Access the full text.
Sign up today, get DeepDyve free for 14 days.
J. Arkat, M. Farahani, F. Ahmadizar (2012)
Multi-objective genetic algorithm for cell formation problem considering cellular layout and operations schedulingInternational Journal of Computer Integrated Manufacturing, 25
M. Jiménez, M. Parra, A. Bilbao-Terol, Maria Rodríguez (2007)
Linear programming with fuzzy parameters: An interactive method resolutionEur. J. Oper. Res., 177
M. Hajiaghaei-Keshteli, A. Fard (2018)
A set of efficient heuristics and metaheuristics to solve a two-stage stochastic bi-level decision-making model for the distribution network problemComput. Ind. Eng., 123
Xu Liu, Guangdong Tian, A. Fathollahi-Fard, M. Mojtahedi (2020)
Evaluation of ship’s green degree using a novel hybrid approach combining group fuzzy entropy and cloud technique for the order of preference by similarity to the ideal solution theoryClean Technologies and Environmental Policy, 22
M. Paydar, M. Saidi‐Mehrabad (2015)
Revised multi-choice goal programming for integrated supply chain design and dynamic virtual cell formation with fuzzy parametersInternational Journal of Computer Integrated Manufacturing, 28
A. Fard, M. Hajiaghaei-Keshteli, Guangdong Tian, Zhiwu Li (2020)
An adaptive Lagrangian relaxation-based algorithm for a coordinated water supply and wastewater collection network design problemInf. Sci., 512
Behrang Bootaki, I. Mahdavi, M. Paydar (2014)
A hybrid GA-AUGMECON method to solve a cubic cell formation problem considering different worker skillsComput. Ind. Eng., 75
Soraya Bahadori-Chinibelagh, A. Fathollahi-Fard, Mostafa Hajiaghaei-Keshteli (2019)
Two Constructive Algorithms to Address a Multi-Depot Home Healthcare Routing ProblemIETE Journal of Research, 68
S. Benjaafar (2002)
Modeling and Analysis of Congestion in the Design of Facility LayoutsManag. Sci., 48
A. Fard, M. Hajiaghaei-Keshteli, S. Mirjalili (2018)
Multi-objective stochastic closed-loop supply chain network design with social considerationsAppl. Soft Comput., 71
Aidin Delgoshaei, Ahad Ali, M. Ariffin, C. Gomes (2016)
A multi-period scheduling of dynamic cellular manufacturing systems in the presence of cost uncertaintyComput. Ind. Eng., 100
(2013)
Keshtel algorithm (KA); a new optimization algorithm inspired by Keshtels
(1987)
A successful implementation of group technology and cell manufacturing, 28
K. Forghani, M. Mohammadi, V. Ghezavati (2015)
Integrated cell formation and layout problem considering multi-row machine arrangement and continuous cell layout with aisle distanceThe International Journal of Advanced Manufacturing Technology, 78
K. Deep, Pardeep Singh (2016)
Dynamic cellular manufacturing system design considering alternative routing and part operation tradeoff using simulated annealing based genetic algorithmSādhanā, 41
Ming-Ying Chen (1998)
A mathematical programming model for system reconfiguration in a dynamic cellular manufacturing environmentAnnals of Operations Research, 77
Biao Zhang, Q. Pan, Liang Gao, Xinyu Li, Lei-lei Meng, Kunkun Peng (2019)
A multiobjective evolutionary algorithm based on decomposition for hybrid flowshop green scheduling problemComput. Ind. Eng., 136
J. Schaller (2007)
Designing and redesigning cellular manufacturing systems to handle demand changesComput. Ind. Eng., 53
A. Samadi, N. Mehranfar, A. Fard, M. Hajiaghaei-Keshteli (2018)
Heuristic-based metaheuristics to address a sustainable supply chain network design problemJournal of Industrial and Production Engineering, 35
D. Montgomery (1985)
Introduction to Statistical Quality Control
F. Chan, K. Lau, L. Chan, V. Lo (2008)
Cell formation problem with consideration of both intracellular and intercellular movementsInternational Journal of Production Research, 46
Shine-Der Lee, Chih-Ping Chiang (2001)
A cut-tree-based approach for clustering machine cells in the bidirectional linear flow layoutInternational Journal of Production Research, 39
Chin-Chih Chang, Tai-Hsi Wu, Chien-Wei Wu (2013)
An efficient approach to determine cell formation, cell layout and intracellular machine sequence in cellular manufacturing systemsComput. Ind. Eng., 66
A. Greasley (2019)
Facility designAbsolute Essentials of Operations Management
J. Balakrishnan, C. Cheng (2009)
The dynamic plant layout problem : Incorporating rolling horizons and forecast uncertaintyOmega-international Journal of Management Science, 37
Tamal Ghosh, B. Doloi, P. Dan (2016)
An Immune Genetic algorithm for inter-cell layout problem in cellular manufacturing systemProduction Engineering, 10
A. Fard, M. Ranjbar-Bourani, N. Cheikhrouhou, M. Hajiaghaei-Keshteli (2019)
Novel modifications of social engineering optimizer to solve a truck scheduling problem in a cross-docking systemComput. Ind. Eng., 137
K. Rafiee, M. Rabbani, H. Rafiei, A. Rahimi-Vahed (2011)
A NEW APPROACH TOWARDS INTEGRATED CELL FORMATION AND INVENTORY LOT SIZING IN AN UNRELIABLE CELLULAR MANUFACTURING SYSTEMApplied Mathematical Modelling, 35
M. Bagheri, M. Bashiri (2014)
A new mathematical model towards the integration of cell formation with operator assignment and inter-cell layout problems in a dynamic environmentApplied Mathematical Modelling, 38
F. Jolai, R. Tavakkoli-Moghaddam, A. Golmohammadi, B. Javadi (2012)
An Electromagnetism-like algorithm for cell formation and layout problemExpert Syst. Appl., 39
I. Mahdavi, E. Teymourian, Nima Baher, V. Kayvanfar (2013)
An integrated model for solving cell formation and cell layout problem simultaneously considering new situationsJournal of Manufacturing Systems, 32
I. Mahdavi, B. Mahadevan (2008)
CLASS: An algorithm for cellular manufacturing system and layout design using sequence dataRobotics and Computer-integrated Manufacturing, 24
A. Fathollahi-Fard, M. Hajiaghaei-Keshteli, S. Mirjalili (2019)
A set of efficient heuristics for a home healthcare problemNeural Computing and Applications, 32
M. Hajiaghaei-Keshteli, K. Abdallah, A. Fathollahi-Fard (2018)
A Collaborative Stochastic Closed-loop Supply Chain Network Design for Tire IndustryInternational Journal of Engineering
A. Zohrevand, H. Rafiei, A. Zohrevand (2016)
Multi-objective dynamic cell formation problem: A stochastic programming approachComput. Ind. Eng., 98
M. Leung, R. Quintana, An-Sing Chen (2008)
A paradigm for Group Technology cellular layout planning in JIT facility2008 IEEE International Conference on Industrial Engineering and Engineering Management
A. Fathollahi-Fard, K. Govindan, M. Hajiaghaei-Keshteli, Abbas Ahmadi (2019)
A green home health care supply chain: New modified simulated annealing algorithmsJournal of Cleaner Production, 240
D. Goldberg (1988)
Genetic Algorithms in Search Optimization and Machine Learning
N. Safaei, R. Tavakkoli-Moghaddam (2009)
Integrated multi-period cell formation and subcontracting production planning in dynamic cellular manufacturing systemsInternational Journal of Production Economics, 120
(2009)
Integrated cellular manufacturing systems design with production planning and dynamic system reconfiguration, 192
K. Krishnan, S. Mirzaei, Vijayaragavan Venkatasamy, V. Pillai (2012)
A comprehensive approach to facility layout design and cell formationThe International Journal of Advanced Manufacturing Technology, 59
Elin Wicks, Roderick Reasor (1999)
Designing cellular manufacturing systems with dynamic part populationsIIE Transactions, 31
Yaping Fu, Guangdong Tian, A. Fathollahi-Fard, Abbas Ahmadi, Chaoyong Zhang (2019)
Stochastic multi-objective modelling and optimization of an energy-conscious distributed permutation flow shop scheduling problem with the total tardiness constraintJournal of Cleaner Production
Grammatoula Papaioannou, John Wilson (2010)
The evolution of cell formation problem methodologies based on recent studies (1997-2008): Review and directions for future researchEur. J. Oper. Res., 206
