; YCCapU 2fg 0; 1 The assembly of each product type requires one speciﬁc t t t ð47Þ component, M1 for P1- and M3 for P2-products, and one 8y 2 F [ V [ R; t 2 T component, M2, which is commonly used for both product Binary variables indicate the opening and closing of types. For simplicity the disassembly process is assumed to facilities and the capacity increase. be the reverse of the assembly process. 5 Numerical analysis In this section, the previously stated FLCAPPR model is solved for an example data set. At ﬁrst, the example, its data and the solution are described, and then, the sensitivity of the network to changes in the data is studied. The inﬂuence of the cost parameters on the decision to remanufacture is explored. Furthermore, the robustness of the solution with respect to the quantity of returned prod- ucts and the length of the planning horizon is examined by varying the return rate and the number of periods in the planning horizon. Selected interesting results are discussed. 5.1 Initial setting and solution In the copier industry, CLSCNs as the one described in Sect. 3 can be found. At copier manufacturer Xerox, for example, ’’remanufactured parts are put onto the assembly line for reuse in brand new copiers’’ . Fleischmann et al  study the facility location problem in a CLSCN of a European copier remanufacturer for a single-period plan- ning horizon. In this paper a CLSCN for the copier industry in Ger- many is to be designed. The product demand is assumed to Fig. 2 Possible facility locations and the location of suppliers and customers with their respective demand be bundled in the ﬁfteen biggest German cities. As in  123 Logist. Res. (2016) 9:24 Page 13 of 23 24 The return rate q , where ðs; tÞ2 T : s t, is inde- h. This results from the following calculation: in Germany kps contractual labour hours per week often are 35 h. The pendent of customer location and product type, as in . holiday entitlement is six weeks per calendar year. The multi-period modelling framework of the FLCAPPR Therefore, the number of labour hours of one worker per model allows to model a temporal shift between the for- year is ð52 6Þ (’’working’’ weeks in a year) 35 (hours ward and reverse product ﬂows in the network of t s ¼ per week) ¼ 1610 (hours per year), neglecting public mr periods, i.e. a residence time of a product with a cus- holidays and downtime due to sickness. tomer can be deﬁned. In this work a residence time of one The FLCAPPR problem with the described data setting year is assumed. Moreover, following  the return frac- can be solved by the optimization software Gurobi 6.5.0 on tion is assumed to be 50%, i.e. in the initial setting in this a two 3.10 GHz Intel Xeon Processor E5-2687W and 128 work, 50% of products shipped to the customers are GB RAM computer in 197.71 seconds. The total dis- returned at the beginning of the following period. There- counted costs are 19,534,389.05 MU. fore, for 5 planning periods the return rate is In the solution, only one DCC and one plant are used; 1 3 4 5 2 4 5 3 q ¼ q ¼ q ¼ q ¼ q ¼ q ¼ q ¼ q kp1 kp1 kp1 kp1 kp2 kp2 kp2 kp3 both are located in Berlin and are open during the total 5 4 5 planning horizon. The open facilities and their capacity ¼ q ¼ q ¼ q ¼ 0 kp3 kp4 kp5 equipments in the planning periods can be found in Fig. 3. 2 3 4 5 and q ¼ q ¼ q ¼ q ¼ 0:5. In every planning period products are shipped from the kp1 kp2 kp3 kp4 The other relevant parameters of the initial example and open DCC in Berlin to the customers to meet their demand. their values can be found in Table 4. The fraction of the The products at the DCC originate from the plant in Berlin, returned products that has to be disposed, i.e. leaving the where these product quantities are assembled in every network, is 0.6, as stated in . However, in the CLSCN period using components that are delivered from the sup- studied in this work, returned products and components can plier in Berlin. In Fig. 4 the product and component ﬂows be disposed; therefore, here the sum of the fractions of in the network are depicted. returned products md and components md that has to be The workforce and volume capacity at the open plant is disposed is set to 0.6, i.e. md ¼ md ¼ 0:3. The trans- at the same level for every period, see Fig. 3, because in p p p p c c portation costs in the network c , c , c , c , c and c every planning period the same amount of products and vk kv vr rf zf fv components, respectively, are processed at the plant. are taken from . It is assumed that the costs for shipping Since in the second period customers start to return goods between facilities of the same type are identical; the products at the DCC in Berlin, the workforce and volume distances between the locations are taken from . capacity at the DCC is increased from the ﬁrst to the second The cost difference between the procurement costs c period, see Fig. 3. The customer demand and the amount of and remanufacturing costs c is assumed as 10 MU per