J. Balakrishnan, C. Cheng (2007)
Multi-period planning and uncertainty issues in cellular manufacturing: A review and future directionsEur. J. Oper. Res., 177
Xiaoqing Wang, Jiafu Tang, K. Yung (2009)
Optimization of the multi-objective dynamic cell formation problem using a scatter search approachThe International Journal of Advanced Manufacturing Technology, 44
M. Hassan (1995)
Layout design in group technology manufacturingInternational Journal of Production Economics, 38
Xiaodan Wu, Chao-Hsien Chu, Yunfeng Wang, Weili Yan (2007)
Production , Manufacturing and Logistics A genetic algorithm for cellular manufacturing design and layout
Z. Afrouzy, S. Nasseri, I. Mahdavi, M. Paydar (2016)
A fuzzy stochastic multi-objective optimization model to configure a supply chain considering new product developmentApplied Mathematical Modelling, 40
M. Mohammadi, K. Forghani (2016)
Designing cellular manufacturing systems considering S-shaped layoutComput. Ind. Eng., 98
(2016)
Red Deer algorithm (RDA); a new optimization algorithm inspired by Red Deers’ mating. In: International Conference on Industrial Engineering, 2016
A. Fard, M. Hajiaghaei-Keshteli, R. Tavakkoli-Moghaddam (2018)
The Social Engineering Optimizer (SEO)Eng. Appl. Artif. Intell., 72
R. Kia, A. Baboli, N. Javadian, R. Tavakkoli-Moghaddam, M. Kazemi, Javad Khorrami (2012)
Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealingComput. Oper. Res., 39
Mostafa Moradgholi, M. Paydar, I. Mahdavi, J. Jouzdani (2016)
A genetic algorithm for a bi-objective mathematical model for dynamic virtual cell formation problemJournal of Industrial Engineering International, 12
M. Mohammadi, K. Forghani (2014)
A novel approach for considering layout problem in cellular manufacturing systems with alternative processing routings and subcontracting approachApplied Mathematical Modelling, 38
M. Rheault, J. Drolet, G. Abdul-Nour (1995)
Physically reconfigurable virtual cells: a dynamic model for a highly dynamic environment, 29
I. Mahdavi, M. Paydar, M. Solimanpur, Armaghan Heidarzade (2009)
Genetic algorithm approach for solving a cell formation problem in cellular manufacturingExpert Syst. Appl., 36
Steve kioon, A. Bulgak, T. Bektaş (2009)
Production, Manufacturing and LogisticsIntegrated cellular manufacturing systems design with production planning and dynamic system reconfigurationEuropean Journal of Operational Research, 192
Aidin Delgoshaei, M. Ariffin, Z. Leman, B. Baharudin, C. Gomes (2016)
Review of evolution of cellular manufacturing system’s approaches: Material transferring modelsInternational Journal of Precision Engineering and Manufacturing, 17
M. Yadollahi, I. Mahdavi, M. Paydar, J. Jouzdani (2014)
Design a bi-objective mathematical model for cellular manufacturing systems considering variable failure rate of machinesInternational Journal of Production Research, 52
Shima Golmohamadi, R. Tavakkoli-Moghaddam, M. Hajiaghaei-Keshteli (2017)
Solving a fuzzy fixed charge solid transportation problem using batch transferring by new approaches in meta-heuristicElectron. Notes Discret. Math., 58
(2013)
Keshtel algorithm (KA); a new optimization algorithm inspired by Keshtels’ feeding
J. Drolet, Y. Marcoux, G. Abdulnour (2008)
Simulation-based performance comparison between dynamic cells, classical cells and job shops: a case studyInternational Journal of Production Research, 46
A. Fathollahi-Fard, M. Hajiaghaei-Keshteli, R. Tavakkoli-Moghaddam (2018)
A bi-objective green home health care routing problemJournal of Cleaner Production
R. Tavakkoli-Moghaddam, N. Javadian, B. Javadi, N. Safaei (2007)
Design of a facility layout problem in cellular manufacturing systems with stochastic demandsAppl. Math. Comput., 184
A. Fard, M. Hajiaghaei-Keshteli, R. Tavakkoli-Moghaddam (2020)
Red deer algorithm (RDA): a new nature-inspired meta-heuristicSoft Computing, 24
N. Safaei, M. Saidi‐Mehrabad, M. Jabalameli (2008)
A hybrid simulated annealing for solving an extended model of dynamic cellular manufacturing systemEur. J. Oper. Res., 185
R. Tavakkoli-Moghaddam, N. Javadian, A. Khorrami, Y. Gholipour-Kanani (2010)
Design of a scatter search method for a novel multi-criteria group scheduling problem in a cellular manufacturing systemExpert Syst. Appl., 37
(1987)
A successful implementation of group technology and cell manufacturing. Prod Inventory Manage
Behrang Bootaki, I. Mahdavi, M. Paydar (2015)
New bi-objective robust design-based utilisation towards dynamic cell formation problem with fuzzy random demandsInternational Journal of Computer Integrated Manufacturing, 28
Zahra Afrouzy, M. Paydar, S. Nasseri, I. Mahdavi (2018)
A meta-heuristic approach supported by NSGA-II for the design and plan of supply chain networks considering new product developmentJournal of Industrial Engineering International, 14
F. Chan, K. Lau, P. Chan, K. Choy (2006)
Two-stage approach for machine-part grouping and cell layout problemsRobotics and Computer-integrated Manufacturing, 22
Hüsamettin Bayram, R. Sahin (2016)
A comprehensive mathematical model for dynamic cellular manufacturing system design and Linear Programming embedded hybrid solution techniquesComput. Ind. Eng., 91
FUZZY INFORMATION AND ENGINEERING 2020, VOL. 12, NO. 2, 204–222 https://doi.org/10.1080/16168658.2020.1747162 A bi-objective Optimization Model for a Dynamic Cell Formation Integrated with Machine and Cell Layouts in a Fuzzy Environment a a a Amir-Mohammad Golmohammadi , Mahnoobeh Honarvar , Hassan Hosseini-Nasab and Reza Tavakkoli-Moghaddam a b Department of Industrial Engineering, Yazd University, Yazd, Iran; School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran ABSTRACT ARTICLE HISTORY Received 28 March 2019 In this paper, a bi-objective optimization model is developed to inte- Revised 31 December 2019 grate the cell formation and inter/intra-cell layouts in continuous Accepted 15 January 2020 space by considering fuzzy conditions to minimize the total cost of parts relocations as well as cells reconfigurations. The intra- and inter- KEYWORDS cell movements for both parts and machines using batch sizes for Cellular manufacturing transferring parts are related to the distance traveled through a rec- system; cell formation; tilinear distance in a fuzzy environment. To solve the proposed prob- inter/intra-cell layout; Pareto-based algorithms; lem as a bi-objective mixed-integer non-linear programming model hybrid meta-heuristic is NP-hard, four meta-heuristic algorithms based on a multi-objective algorithm optimization structure are tackled to address the problem. In this regard, not only Genetic Algorithm (GA), Keshtel Algorithm (KA) and Red Deer Algorithm (RDA) are employed to solve the problem, but also a novel hybrid meta-heuristic algorithm based on the benefits of aforementioned algorithms is developed. Finally, by considering some efficient assessment metrics of Pareto-based algorithms, the results indicate that the proposed hybrid algorithm not only is more appropriate than the exact solver but it also outperforms the per- formance of individual ones particularly in medium- and large-sized problems. 1. Introduction and Literature Review The facility design is a significant requirement in the field of manufacturing systems engi- neering. Approximately, $250 billion is spent annually in the U.S for the facility designing, planning, and re-planning [1–3]. Also, it is estimated that around 20–50% of the total cost of manufacturing systems is attributed to material handling. The same source also reports that effective planning can reduce such costs by over 10–30% [4–7]. Minimizing material movements may be among the initial reasons for developing a Cellular Manufacturing Sys- tem (CMS) [5–8]. In general, the CMS based on Group Technology (GT) is an approach to apply the advantages of both flexible and mass production properties. The main role of the CMS is to assign a number of parts and machines to each other to produce some cells on the CONTACT Mahnoobeh Honarvar mhonarvar@yazd.ac.ir © 2020 The Author(s). Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. FUZZY INFORMATION AND ENGINEERING 205 basis of their similarities in the production process, design and geometrical characteristics comprehensively [1,7–9]. Recent decades have seen a great deal of interest in employing different applications of CMSs. There are numerous advantages of using the CMS included but not limited to reduce the material transferring cost, the setup time, the delivery time, the lot size and the amount of the Work-In-Process (WIP) inventory. Another main benefit is to better cause the supervisory control and the improvement of the product quality and productivity [9–11]. These benefits can be accrued only if a cell configuration and a scheduling system of a CMS are effectively designed. One of the crucial steps in designing a CMS is the Cell Formation (CF) problem as a well-known work extensively studied in the literature [10–13]. Given a definition of a CF, it involves two fundamental tasks (i.e. part-family formation and machine- cell formation) to minimize some objectives, such as the inter- and intra-cell movements. As indicated by these factors, the Exceptional Elements (EEs) are a common issue in a CMS of manufacturing environments recognized as the major obstacle in the cell formation and its scheduling processes [12–15]. An EE can be defined generally as a product that needs to be produced in more than one cell and causes inter-cell transfer of materials. In conclusion, a well-known objective in a CF problem is to minimize the number of EEs. There are also other common objectives involving the minimization of the inter-cell material handling cost as well as the materials flow. The facility layout is also a key element in designing a CMS considering the layout of machines within cells (intra-cell layout) and the layout of cells (inter-cell Layout) on the shop floor. An efficient facility layout can reduce the material handling cost, work-in-process, and throughput rate [13–17]. A competent layout not only enhances the system performance but also minimizes around 40–50% of the production costs on average [16–19]. Although minimizing the number of EEs or other common objectives (e.g. minimization of inter-cell movement cost) may reduce flows between cells, they do not necessarily lead to a minimum of the material handling cost since the real parameters related to the facility layout problem are ignored in the calculation of these objectives. Hence, incorporating the facility layout problem in the CMS design process is of high significance. However, the layout design in a CMS has not paid much attention since most of the relevant research only investigates the CFP [20–24]. As stated in Alfa et al. [2], facility layout and CF decisions are interrelated and tellingly addressing them simultaneously is important for the successful CMS design. How- ever, each of these decisions is proven to be complex [21–25]. As a result, the simultaneous addressing of these decisions is a difficult issue. There are some new trends (e.g. the reliability of CMS) in recent studies. Most of them either investigate some of these decisions or handle all of them, but in a sequential fashion [24–28]. On the other hand, a majority of approaches in the area of facility layout and CF problems to ease of making mathematical formulation usually consider the minimization of the number of inter- or intra-cell movements or both [26–29]. Accordingly, to minimize the material handling cost, the exact information about the facility layout design in addition to the notion of distance must be considered. Moreover, those approaches that aim at mini- mizing the material handling cost usually apply unrealistic assumptions, such as the fixed cells and machines locations in the layout problem. Based on this drawback, the layout may be inefficient. As such, for locating the machines in the manufacturing cell space, the line formed locations are the only consideration and the machines are assigned to these posi- tions in the majority of previous studies. As it may be evident, if assigning the number of 206 A.-M. GOLMOHAMMADI ET AL. machines to a cell cannot be a line formed, it turns into a U-form imposing additional costs to the system [29–35]. Considering different real-life constraints and practical assumptions make the model difficult to solve. Due to decisions of the proposed system as a type of tactical and oper- ational levels, the computational cost is very important for the decision-makers of a CMS to be less. Therefore, efficient solution algorithms are needed to address this dilemma. Meta- heuristics are the popular feasible alternatives to solve this complicated problem form the literature [33–39]. As one of the NP-hard problems, this chance even with low possibil- ity always exists for a new meta-heuristic algorithm to better solve such a complicated model to get a near-optimal solution in less time [35–40]. This reason motivates several researchers to employ different types of meta-heuristics in this research area [37–43]. To cover the limitations of several meta-heuristics employed in the literature, this study not only uses Genetic Algorithm (GA) [27] as a well-known in the field and two recent meta- heuristics, namely, Red Deer Algorithm (RDA) [18] and Keshtel Algorithm (KA) [29] but also develops a new hybrid meta-heuristic algorithm to consider the benefits of these individual algorithms. Given a general view of other sections of this paper, its remaining is structured as fol- lows. Problem definition and formulation is discussed in Section 2. The proposed solution approaches including GA, RDA, KA and the developed hybrid meta-heuristic algorithm are given in Section 3. Computational results and analyses of the algorithms are explored in Section 4. Finally, concluding remarks and future research directions are provided in Section 5. 2. Proposed Model The aim of this model is to determine concurrently the formation of cells, the layout of machines inside cells and the layout of cells on the shop floor in dynamic conditions in a way that the total transportation cost of parts and reconfiguration cost of cells and the number of EES are minimized. The proposed mixed-integer non-linear programming model with a number of assumptions, parameters, and decision variables are discussed below. 