DEnt products which are returned by customers remain the same in component, as described in . Disposal costs c and x the following periods, therefore, the workforce and volume sh ; 8y 2 F [ R; x 2 C [ P are taken from  as well. capacity at the DCC stay at the same level for the remaining Following Silver’s  recommendations the inventory periods of the planning horizon. p c c holding costs h ¼ h ¼ h ; 8p 2 P; r 2 R; c 2 C; f 2 F are r r f Every returned product is collected in the DCC in Berlin assumed as 0.25 MU per unit per year. and then disposed. There is no open remanufacturing centre The opening costs for the facilities, f , f and f ; are v f r in the network and no component remanufacturing takes taken from . The costs and revenues for capacity place in any period. adjustments are based on these costs and assumed as It is difﬁcult to compare the results of the initial example Cost Rev fcap ¼ fcap ¼ 1000 MU. This assumption is dis- y y with previous studies of FLPs with reverse product ﬂows, cussed in the following sensitivity analysis. e.g. in , since the planning problem is extended in this The volume capacity can be adjusted in steps of 1000 work. Hence, additional parameters had to be introduced units. The lower volume capacity limits at facilities are and, therefore, the planning problems differ. 1000 m ; an open facility has to be equipped at least with However, it is to be noticed that the solution of the one volume capacity step. The capacity upper bound is single-period facility location model presented in  rec- chosen such that one open DCC, remanufacturing centre ommends to open remanufacturing locations and that and plant is sufﬁcient for the total product or component recovered products should be used to meet demand, which ﬂow, respectively. is different from the solution of the initial example of the It is assumed that capacity in labour hours can be FLCAPPR problem in this work. Due to the fact that in the increased or decreased, respectively, by multiples of 1610 multi-period approach taken here costs for volume capacity 123 24 Page 14 of 23 Logist. Res. (2016) 9:24 Table 4 Deﬁnition of parameter data Parameter Value a 0.01 O 3 Cap 500,000 m , 8y 2 F [ R; t 2 T yt O 3 Cap 800,000 m , 8v 2 V ; t 2 T vt U 3 Cap 1000 m , 8y 2 F [ R [ V; t 2 T c 10 MU per component, 8c 2 C; z 2 Z DEnt 2.5 MU per unit 1000 MU per unit, 8k 2 K c 0.0030 MU per km, 8c 2 C; y 2 Z [ R; w 2 F yw c 0.01 MU per km, 8p 2 P; v 2 V ; k 2 K vk 0.005 MU per km, 8p 2 P; v 2 V; k 2 K kv c 0.003 MU per km, 8p 2 P; v 2 V; r 2 R vr c 0.0045 MU per km, 8p 2 P; v 2 V; f 2 F fv c 1 MU per unit, 8f 2 F c 0 MU per unit, 8r 2 R dV 0.5 h, 8p 2 P dR 2h, 8c 2 C dF 1h, 8p 2 P 1000 m Cost fcap 1000 MU, 8y 2 F [ V [ R Rev fcap 1000 MU, 8y 2 F [ V [ R f 500,000 MU, 8r 2 R f 5,000,000 MU, 8f 2 F f 1,500,000 MU, 8v 2 V f 10,000 MU, 8y 2 F [ V [ R; t 2 T p 10 m , 8p 2 P 2m , 8c 2 C h 0.25 MU per unit, 8x 2 C [ P; r 2 R h 0.25 MU per unit, 8c 2 C; f 2 F 1,000,000 h, 8y 2 F [ V [ R; t 2 T LabCap yt labcc 15 MU per hour, 8y 2 F [ V [ R le 1610 h md 0.3 md 0.3, 8c 2 C mr 1 sf 50,000 MU, 8y 2 F [ V [ R sh 2.5 MU per unit, 8y 2 F [ R; x 2 C [ P 123 Logist. Res. (2016) 9:24 Page 15 of 23 24 5.2 Sensitivity analysis In this section the sensitivity of the network structure to changes in the data is studied. First, the impact of the cost parameters on the decision to remanufacture is examined. Then the effect of the return rate on the network design is studied. Thereafter, the length of the planning horizon is varied and the inﬂuence on the network design and espe- t CapV t LabCapV 1 463,000 m³ 1 24,150 hours cially on the remanufacturing decision is discussed. 2 695,000 m³ 2 35,420 hours 3 695,000 m³ 3 35,420 hours Due to rather extensive computing times the following 4 35,420 hours 4 695,000 m³ 5 695,000 m³ 5 35,420 hours tests were implemented allowing an optimality gap of up to t CapF t LabCapF 0:01%. The exceptional cases are marked. 1 463,000 m³ 1 46,690 hours 2 463,000 m³ 2 46,690 hours 3 463,000 m³ 3 46,690 hours 4 463,000 m³ 4 46,690 hours Open DCC in 5 463,000 m³ 5 46,690 hours 5.2.1 Inﬂuence of cost parameters every period Open plant in every period By extending the FLP to a multi-period planning problem in which facility locations, capacities and aggregate pro- duction are optimized, additional cost parameters are introduced in the objective function. In this section the impact of these cost parameters on the decision to reman- ufacture is studied. Cost r Therefore, in the following fcap ; labcc ; f and c ; r r r t 8r 2 R; t 2 T, i.e. the cost parameters for volume capacity Fig. 3 Open facilities with their capacity levels and labour hours at the remanufacturing centres, for open remanufacturing centres and for remanufacturing, are var- ied, and the results are discussed. Inﬂuence of volume capacity cost parameters In previous facility location models in networks with pro- HH � duct recovery, as i.e. in , the capacity level of a facility HB is assumed