2.1. Assumptions • The flow between machines in each period is determined. This number is obtained from the parts demand and parts operational paths as well as the batch size of parts transportation. • The parts are moved within the batches, in which the largeness of the batches per prod- uct is known and constant for all periods. In addition, the size of the part batches is assumed the same for both inter and intra-cell relocations. • The material handling cost is calculated according to center-to-center distance between machines through a rectilinear distance. • The material handling cost of inter and intra-cell movements for both parts and machines is related to the distance traveled. • The unit cost of inter and intra-cell movements for each part type is predetermined and remain the same planning horizon. • The unit cost of machine relocation during the periods is constant and predetermined for each machine type. This cost includes opening, transferring, and resetting the machine. FUZZY INFORMATION AND ENGINEERING 207 • The number of cells to be formed in each period is determined in advance. This predeter- minednumberofcellsinthesystemisonthebasisoftheexpectedworkloadineachcell. However, the shape of the cells is not predetermined and cells are flexibly configured during the planning horizon. • There is only one number of each machine type. • The maximum capacity of cells is known and remains the same planning horizon. • Machines are considered as squares of equal area and hence supposed to have a unit dimension. It is examined that the proposed considerations provide a suitable approxi- mation to the real-world conditions where machines are not exact squares or rectangles [41–47]. The cells are considered in a rectangular shape. • There is no excess inventory between the periods, delayed orders are not allowed and demands per period must be supplied in that period. • The efficiency of machines and production is assumed to be 100%. In the following section, the sets, parameters and decision variables of the proposed model are presented. It should be noted that the tilde sign ( ∼ ) is utilized for fuzzy parameters as one of the main innovations of this study in this field. Sets: i, i ={1, 2, ... , m} Index set of machines j ={1, 2, ... , n} Index of parts l, k, k ={1, 2, ... , c} Index set of cells h ={1, 2, ... ,, H} Index set for time periods Parameters: D Demand for part type j in period h jh B Largeness of batch for the transportation of part type j C Intra-cell material handling cost for transporting part j per unit distance ($/unit) intra C Inter-cell material handling cost for transporting part j per unit distance ($/unit) inter C Relocation cost of machine i($/unit) R Operation number done on part j using machine i ij E Horizontal length of the shop floor (i.e. length of the shop floor) F Vertical length of the job shop (the width of the shop floor) SP Set of pairs (i, j) such that a ≥ 1 (the set of non-zero elements of a part-machine ij matrix) NM Maximum number of machines relocated in each cell per period. N Appropriate large positive number A , B Zero and one random variables kl kl A , B Zero and one random variables ii h ii h f Number of trips for moving part type j between machines i and i in period h ii h [D /B ] if R − R = 1 j j ij jh i j f = (1) ii h 0 if R − R = 1 ij i j 208 A.-M. GOLMOHAMMADI ET AL. Decision variables: X = If machine i is assigned to cell k in period h ikh Otherwise Y = If part j is assigned to cell k in period h jkh Otherwise Z = If machine i relocates during periods h and (h + 1) ih Otherwise U = If Y = 0and X = 1 ijkh jkh ikh Otherwise V = If Y = 1and X = 0 ijkh jkh ikh Otherwise x Horizontal coordinate of the center of machine i in period h ih y Vertical coordinate of the center of machine i in period h ih p Horizontal coordinate of the left side of cell k in period h kh p Horizontal coordinate of the right side of cell k in period h kh q Vertical coordinate of the bottom side of cell k in period h kh q Vertical coordinate of the top side of cell k in period h kh Therefore, the relocation cost of part j between machines i and i in period h, regarding inter-cell or intra-cell movement can be determined below: If X , X > 0, this cost equals to Equation (2) as follows: ikh i kh j j C = (|x − x |+|y − y |)C (2) ih i h ih i h ii h intra If X .X = 0andX .X > 0, this cost equals to Equation (3) as follows: ikh i kh ikh i k h j j C = (|x − x |+|y − y |)C (3) ih i h ih i h ii h inter 2.2. Mathematical Formulation With respect to input parameters and variables, the presented nonlinear model for this problem is as follows: H n m m H m j j Min f C + C Z (4) i ih ii h ii h h=1 j=1 i=1 i =1 h=2 i=1 FUZZY INFORMATION AND ENGINEERING 209 H C (U + V ) ijk ijk Min (5) h=1 k=1 (i,j)∈sp s.t. X = 1, i = 1, 2, ... , m, ∀h (6) ikh k=1 Y = 1, j = 1, 2, ... , n, ∀h (7) jkh k=1 1 ≤ X ≤ NM, k = 1, 2, ... , C, ∀h (8) ikh i=1 NZ ≥|x − x |+|y − y |∀i, h < H.(9) ih ih i(h+1) ih i(h+1) |x − x |+|y − y |≥ 1 (10) ih i h ih i h x ≥ p − N(1 − X ) ⎪ ih ikh kh x ≤ p + N(1 − X ) ih ikh kh ∀i, k, h (11) ⎪ y ≥ q − N(1 − X ) ih ikh kh y ≤ q + N(1 − X ) ih ikh kh p ≥ 0 kh q ≥ 0 kh ∀k, h (12) ⎪ p ≤ E kh q ≤ F kh 1 2 p − p + NA + NB ≥ 0 kl kl kh lh 2 1 p − p − NA − N(1 − B ) ≤ 0 ⎨ kl kl kh lh 1 2 q − q + N(1 − A ) + NB ≥ 0 (13) kl kl kh lh ⎪ 2 1 ⎪ q − q − N(1 − A ) − N(1 − B ) ≤ 0 kl kl kh lh 0 ≤ k < l ≤ C X , Y , Z , U , V = 0 or 1 (14) ikh jkh ih ijkh ijkh 1 2 1 2 x , y , p , p , q , q ≥ 0 and Integer (15) ih ih kh kh kh kh The first objective function represents the intra- and inter-cellular material transferring costs. The following term denotes the cells reconfiguration cost that may vary from period to period. The second objective function correlates with minimizing the number of excep- tional parts. The coefficient of 1\2 in this relationship is due to the double calculation of decision variables when there are equal to 1. Constraint (6) guarantees that each machine allocated to only one cell. Constraint (7) shows that each part is allocated to a part family. The number of machines in a single cell is limited by Constraint (8). Constraint (9) shows that by relocating machine type i during periods h and (h + 1), variable Z equals 1. Constraint ih 210 A.-M. GOLMOHAMMADI ET AL. (10) according to the machine dimension is assumed to be 1×1, causes the machines do not overlap. Constraint (11) makes that each machine will be inside its corresponding cell space. Constraint (12) shows that the cells are placed inside the job shop space. Constraint (13) shows that the cells do not overlap. Constraints (14) and (15) determine the type of problem variables. 2.3. Proposed Fuzzy Circumstances In this section, the mathematical model presented in this paper is a mixed-integer program- ming model. Since an inevitable factor is inevitable in the real world of uncertainty, most of the parameters used are considered triangular fuzzy numbers because of their uncertain nature. In general, the fuzzy programming problem must first be transformed into a defi- nite equivalent problem and then solved with standard methods and the optimal answer is obtained. As a result, the final solution to the problem is obtained with respect to the fuzzy structure of the problem. In the following section, a two-step approach is used to solve the model. In the first step, the proposed model with fuzzy parameters is transformed into a certain auxiliary model by a method proposed by Khimens et al. [48]. In the second stage, we solve the multi- objective certain model by using the Torabi-Hosseini method [49], which was obtained in the first stage. Khimens et al. [48] presented a method for ranking fuzzy numbers. In this method, defining the fuzzy parameters of the objective functions is calculated based on the concepts of the expected distance and the expected value for triangular fuzzy numbers p m o C = (C , C , C ) based on the following relations. 1 1 1 c c −1 −1 m p p ∫ ∫ ∫ EI(C) = [E , E ] = f (x)d , g (x)d = (x(c − c ) + c )d x x x 1 1 c c 0 0 0 1 1 o m o p m m o = ∫(x(c − c ) + c )d = (c + c ), (c + c ) (16) 2 2 c c p m o E + E c + 2c + c 1 1 EV(C) = = (17) 2 4 Based on Khaminz’s method, we consider Equation (19) for Constraint (a ˜ X ≥ b ; i = i i 1, 2, ... , I). p p o m m o m m a + a a + a b + b b + b i i i i i i i i α + (1 − α). X ≥ α + (1 − α). (18) 2 2 2 2 For equal constraints (a ˜ X = b ; i = 1, 2, ... , I), we convert into the certain equivalent con- i i straints as represented by: p p o m m o m m α a + a α a + a α b + b α b + b i i i i i i i i . + 1 − . X ≥ . + 1 − . (19) 2 2 2 2 2 2 2 2 p p o m m o m m α a + a α a + a α b + b α b + b i i i i i i i i 1 − . + . X ≥ 1 − . + . (20) 2 2 2 2 2 2 2 2 FUZZY INFORMATION AND ENGINEERING 211 After defuzzifying by the help of Equation (17), the membership function for the minimiza- tion objective function is obtained using Torabi-Hessian’s method of Equation (21). α−PIS ⎪ 1 if Z < Z α−NIS Z − Z α−PIS α−NIS μ = (21) F if Z < Z < Z ⎪ α−NIS α−PIS ⎪ Z − Z α−NIS 0 if Z > Z Then, the membership function for the maximization objective function is obtained by: α−PIS 1 if Z > Z α−NIS Z − Z α−NIS α−PIS μ = (22) F if Z ≤ Z ≤ Z α−PIS α−NIS Z − Z α−NIS 0 if Z > Z where the positive ideal solution (α − PIS) and the negative ideal solution (α − NIS) for each objective function and at the level of feasibility (α). In the following section, we aim to present the proposed solution algorithms for solving the developed model. 3. Proposed Solution Algorithm As stated in [36], the CMS scheduling models are non-polynomial time hard (NP-hard) prob- lems that are difficult to solve using different types of exact methods. In addition to its natural complexity, considering dynamic conditions increase its difficulty and combinato- rial nature. Hence, meta-heuristic approaches should be employed to obtain a satisfying solution in a reasonable time. Several algorithms have been applied in the context of the DCMS design. One of the most popular algorithms is the Genetic Algorithm (GA). This moti- vates us to use the GA in this study based on the previous studies in the literature [50–55]. Due to a No Free Lunch theory, this chance for a new meta-heuristic algorithm always exists to reveal a better output in comparison with other existing algorithms [23]. In regards to this theory, this study employs two recent nature-inspired meta-heuristics including Keshtel Algorithm (KA) and Red Deer Algorithm (RDA) [56, 57]. At last but not least, the main innova- tion of this study is to propose a novel hybrid metaheuristic based on the advantages of the aforementioned algorithms. Here, first of all, due to the proposed multi-objective model, the structure of multi-objective optimization to be used in all algorithms is described. The next is the encoding plan of meta-heuristics and after that, the procedures of the pro- posed hybrid meta-heuristic algorithm are addressed in the following sub-sections. Note that since there is no innovation in the procedures of the GA, KA and RDA, individually, more explanation and details about these three algorithms are referred to their main papers [53–55,58–61]. 3.1. Multi-objective Optimization The proposed problem requires a trade-off between the objectives. In this case, the answer is a set of solutions, called Pareto-optimal solutions set. This set includes Pareto-optimal solutions, which explains the best trade-offs between the objectives. A solution dominates the other solution when it had better than in all objective functions [59–65]. Furthermore, the selection of the best solution in the first front of solutions is considered by calculating 212 A.-M. GOLMOHAMMADI ET AL. Figure 1. General view of the solution representation. Figure 2. Detailed view of solution representation in the first step. the crowding distance between solutions. To get the Pareto-optimal solutions, we set a normal constraint method presented by [21]. 3.2. Solution Representation To show that how the constraints of the model will be handled by the presented solution algorithms, an encoding procedure is used to consider the solution representation in the format of a string-based presentation [64–66]. The solution can be a set of binary and inte- ger numbers, matrices, or the combination of characters [67–69]. These ways are viewed to determine how a problem is formulated in the form of an algorithm and what operators of meta-heuristics are applied. The first step of the proposed encoding procedure includes a matrix with H rows and M columns, which can be divided into the following sub-matrices. • Sub-matrix of Z is related to the assignment of machines for manufacturing cells. This sub-matrix consists of H (i.e. the number of periods) rows and M (i.e. the number of machines) columns. Each element of this matrix is a number between 1 and C (i.e. the number of cells) and element Z represents the number of cells including machine type ih i in period h. • Sub-matrix X is related to the horizontal component of the machines’ location. This sub- matrix also consists of H rows and M columns. With respect to the machines’ dimension (1×1), one integer is sufficient to represent per horizontal and vertical components of the machines. Each element of this matrix is a number between 1 and E (i.e. the length of the job shop) and element x represents the horizontal component of location involving ih machine i in period h. • Sub-matrix Y is related to the vertical component of the machines’ location. This sub- matrix also consists of H rows and M columns. Each element of this matrix is a number between 1 and F (i.e. the width of the job shop) and element y represents the vertical ih component of location involving machine i in period h. Figures 1 and 2 illustrate the general and detailed views of the solution presentation of the algorithms related to the machines alignment for the manufacturing cells, respectively. FUZZY INFORMATION AND ENGINEERING 213 Figure 3. Detailed view of the solution representation in the second step The considered solution for the second step of this problem includes a matrix with H rows and N columns. Its detailed structure related to parts alignment to part families is shown in Figure 3. 3.3. Proposed Novel Hybrid Meta-heuristic Algorithm (H-RDKGA) As indicated from literature, the KA is very good at doing the exploitation action [56,70]. It seems that the swirling process can be done instead of two processes including roaring and fighting in RDA. Accordingly, for each male, the closest neighbor is specified and the swirling action is done. Due to the mating process, the GA mechanism is considered in this regard. Having a brief illustration, the KA is chosen as the intensification properties as well as the GA is measured the diversification phase. This opinion is employed to examine the proposed method with their individual methods and also other feasible alternatives for combinations. Given more details of proposed H-RDKGA, a pseudo-code is provided as seen in Figure 4. 4. Computational Results A comparative study is presented in this section. First of all, to enhance the performance of employed metaheuristics and having a fair comparison, a full factorial design method is applied to tune the algorithms’ parameters properly. After that, an extensive com- parison among meta-heuristics based on different criteria is presented in the following sub-sections. 4.1. Tuning the Meta-heuristics For tuning the parameters of the meta-heuristics, we use the Design of Experiment (DOE) method discussed in Montgomery [46]. The reason why we use this method compared to more efficient calibration techniques is that the method is simple and coarse [51–55,58,59] and hence, the direct impact of the algorithms on the problem solutions can be understood without the presence of a good calibration technique. As given in the solution algorithm, the main parameters under consideration for the GA are the population size, maximum number of iterations, mutation and crossover rates. In the proposed KA, the population size, maximum number of iterations, the percentage of N1 and N2, maximum number of swirling are the key parameters. As such, the main parameters of the RDA are the population size, maximum number of iterations, number of males, and the rate of alpha, beta and gamma. At the last, the proposed parameters of the H-RDKGA are only the population size, maximum number of iterations, the number of males and the maximum number of swirling. We use the full factorial design to evaluate the different sets 214 A.