as given and it is not cost-optimally determined. Without taking into account costs for volume capacity, over-capacities in the network can occur. DO Furthermore, the capacity requirements resulting from DU the ﬂow of goods in a network with product recovery, � DD especially the increased capacity requirements induced by the returned product ﬂow additional to the requirements of Open DCC forward product ﬂows, are not considered as costs in the Open plant decision problem. In the FLCAPPR model building up Foward and reverse product flow volume capacity at a remanufacturing centre leads to costs; Component flow Cost it is weighted with fcap ; 8r 2 R, in the objective function. In the initial example this cost is assumed as 1000 MU. Since in the solution of the initial example it is cost-opti- mal to dispose returned products and procure all compo- nents from a supplier, now the capacity cost is decreased to study if it has an impact on the remanufacturing decision. Fig. 4 Product and component ﬂows in the network The solution of the initial example stays optimal until Cost Cost and workforce are included which were not considered in fcap ¼ 400; 8r 2 R. When fcap 400 MU, no rea- r r  remanufacturing becomes less attractive and according sonable solutions are obtained. Now, it is optimal to open to the FLCAPPR model, opening a remanufacturing centre every remanufacturing centre in periods 2–5, and volume and remanufacturing components is not cost-optimal. capacity is built up in one period and removed in the 123 24 Page 16 of 23 Logist. Res. (2016) 9:24 following period again and again over the planning horizon to gain the revenues from the volume capacity decrease, Rev Cost since fcap ¼ 1000 [ 400 ¼ fcap . No returned prod- r r ucts are processed at any remanufacturing centre. This HH � solution is hardly realistic and shows that the parameters HB Cost Rev fcap and fcap have to be carefully determined. r r Cost Rev Decreasing both parameters fcap and fcap down H � r r to zero has no inﬂuence on the network, especially it DO remains optimal to dispose every returned product instead E DU � of opening remanufacturing centres and processing L � returned products. � DD Open remanufacturing centre in period 2-5 Inﬂuence of labour hour cost parameter Open DCC Open Plant In previous studies, as in , the workforce at facilities Foward and reverse product flow necessary for the respective operations at the facilities is N Reverse product flow not considered. However, the decisions to open a reman- Component flow ufacturing centre and to remanufacture components are interrelated. For remanufacturing, workforce at a remanu- facturing centre is needed whose labour hours cost money. � In this work, the workforce at facilities induces costs that are taken into account in the objective function. It is assumed that a labour hour at the remanufacturing Fig. 5 Network with no labour hour costs for remanufacturing, centre costs labcc ¼ 15 MU, 8r 2 R. The impact of this labcc ¼ 0; 8r 2 R cost parameter on the decision to remanufacture is studied in the following. components used at the plant for product assembly are It turns out that for every value of labcc [ 0 the from the remanufacturing centre, the other components are solution of the initial example remains cost-optimal. procured from the supplier in Berlin. (The maximum per- However, setting this parameter to zero has an impact on centage results from the limited number of returned prod- the network design. Now, it is cost-optimal to open a ucts, which in turn results from the return rate.) remanufacturing centre in the second period additional to The workforce at the remanufacturing centre is set at the the DCC and the plant in Berlin; the remanufacturing highest possible level in the second until the last period, see centre remains open for the remaining periods. The net- Fig. 8, because workforce induces no labour hour costs work and the open location with the respective capacity (labcc ¼ 0). equipment are shown in Fig. 5. r The volume capacity at the remanufacturing centre is The total discounted costs are 19,345,018.28 MU. With determined cost-optimally at 227,000 m for the second no labour hour cost at the remanufacturing centre, returned until the fourth period. In the last planning period the products are shipped to the remanufacturing centre. There returned products are stored or disassembled, and suit- capacity is reduced by one step, thus 1000 m , to obtain able components are remanufactured and used for product revenues for capacity reduction. To comply with this assembly at the plant. The processed and stored quantities reduced volume capacity the returned product quantity are mapped in Figs. 6 and 7, respectively. In period 2-4 the shipped to the remanufacturing centre is slightly decreased, distribution quantities between the DCC and remanufac- as the processed quantities at the remanufacturing centre, turing centre are the same, in the last period the reverse see Fig. 