-M. GOLMOHAMMADI ET AL. Figure 4. Pseudo-code of the H-RDKGA. of values considered for conducting the DOE (given in Table 1). These ranges of values are decided based on the parameter settings provided in the literature [59–69]. 4.2. Comparison among Employed Metaheuristics This sub-section aims to probe the effectiveness and efficiency of the presented algorithms. Due to it, each meta-heuristic algorithm is performed in all the test problems for 30 times runs. In this case, the behavior of the algorithms in the two objective functions during 30 run times is considered. The behavior of the algorithms in terms of computational time is presented in Figure 5. As shown in this figure, the behavior of the algorithms is as the same overall. The proposed hybrid algorithm and KA show competitive results in this item. In general, the best algorithm in this criterion is KA. However, the worst behavior can be concluded from the RDA in most of the testes. Finally, the average of outputs is saved and utilized to be evaluated by the assessment metrics of Prato-based algorithms. In this regard, Diversification Metric (DM), Spread of Non- dominance Solutions (SNS), Data Evolvement Analysis (DEA) and Percentage of Dominance (POD) are utilized. In all of them, a higher value brings a better capability of algorithms. The details about the evaluation metrics can be referred to some recent studies such as [65–69] Based on the calculation of these metrics, the outputs of the algorithms for test problems in medium and large sizes are noted in Table 2. FUZZY INFORMATION AND ENGINEERING 215 Table 1. Tuning the meta-heuristics. Meta-heuristics Parameters Levels Tuned value GA Population size 100 150 200 200 Maximum No. of iterations 300 500 700 500 Rate of mutation 0.05 0.15 0.25 0.15 Rate of crossover 0.6 0.7 0.8 0.8 KA Population size 100 150 200 100 Maximum No. of iterations 300 500 700 300 Percentage of N1 0.1 0.2 0.3 0.1 Percentage of N2 0.4 0.5 0.6 0.6 Maximum No. of swirling 5 10 15 10 RDA Population size 100 150 200 150 Maximum No. of iterations 300 500 700 700 No. of males 15 25 30 25 Alpha 0.5 0.6 0.7 0.6 Beta 0.7 0.8 0.9 0.7 Gamma 0.8 0.9 1 0.8 H-RDKGA Population size 100 150 200 150 Maximum number of iterations 300 500 700 500 Number of males 15 25 30 30 Maximum number of swirling 5 10 15 15 Figure 5. Behavior of algorithms in terms of computational time. Later, the obtained results for each problem are converted to the Relative Percentage Deviation (RPD) computed by: |Alg − Best | sol sol RPD = (23) Best sol where Alg is the output of algorithm and Best is the best value ever found in the sol sol problem size. It should be noted that the lower value for the RPD is preferred. 216 A.-M. GOLMOHAMMADI ET AL. Table 2. Evaluation metrics (i.e. DM, SNS, DEA and POD) to the performance of the algorithms. DM SNS DEA POD Instances GA KA RDA H-RDKGA GA KA RDA H-RDKGA GA KA RDA H-RDKGA GA KA RDA H-RDKGA 3*5 14,962 14,389 16,452 16,765 2498 2267 1748 2699 0.18 0.16 0.12 0.15 0.16 0.22 0.14 0.22 4*6 17,641 17,275 19,743 18,746 6122 7210 5426 7495 0.20 0.12 0.18 0.12 0.18 0.18 0.19 0.21 5*8 8124 6833 7491 8945 7445 7296 6948 8155 0.24 0.22 0.26 0.18 0.22 0.20 0.10 0.18 6*9 34,685 29,164 34,112 35,647 3485 3105 2915 4039 0.28 0.14 0.22 0.14 0.15 0.14 0.11 0.16 7*11 13,418 12,742 13,671 14,289 2143 1834 7501 2867 0.16 0.26 0.18 0.16 0.17 0.18 0.16 0.12 8*13 24,914 25,199 23,749 28,763 1077 1282 675 2049 0.24 0.12 0.12 0.19 0.19 0.14 0.12 0.18 10*12 26,493 22,102 25,761 26,714 5482 4912 4466 4288 0.18 0.14 0.20 0.22 0.22 0.16 0.14 0.12 11*13 31,749 31,054 32,144 33,849 6388 5187 5514 6382 0.26 0.18 0.14 0.18 0.22 0.18 0.14 0.16 12*15 4784 7401 6195 7225 6237 5853 6432 7528 0.14 0.22 0.20 0.35 0.20 0.16 0.08 0.22 FUZZY INFORMATION AND ENGINEERING 217 Figure 6. Means plot and LSD intervals to specify the RPD for the evaluation metrics (i.e. DM(a), SNS(b), DEA(c) and POD(d)).to compare the algorithms. 218 A.-M. GOLMOHAMMADI ET AL. In the end, to verify the statistical validity of the results, we perform an analysis of variance (ANOVA) method to accurately analyze the results (as seen in Table 2 based on the RPD). The results demonstrate that there is a clear statistically significant difference between the performances of the algorithms. The means plot and LSD intervals (at the 95% confidence level) for all methods are shown in Figure 6. The results show the superiority of the proposed hybrid algorithm in all assessment metrics in this study. 5. Conclusion The dynamic cell formation decision-making seeks to optimize the layouts of machines and the right allocations of products flow using a simplified objective function to formu- late the manufacturing system. In many contexts, however, and perhaps most especially in developing countries such as Iran where the management of manufacturing system is of particular concern, such a simplified approach to dynamic cell formation is failing to deliver satisfactory all outcomes under the recent advances of the supply chain and manufactur- ing technologies. To this end, a practical cell formation decision-making model in a fuzzy environment was introduced by this study. More practicality and efficiency need capable algorithms for this complicated optimization problem, which are robust and computation- ally manageable. Hence, a novel hybrid meta-heuristic algorithm based on the advantages of GA, KA and RDA simultaneously, is proposed to compare with the general ones. In this paper, a new bi-objective mixed-integer non-linear programming model was pre- sented to consider the dynamic cell formation and inter/intra-cell layouts in the continuous space simultaneously. The purpose of the model was to determine concurrently the forma- tion of cells and the intra- and inter-cellular layouts in a way that the total transportation cost of parts, the reconfiguration cost of cells, and the number of exceptional elements (EEs) were minimized. One of the main contributions of the presented model was the fuzzy conditions related to some parameters. In this regard, a Khimens’ method was utilized to de-fuzzify the uncertain parameters. As a complicated optimization problem with several real-life constraints and operational decisions that should be taken in less time, four dif- ferent meta-heuristics were employed to tackle the problem. Another innovation of this study was to propose a novel hybrid meta-heuristic algorithm based on the advantages of GA, KA and RDA simultaneously. The results showed that the proposed hybrid algorithm, called H-RDKGA, showed a better performance in comparison with its main individual algo- rithms. There are several recommendations for future directions of this study. For example, it is interesting to integrate the proposed model with a scheduling problem. The other approach is to use a two-stage or multi-stage stochastic programming method to tackle the uncertainty. From the aspect of the novel proposed hybrid algorithm, more in-depth anal- yses by other large-scale optimization problems may be considered. At last but not least, new meta-heuristics can be suggested to compare the results of the proposed algorithms. Disclosure statement The authors of this research certify that there is no any affiliation with or involvement in any organi- zation or entity with financial and non-financial interests in the subject matter or materials discussed in this paper. FUZZY INFORMATION AND ENGINEERING 219 Notes on contributors Amir-Mohammad Golmohammadi is received his BSc, MSc, and PhD degrees in Industrial Engineer- ing from University of Kurdistan, Islamic Azad University, and Yazd University in Iran, respectively. His has worked for few years in industry and presented his research in several international journals and conferences. His current research interests include Facility Design & Planning, Cellular Manufacturing Systems and Meta-heuristic Algorithms. Mahboobeh Honarvar is the assistance professor in Department of Industrial Engineering at Yazd University. She received BSc, MSc, and PhD degrees in Industrial Engineering from Sharif University of Technology, University of Tehran, and Tarbiat Modarres University in Iran, respectively. Her research interests include Her main research interests include Revenue Management and Dynamic Pricing, Supply Chain Management, Production Management and Meta-Heuristics. She has published several articles in journals, such as Computers and Industrial Engineering, Scientia Iranica, International Journal of Engineering, Computational and Applied Mathematics, Energy, Journal of Industrial Engineering Inter- national, International Journal of Industrial and Systems Engineering, Journal of Industrial and Systems Engineering, International Journal of Industrial Engineering & Production Research. HassanHosseini-Nasab is a Professor in Industrial Engineering from Yazd University. His main research interests are in the area of Supply Chain Management, Green Logistics and Sustainable Operations Management, Inventory Management, Combinatorial optimization and heuristics/metaheuristics. He is also a peer reviewer in top journals (e.g., ASOC, NCAA, CAIE, IJSS, ESWA and JCLP). He has published more than 60 scientific papers in high-ranked journals (e.g., ASOC, CAIE and IJAMT) and international conferences (e.g., IE and IEEE). Reza Tavakkoli-Moghaddamis the professor of Industrial Engineering at College of Engineering, Uni- versity of Tehran in Iran. He obtained his BSc, MSc, and PhD from Iran University of Science and Technology in Tehran (1989), University of Melbourne in Melbourne (1994) and Swinburne University of Technology in Melbourne (1998), respectively. He serves as the Editor-in-Chief of one journal and the Editorial Board of 10 journals. He was the recipient of the 2009 and 2011 Distinguished Researcher Awards as well as the 2010 and 2014 Distinguished Applied Research Awards by University of Tehran in Iran. He was also selected as National Iranian Distinguished Researcher in 2008 and 2010 by the Ministry of Science, Research and Technology in Iran. He has obtained the outstanding rank as the top 1% scientist and researcher in the world elite group since 2014, reported by Thomson Reuters. Also, he received the Order of Academic Palms Award as a distinguished educator and scholar for the insignia of Chevalier dans l’Ordre des Palmes Academiques by the Ministry of National Education of France in 2019. Professor Tavakkoli-Moghaddam has published 5 books, 25 book chapters, more than 1000 papers in reputable academic journals and conferences. ORCID Reza Tavakkoli-Moghaddam http://orcid.org/0000-0002-6757-926X References [1] Ah kioon S, Bulgak AA, Bektas T. Integrated cellular manufacturing systems design with produc- tion planning and dynamic system reconfiguration. Eur J Oper Res. 2009;192(2):414–428. [2] Afrouzy ZA, Nasseri SH, Mahdavi I, et al. A fuzzy stochastic multi-objective optimization model to configure a supply chain considering new product development. Appl Math Model. 2016;40(17- 18):7545–7570. [3] Arkat J, Farahani MH, Ahmadizar F. Multi-objective genetic algorithm for cell formation prob- lem considering cellular layout and operations scheduling. Int J Computer Integr Manuf. 2012;25(7):625–635. [4] Bagheri M, Bashiri M. A new mathematical model towards the integration of cell formation with operator assignment and inter-cell layout problems in a dynamic environment. Appl Math Model. 2014;38(4):1237–1254. 220 A.-M. GOLMOHAMMADI ET AL. [5] Balakrishnan J, Cheng CH. Multi-period planning and uncertainty issues in cellular manufactur- ing: a review and future directions. Eur J Oper Res. 2007;177(1):281–309. [6] Balakrishnan J, Cheng CH. The dynamic plant layout problem: incorporating rolling horizons and forecast uncertainty. Omega (Westport). 2009;37(1):165–177. [7] Bayram H, Şahin R. A comprehensive mathematical model for dynamic cellular manufacturing system design and linear programming embedded hybrid solution techniques. Comput Ind Eng. 2016;91:10–29. [8] Bahadori-Chinibelagh S, Fathollahi-Fard AM, Hajiaghaei-Keshteli M. Two constructive algo- rithms to address a multi-depot home healthcare routing problem. IETE J Res. 2019:1–7. doi:10.1080/03772063.2019.1642802 [9] Benjaafar S. Modeling and analysis of congestion in the design of facility layouts. Manage Sci. 2002;48(5):679–704. [10] Chan F, Lau K, Chan L, et al. Cell formation problem with consideration of both intracellular and intercellular movements. Int J Prod Res. 2008;46(10):2589–2620. [11] Chan FT, Lau KW, Chan PL, et al. Two-stage approach for machine-part grouping and cell layout problems. Robot Comput Integr Manuf. 2006;22(3):217–238. [12] Chang C-C, Wu T-H, Wu C-W. An efficient approach to determine cell formation, cell lay- out and intracellular machine sequence in cellular manufacturing systems. Comput Ind Eng. 2013;66(2):438–450. [13] Chen M. A mathematical programming model for system reconfiguration in a dynamic cellular manufacturing environment. Ann Oper Res. 1998;77:109–128. [14] Deep K, Singh PK. Dynamic cellular manufacturing system design considering alternative rout- ing and part operation tradeoff using simulated annealing based genetic algorithm. Sadhan ¯ a. ¯ 2016;41(9):1063–1079. [15] Delgoshaei A, Ali A, Ariffin MKA, et al. A multi-period scheduling of dynamic cellular manufactur- ing systems in the presence of cost uncertainty. Comput Ind Eng. 2016;100:110–132. [16] Delgoshaei A, Ariffin MKAM, Leman Z, et al. Review of evolution of cellular manufactur- ing system’s approaches: material transferring models. Int J Prec Eng Manuf . 2016;17(1): 131–149. [17] Drolet J, Marcoux Y, Abdulnour G. Simulation-based performance comparison between dynamic cells, classical cells and job shops: a case study. Int J Prod Res. 2008;46(2):509–536. [18] Fard AMF, Hajiaghaei-Keshteli M. Red Deer algorithm (RDA); a new optimization algorithm inspired by Red Deers’ mating. In: International Conference on Industrial Engineering. IEEE. 2016;2016:33–34. [19] Fathollahi-Fard AM, Ranjbar-Bourani M, Cheikhrouhou N, et al. Novel modifications of social engineering optimizer to solve a truck scheduling problem in a cross-docking system. Comput Ind Eng. 2019;137:106103. [20] Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R. A bi-objective green home health care routing problem. J Clean Prod. 2018a;200:423–443. [21] Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Mirjalili S. Multi-objective stochastic closed-loop supply chain network design with social considerations. Appl Soft Comput. 2018b;71: 505–525. [22] Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Mirjalili S. A set of efficient heuristics for a home healthcare problem. Neural Comput Appl. 2019: 1–21. doi:10.1007/s00521-019- 04126-8 [23] Forghani K, Mohammadi M, Ghezavati V. Integrated cell formation and layout problem consid- ering multi-row machine arrangement and continuous cell layout with aisle distance. Int J Adv Manuf Technol. 2015;78(5–8):687–705. [24] Fry T, Wilson M, Breen M. A successful implementation of group technology and cell manufac- turing. Prod Inventory Manage. 1987;28(3):4–6. [25] Fu Y, Tian G, Fathollahi-Fard AM, et al. Stochastic multi-objective modelling and optimization of an energy-conscious distributed permutation flow shop scheduling problem with the total tardiness constraint. J Clean Prod. 2019;226:515–525. FUZZY INFORMATION AND ENGINEERING 221 [26] Ghosh T, Doloi B, Dan PK. An Immune Genetic algorithm for inter-cell layout problem in cellular manufacturing system. Prod Eng. 2016;10(2):157–174. [27] Golberg DE. Genetic algorithms in search, optimization, and machine learning. Addion Wesley. 