6. Hence, the decisions regarding the volume product ﬂow between the DCC and the remanufacturing capacity level and the processed quantities at the remanu- centre is lower: less P2-products are transported to the facturing centre and the reverse product ﬂows in the net- remanufacturing centre. Since the quantity of products work are interrelated. returned from customers stays the same from the second to The capacity equipments of the plant and the DCC in the last period, the quantity of returned P2-products which Berlin stay at the same levels as in the initial example, are disposed is increased and at the remanufacturing centre because the product ﬂows between the plant and the DCC less P2-products are disassembled in period 5. Therefore, and between the DCC and the customers are not inﬂuenced over the total planning period just 24.48% of the compo- by the labour hour costs at the remanufacturing centre. nents instead of the maximal possible 24.5% of the Furthermore, if a remanufacturing centre is opened, this 123 Logist. Res. (2016) 9:24 Page 17 of 23 24 does not have an impact on the DCC and plant location nor on their capacity equipment. Inﬂuence of costs for open remanufacturing centres The FLCAPPR model optimizes the CLSCN over multiple periods. It is assumed that a facility in this network can be opened in any period and in the later periods the open 2345 facility can be closed or stay open. Disassembled P1-products 8096 8100 8100 8100 Disassembled P2-products 8097 8100 8100 8043 The opening costs are taken from  and the cost per Remanufactured M1- 5667 5670 5670 5670 period for an open remanufacturing centre, components at plant Remanufactured M2- f ; 8r 2 R; t 2 T, are assumed in the initial example as 11335 11340 11340 11300 components at plant 10,000 MU. In the initial example no remanufacturing Remanufactured M3- 5667 5670 5666 5634 components at plant centre is opened. To study if and how this cost inﬂuences Period this decision, the cost is decreased until f ¼ 0. Fig. 6 Processed quantities at remanufacturing centre, At f ¼ 0 it is still not cost-optimal to open a remanu- labcc ¼ 0; 8r 2 R facturing centre. Hence, decreasing the cost parameter f ; 8r 2 R; t 2 T has no impact on the decision to open a remanufacturing centre under this data setting. Inﬂuence of remanufacturing cost parameter As in , the difference between the remanufacturing and procurement costs c ; 8r 2 R and c ; 8c 2 C; z 2 Z, Stored returned P1-products 3210 respectively, is assumed as 10 MU, that is c ¼ 0; 8r 2 R Stored returned P2-products 2100 and c ¼ 10 MU; 8c 2 C; z 2 Z. The solutions presented in Period  recommend remanufacturing of copiers unlike the solu- Fig. 7 Stored product quantities at remanufacturing centre, tion of the initial example in this work. In this section it is labcc ¼ 0; 8r 2 R studied, if and how the remanufacturing costs in relation to the procurement costs inﬂuence the remanufacturing decision. The FLCAPPR problem is solved with different values for c ; 8r 2 R. Since no remanufacturing takes place at c ¼ 0; 8r 2 R, just negative values of c ; 8r 2 R are r r studied, i.e. remanufacturing a component is subsidized. For every 0 [ c [ 30 MU; 8r 2 R the solution remains the same as described in the solution of the initial � B t CapV t LabCapV example. From c ¼30 MU; 8r 2 R it is cost-optimal to 1 463,000 m³ 1 24,150 hours 2 695,000 m³ 2 35,420 hours remanufacture. Hence, a difference of 40 MU between the 3 695,000 m³ 3 35,420 hours 4 35,420 hours 4 695,000 m³ remanufacturing and procurement costs is necessary in 5 695,000 m³ 5 35,420 hours order to make remanufactured components preferable to t CapF t LabCapF 1 463,000 m³ 1 46,690 hours procured components. Because costs for volume capacity 2 463,000 m³ 2 46,690 hours 3 463,000 m³ 3 46,690 hours and workforce are included in the FLCAPPR model, this Open remanu- 4 463,000 m³ 4 46,690 hours facturing centre 5 463,000 m³ 5 46,690 hours difference has to be bigger than in other studies where in period 2 - 5 t CapR t LabCapR Open DCC in these costs are ignored, e.g. in . At c ¼30 MU ; 8r 2 2 227,000 m³ 2 999,810 hours every period 3 227,000 m³ 3 999,810 hours R a remanufacturing centre in Berlin is opened in the Open plant in 4 227,000 m³ 4 999,810 hours every period second period and stays open in the remaining periods. 5 226,000 m³ 5 999,810 hours Like in the solution of the initial example a DCC and a plant in Berlin are open in every planning period. The network and capacity levels at open facilities are mapped in Fig. 9. The total discounted costs are 19,346,946.96 MU, i.e. costs can be slightly decreased. The capacity level and product ﬂows between the plant and the DCC and the DCC and the customers remain as in Fig. 8 Open facilities with their capacity levels for labcc ¼ 0; 8r 2 R 123 24 Page 18 of 23 Logist. Res. (2016) 9:24 �B t CapV t LabCapV 1 463,000 m³ 1 24,150 hours 2 695,000 m³ 2 35,420 hours 3 695,000 m³ 3 35,420 hours 4 695,000 m³ 4 35,420 hours 5 695,000 m³ 5 35,420 hours t CapF t LabCapF 1 463,000 m³ 1 46,690 hours 2 463,000 m³ 2 46,690 hours 3 463,000 m³ 3 46,690 hours Open remanu- 4 463,000 m³ 4 46,690 hours facturing centre 5 463,000 m³ 5 46,690 hours in period 2-5 Fig. 10 Processed quantities at remanufacturing centre, t CapR t LabCapR Open DCC in c ¼30; 8r 2 R 2 227,000 m³ every period 2 64,400 hours r 3 227,000 m³ 3 64,400 hours Open plant in every period 4 227,000 m³ 4 64,400 hours 5 228,000 m³ 5 66,010 hours Stored returned P1-products 98 107 0 Stored returned P2-products 89 188 187 0 Fig. 9 Network with negative remanufacturing costs, Period c ¼30; 8r 2 R Fig. 11 Stored product quantities at remanufacturing centre, c ¼30; 8r 2 R the solution of the initial example, see Fig. 4. However, r there is a product ﬂow between the DCC and the reman- remanufacturing centre are adapted to the requirements of ufacturing centre in Berlin, as shown in Fig. 5. the processed and stored quantities, see Figs. 10 and 11.By From the second until the last period products collected storing products from the second to the fourth period at the DCC are shipped to the remanufacturing centre. At instead of processing them immediately at the remanu- the remanufacturing centre the returned products are stored facturing centre, less workforce is necessary at the and disassembled to components and suitable components remanufacturing centre in these periods, see Fig. 9. How- are remanufactured. After remanufacturing, the compo- ever, due to building up inventory at the remanufacturing nents are shipped to the plant. The processed and stored centre from the second until the fourth period, more vol- quantities at the remanufacturing centre are mapped in ume capacity is necessary in the ﬁfth period; in the last Figs. 10 and 11, respectively. period the capacity has to be increased to comply with the Every remanufacturable returned product and compo- increased volume requirements. In the last planning period nent is processed at the remanufacturing centre and then all items on inventory are processed, therefore, the work- shipped from the remanufacturing centre to the plant, i.e. force in the last period is increased, too, see Fig. 9. there are no items on inventories at the end of period 5. In addition to remanufactured components, components 5.2.2 Inﬂuence of return rate have to be procured from the supplier in Berlin; only 24.5% of the components used in the product assembly are The FLCAPPR model is solved with different values for remanufactured components. Compared to the solution of q ; 8 k 2 K; p 2 P; ðs; tÞ2 T : s t, i.e. with return rates the previous section for labcc ¼ 0; 8r 2 R, this fraction is r kps slightly increased. For c ¼30; 8r 2 R every remanu- from 0 to 1, increasing in steps of 0.1. The respective total facturable product is processed at the remanufacturing discounted costs and selected decision variable values for centre. the results can be found in Fig. 12. There is an interrelation between the decisions to store When there are no returned products at all, a plant and and process products and the capacity equipment at the DCC are opened in Berlin, but of course no remanufac- remanufacturing centre, as the capacity levels at the turing centre is opened. The total discounted costs are 123 Logist. Res. (2016) 9:24 Page 19 of 23 24 25000000 1000000 20000000 800000 15000000 600000 10000000 400000 5000000 200000 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Labour Hours at DCCs in period 1 24150 24150 24150 24150 24150 24150 24150 24150 24150 24150 24150 Labour Hours at DCCs in period 2-5 24150 25760 28980 30590 33810 35420 37030 40250 41860 45080 46690 Capacity at DCCs in 1 in m3 463000 463000 463000 463000 463000 463000 463000 463000 463000 463000 463000 Capacity at DCCs in 2 - 5 in m3 463000 510000 556000 602000 648000 695000 741000 787000 834000 880000 926000 Sum of disposed returned products 0 18530 37024 55536 74048 92560 111072 129584 148096 166608 185120 Total Cost in MU 18266248 18482777 18792549 19008088 19317860 19534389 19749928 20059700 21562548 21858757 22060733 Return rate Fig. 12 Variation of return rate with c ¼ 0; 8r 2 R 18, 266, 247.79 MU and, hence, lower than before, as no transportation and other costs for returned products occur. For every return rate from 0 to 1, the decision regarding the opening and the capacity equipment of the plant HH remains the same. Moreover, for every return rate no HB remanufacturing centre is opened, every returned product is disposed and every component used in the product H assembly is procured from the supplier in Berlin. DO The total discounted costs of the CLSCN increase with E � DU the return rate, see Fig. 12. This cost increase is induced by � higher capacity and by disposal and opening costs due to an DD � increased quantity of returned products which are collected Reverse product flow in the DCCs and disposed afterwards. in period 1-5 Component flow Due to the assumption that returned products have to be Foward Product flow collected at DCCs, the return rate has an inﬂuence on the Foward Product flow � N in period 1 capacity equipment at the DCC and the opening decision Foward Product flow in period 2-5 regarding DCCs, as every returned product ﬂows through a DCC and requires handling times and space, see Fig. 12. For a return rate between 0.8 and 1 the volume capacity of one DCC is not sufﬁcient any more; therefore, a DCC in Dortmund is opened additional to the DCC in Berlin. The resulting network with the product and component ﬂows is displayed in Fig. 13. Fig. 13 Network with two DCCs for q ¼fg 0:8; 0:9; 1 kps From the DCC in Dortmund products are shipped to customers in Dortmund, Duisberg, Du¨sseldorf, Essen, structure, if the quantity of returned products is high, as in Frankfurt am Main and Cologne in every planning period, . Therefore, the forward and reverse product ﬂows have and in the ﬁrst period the demand of customers in Stuttgart to be planned simultaneously in order to achieve an optimal is met by products from the DCC in Dortmund. The network. remaining customers receive their products from the DCC Moreover, it turns out that a higher quantity of returned in Berlin. products increases the total costs, but does not necessarily Some reverse product ﬂows are different from the for- result in a network with remanufacturing. There is no ward product ﬂows. Customers in Bremen and Hannover return rate at which it is cost-optimal to open a remanu- return their products to the DCC in Dortmund, although facturing centre and use remanufactured components in the they get products from the Berlin DCC. The other cus- product assembly under the initial data setting, in particular tomers return their products to the DCC which delivered for the assumed cost parameters. the product. Now, it is examined which results occur when it is cost- The results show that the reverse product ﬂow inﬂuences optimal to open a remanufacturing centre and to remanu- the forward product ﬂow and the optimal network facture all suitable components and the return rate is 123 24 Page 20 of 23 Logist. Res. (2016) 9:24 25000000 500000 20000000 400000 15000000 300000 10000000 200000 5000000 100000 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8* 0.9** 1*** Labour Hours at rem. centre in 2 & 3 0 0 0 0 51520 64400 77280 90160 103040 115920 128800 Labour Hours at rem. centre in 4 0 0 0 0 51520 64400 77280 91770 104650 117530 130410 Labour Hours at rem. centre in 5 0 0 0 0 51520 66010 78890 90160 64400 74060 80500 Capacity at rem. centre in 2 & 3 in m3 0 0 0 0 182000 227000 272000 317000 363000 408000 453000 Capacity at rem. centre in 4 in m3 0 0 0 0 182000 227000 272000 319000 364000 410000 455000 Capacity at rem. centre in 5 in m3 0 0 0 0 178000 228000 273000 316000 225000 258000 280000 Sum of rem. components 0 0 0 0 72128 90708 108754 126786 131294 148198 163976 Sum of disp. ret. products 0 18512 37024 55536 22528 27768 33390 39022 54314 60751 67993 Solution times in seconds 33 2530 2211 1739 2486 1368 1833 1641 8634 418270 431468 Total cost in MU 18266248 18482777 18792549 19008088 19274525 19346947 19417848 19581710 20991910 21149822 21214104 Return Rate Interrupted at:* 0,09% ** 0,22% ***0,19% Fig. 14 Variation of return rate with c ¼30; 8r 2 R varied. Therefore, the FLCAPPR model is solved with c ¼ components, for these return rates the total cost increase in 30; 8r 2 R and for return rates from 0 to 1, increasing in the study with c ¼30 is smaller than for the study with steps of 0.1. The respective total discounted costs of the c ¼ 0 where no remanufacturing takes place, see Fig. 15. resulting network and selected decision variable values for For 0:4 q 0:7, it is cost-optimal to ship returned kps the results can be seen in Fig. 14. products from the DCC in Berlin to the remanufacturing The total discounted costs increase with the return rate, centre in Berlin. The remanufactured components are used like in the study with c ¼ 0; 8r 2 R. However, for c ¼ r r in the product assembly in the plant in Berlin. The network 30; 8r 2 R the cost increase for 0:4 q 1 is slightly for these return rates was shown already in Fig. 5. kps smaller, see Fig. 15. As can be seen in Fig. 14, the capacity level at the At return rates q \0:4, every returned product is remanufacturing centre increases with the return rate, i.e. kps with the quantity of returned products. Over the planning disposed and the network consists of a DCC and plant in periods the capacity levels at the remanufacturing centre Berlin, as in the solution of the initial example. Unlike in can change, too. This happens when returned products are the study with c ¼ 0, with c ¼30 an increase of the r r stored and remanufactured in a later period, instead of return rate has an impact on the decision to open a being remanufactured immediately. remanufacturing centre and to remanufacture components. t t The capacity levels at the DCC increase with the return For values of q ¼ 0:4to q ¼ 1, a remanufacturing kps kps rate, too. At q ¼fg 0:8; 0:9; 1 two DCCs, a DCC in kps centre in Berlin is opened in the second period which stays Berlin and Dortmund, have to be opened to have enough open over the remaining planning periods. For these return capacity for the returned products, as in the study with rates, the respective maximal possible amount of compo- c ¼ 0. The opening costs for the second DCC cause the nents is remanufactured and used in the product assembly r jump in the total costs, see Fig. 15. The location of the instead of procured components. Because remanufactured remanufacturing centre and the plant stays at Berlin. components are cheaper production inputs than procured This analysis has shown that opening a remanufacturing centre and using remanufactured components in the pro- duct assembly is cost-optimal under speciﬁc remanufac- turing costs and only if the return rate is high enough, t t 1000000 q 0:4. Moreover, high return rates, q ¼fg 0:8; 0:9; 1 , kps kps inﬂuence the network design and the distribution system, whether remanufacturing is cost-optimal or not. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5.2.3 Inﬂuence of the number of planning periods Return rate Cost increase with cr = -30 Cost increase with cr = 0 In contrast to previous facility location models with reverse product ﬂows the FLCAPPR model optimizes the CLSCN Fig. 15 Cost increase by variation of return rate with c ¼ 0; 8r 2 R over multiple periods instead of a single period. A period is and c ¼30; 8r 2 R MU Logist. Res. (2016) 9:24 Page 21 of 23 24 assumed as one year, and the length of the planning hori- planning periods, too. Hence, the total discounted costs grow zon can be interpreted as the product life-cycle. In the when the planning periods are increased, see Fig. 16. initial example the CLSCN is planned over 5 periods. In It is examined if the length of the planning horizon does this section, the impact of the length of the planning not inﬂuence the network design and the production and horizon on the network is studied; therefore, the number of stored quantities in the network, if remanufacturing is cost- periods is varied. optimal. Therefore, the FLCAPPR model is solved with The total discounted costs, the satisﬁed product demand c ¼30; 8r 2 R for planning horizons of 2–7 periods. and the disposed returned products over a planning horizon The total discounted costs and selected interesting decision of 2–7 periods are listed in Fig. 16. variables are mapped in Fig. 17. It is assumed that demand and return rate remain the Increasing the planning horizon to six and seven periods same over the planning horizon. The structure of the results in the same network as in the solution with 5 solution of the initial example remains optimal, i.e. the periods, which was already described above. In this solu- network stays the same for an increased number of periods tion, remanufacturing takes place at an open remanufac- in the planning horizon. Especially, the decision to procure turing centre in Berlin, see Fig. 5. the components for the product assembly instead of Decreasing the planning horizon of 5 periods by just one remanufacturing components stays the same for the dif- period, to 4 periods, changes the network design. Now, it is ferent length of the planning horizon under this data cost-optimal to procure every component for the product setting. assembly from the supplier in Berlin instead of remanu- The capacity costs and the costs for open facilities rise when facturing components. The resulting network is as in the the number of periods is increased. Moreover, since products solution of the initial example, where only a DCC and plant and components have to be transported, processed and pro- in Berlin are opened and both stay open over the planning cured, respectively, these costs increase with the number of horizon. 30000000 350000 0 0 2 3 4 5 6 7 Total satisfied product demand 92560 138840 185120 231400 277680 323960 Total disposed returned products 23140 46280 69420 92560 115700 138840 Solution times in seconds 700 340 493 198 343 846 Total cost in MU 12320122 14748845 17153521 19534389 21891684 24225639 Number of planning periods Fig. 16 Variation of planning horizon length with c ¼ 0; 8r 2 R 25000000 350000 0 0 23 456 7 Total satisfied product demand 92560 138840 185120 231400 277680 323960 Total disposed returned products 23140 46280 69420 27768 34808 41838 Solution times in seconds 10 646 729 1368 20529 4341 Total rem.components used in assembly 0 0 0 90708 113248 135797 Total cost in MU 12320122 14748845 17153521 19346947 21482068 23596497 Number of planning periods Fig. 17 Variation of planning horizon length with c ¼30; 8r 2 R 123 24 Page 22 of 23 Logist. Res. (2016) 9:24 Hence, the number of periods in the planning horizon for lower rates. Therefore, the forward and reverse product has an impact on the network design and the decision to ﬂows in the network have to be planned together. remanufacture. A multi-period planning approach in con- The multi-period setting of the FLCAPPR model trast to a single-period approach, as in , for a CLSCN is enables a study of the inﬂuence of the planning horizon on useful and leads to new and different results. Therefore, the the decision to remanufacture and provides new informa- relevant number of periods has to be determined and the tion compared to single-period FLPs, as in . Product network has to be analysed over this planning horizon. recovery is cost-optimal only if remanufacturing costs are sufﬁciently low compared to procurement costs and the planning horizon is sufﬁciently long. For the studied data 6 Conclusions and future research directions setting, this means that there has to be product demand for at least 5 periods, i.e. ﬁve years; only then remanufacturing In this work, the strategic CLSCN design is extended by can be cost-optimal. capacity and production planning on an aggregate level. Following the CLSC-Management deﬁnition in , a The resulting FLCAPPR model determines the cost-opti- CLSCN has to be studied over the total product life-cycle mal network design, the facility locations and capacity with consideration of varying demand and returned product equipment at open facilities, and the cost-optimal pro- quantities and qualities. Hence, in the future the FLCAPPR curement, production and distribution quantities in the problem should be solved with data sets consisting of CLSCN over a ﬁnite planning horizon consisting of mul- varying demand and returned product quantities in order to tiple periods. It is solved for an example from the copier study possible product life-cycle effects. industry with input data based on previously published Moreover, when residence times are longer than one research . Furthermore, possible effects of the extended period, the reverse product ﬂow starts later in the planning planning approach on the network design, especially on the horizon. This can affect decisions regarding the facility decision to recover returned products, are studied in a locations and capacity equipment and, therefore, the sensitivity analysis. Thereafter, the robustness of the net- remanufacturing decision. Hence, different assumptions work design and the production and distribution quantities regarding the residence times of products should be regarding the return rate, i.e. the quantity of returned examined in the future. products, is examined. In a further study the inﬂuence of Linear costs and revenues for adjusting capacity are the planning horizon length is investigated. assumed here, and the effects of economies of scale and Extending a single-period FLP to the FLCAPPR model learning effects gained by higher production quantities and leads to new and different results concerning the decision bigger facilities are not considered. Furthermore, the pos- sibilities to increase or decrease labour hours at facilities by to remanufacture and the effect of the return rate on the network. In contrast to a previous study , in this setting, overtime or part-time, respectively, is not modelled. These it is cost-optimal to dispose returned products instead of aspects require further model extensions, but it has to be recovering them and use the resulting components in the noted that the FLCAPPR model is already large scale with product assembly based on the FLCAPPR model. When rather lengthy solving times. capacity costs, especially labour hour costs at the reman- Finally, uncertainties regarding the quantity and quality ufacturing centre, are included, remanufacturing is cost- of reverse product ﬂows are an issue of CLSCM [11–13]. optimal only if the remanufacturing costs are sufﬁciently They are not considered here, because an APP framework low compared to the procurement costs for new compo- is used. However, other approaches integrating uncertain- nents from suppliers. Hence, production costs, in particular ties might be developed; this is left for future research. remanufacturing costs, have a large impact on facility Open Access This article is distributed under the terms of the location and capacity equipment decisions. Furthermore, Creative Commons Attribution 4.0 International License (http://crea the interdependence between the capacity equipment at the tivecommons.org/licenses/by/4.0/), which permits unrestricted use, remanufacturing centre and the procuring decision, the distribution, and reproduction in any medium, provided you give processing and storing quantities at the remanufacturing appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were centre is determined. Hence, these decisions have to be made. optimized jointly, as in the FLCAPPR model. The decisions regarding facility locations and capacity equipment are robust for low return rates. From return rates References of 40% remanufacturing takes place, if remanufacturing costs are sufﬁciently low. Moreover, for high return rates, 1. 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