1989;1989:102. [28] Golmohamadi S, Tavakkoli-Moghaddam R, Hajiaghaei-Keshteli M. Solving a fuzzy fixed charge solid transportation problem using batch transferring by new approaches in meta-heuristic. Electron Notes Discrete Math. 2017;58:143–150. [29] Hajiaghaei-Keshteli M, Aminnayeri M. Keshtel algorithm (KA); a new optimization algorithm inspired by Keshtels’ feeding. Proceeding IEEE Conf Ind Eng Manag Syst., Rabat, Morocco, 2013: 2249–2253. [30] Hajiaghaei-Keshteli M, Abdallah KS, Fathollahi-Fard AM. A Collaborative stochastic Closed-loop supply chain Network design for Tire Industry. Int J Eng. 2018;31(10):1715–1722. [31] Hajiaghaei-Keshteli M, Fathollahi-Fard AM. A set of efficient heuristics and metaheuristics to solve a two-stage stochastic bi-level decision-making model for the distribution network prob- lem. Comput Ind Eng. 2018;123:378–395. [32] Hassan MMD. Layout design in group technology manufacturing. Int J Prod Econ. 1995;38(2): 173–188. [33] Heragu SS. Facility design. Boston: PWS Publishing Company; 1997. [34] Jolai F, Tavakkoli-Moghaddam R, Golmohammadi A, et al. An electromagnetism-like algorithm for cell formation and layout problem. Expert Syst Appl. 2012;39(2):2172–2182. [35] Bootaki B, Mahdavi I, Paydar MM. A hybrid GA-AUGMECON method to solve a cubic cell forma- tion problem considering different worker skills. Comput Ind Eng. 2014;75:31–40. [36] Kia R, Baboli A, Javadian N, et al. Solving a group layout design model of a dynamic cellular man- ufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing. Comput Oper Res. 2012;39(11):2642–2658. [37] Krishnan KK, Mirzaei S, Venkatasamy V, et al. A comprehensive approach to facility layout design and cell formation. Int J Adv Manuf Technol. 2012;59(5-8):737–753. [38] Lee S-D, Chiang C-P. A cut-tree-based approach for clustering machine cells in the bidirectional linear flow layout. Int J Prod Res. 2001;39(15):3491–3512. [39] Leung MT, Quintana R, Chen A-S. A paradigm for Group Technology cellular layout planning in JIT facility. Proceeding IEEE Conf Ind Eng Eng Manag. 2008: 1174–1178. IEEE. [40] Mahdavi I, Mahadevan B. CLASS: An algorithm for cellular manufacturing system and layout design using sequence data. Robot Comput Integr Manuf. 2008;24(3):488–497. [41] Mahdavi I, Paydar MM, Solimanpur M, et al. Genetic algorithm approach for solving a cell formation problem in cellular manufacturing. Expert Syst Appl. 2009;36(3, Part 2):6598– [42] Mahdavi I, Teymourian E, Baher NT, et al. An integrated model for solving cell formation and cell layout problem simultaneously considering new situations. J Manuf Syst. 2013;32(4):655– [43] Afrouzy ZA, Paydar MM, Nasseri SH, et al. A meta-heuristic approach supported by NSGA-II for the design and plan of supply chain networks considering new product development. J Ind Eng Int. 2018;14(1):95–109. [44] Mohammadi M, Forghani K. A novel approach for considering layout problem in cellular manu- facturing systems with alternative processing routings and subcontracting approach. Appl Math Model. 2014;38(14):3624–3640. [45] Mohammadi M, Forghani K. Designing cellular manufacturing systems considering S-shaped layout. Comput Ind Eng. 2016;98:221–236. [46] Montgomery DC. Introduction to statistical quality control. 7th Edition. Hoboken, NJ: John Wiley & Sons; 2012. [47] Moradgholi M, Paydar MM, Mahdavi I, et al. A genetic algorithm for a bi-objective mathematical model for dynamic virtual cell formation problem. J Ind Eng Int 2016;12(3):343–359. [48] Jiménez M, Arenas M, Bilbao A, et al. Linear programming with fuzzy parameters: an interactive method resolution. Eur J Oper Res. 2007;177(3):1599–1609. 222 A.-M. GOLMOHAMMADI ET AL. [49] Papaioannou G, Wilson JM. The evolution of cell formation problem methodologies based on recent studies (1997–2008): Review and directions for future research. Eur J Oper Res. 2010;206(3):509–521. [50] Rafiee K, Rabbani M, Rafiei H, et al. A new approach towards integrated cell formation and inventory lot sizing in an unreliable cellular manufacturing system. Appl Math Model. 2011;35(4):1810–1819. [51] Rheault M, Drolet JR, Abdulnour G. Physically reconfigurable virtual cells: a dynamic model for a highly dynamic environment. Comput Ind Eng. 1995;29(1):221–225. [52] Safaei N, Saidi-Mehrabad M, Jabal-Ameli M. A hybrid simulated annealing for solving an extended model of dynamic cellular manufacturing system. Eur J Oper Res. 2008;185(2):563–592. [53] Safaei N, Tavakkoli-Moghaddam R. Integrated multi-period cell formation and subcon- tracting production planning in dynamic cellular manufacturing systems. Int J Prod Econ. 2009;120(2):301–314. [54] Samadi A, Mehranfar N, Fathollahi Fard AM, et al. Heuristic-based metaheuristics to address a sustainable supply chain network design problem. J Ind Prod Eng. 2018;35(2):102–117. [55] Schaller J. Designing and redesigning cellular manufacturing systems to handle demand changes. Comput Ind Eng. 2007;53(3):478–490. [56] Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R. Red deer algorithm (RDA): a new nature-inspired meta-heuristic. Soft comput. 2020. doi:10.1007/s00500-020-04812-z [57] Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R. The social engineering optimizer (SEO). Eng Appl Artif Intell. 2018b;72:267–293. [58] Tavakkoli-Moghaddam R, Javadian N, Javadi B, et al. Design of a facility layout problem in cellular manufacturing systems with stochastic demands. Appl Math Comput. 2007;184(2):721–728. [59] Tavakkoli-Moghaddam R, Javadian N, Khorrami A, et al. Design of a scatter search method for a novel multi-criteria group scheduling problem in a cellular manufacturing system. Expert Syst Appl. 2010;37(3):2661–2669. [60] Bootaki B, Mahdavi I, Paydar MM. New bi-objective robust design-based utilisation towards dynamic cell formation problem with fuzzy random demands. Int J Computer Integr Manuf. 2015;28(6):577–592. [61] Yadollahi MS, Mahdavi I, Paydar MM, et al. Design a bi-objective mathematical model for cellular manufacturing systems considering variable failure rate of machines. Int J Prod Res. 2014;52(24):7401–7415. [62] Wang X, Tang J, Yung K-L. Optimization of the multi-objective dynamic cell formation problem using a scatter search approach. Int J Adv Manuf Technol. 2009;44(3-4):318–329. [63] Wicks EM, Reasor RJ. Designing cellular manufacturing systems with dynamic part populations. IIE Trans. 1999;31(1):11–20. [64] Wu X, Chu C-H, Wang Y, et al. A genetic algorithm for cellular manufacturing design and layout. Eur J Oper Res. 2007;181(1):156–167. [65] Paydar MM, Saidi-Mehrabad M. Revised multi-choice goal programming for integrated supply chain design and dynamic virtual cell formation with fuzzy parameters. Int J Computer Integr Manuf. 2015;28(3):251–265. [66] Zohrevand AM, Rafiei H, Zohrevand AH. Multi-objective dynamic cell formation problem: A stochastic programming approach. Comput Ind Eng. 2016;98:323–332. [67] Fathollahi-Fard AM, Govindan K, Hajiaghaei-Keshteli M, et al. A green home health care supply chain: New modified simulated annealing algorithms. J Clean Prod. 2019;240. Article no. 118200. [68] Zhang B, Pan QK, Gao L, et al. A multiobjective evolutionary algorithm based on decomposition for hybrid flowshop green scheduling problem. Comput Ind Eng. 2019;136:325–344. [69] Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tian G, et al. An adaptive Lagrangian relaxation-based algorithm for a coordinated water supply and wastewater collection network design problem. Inf Sci (Ny). 2020;512:1335–1359. [70] Liu X, Tian G, Fathollahi-Fard AM, et al. Evaluation of ship’s green degree using a novel hybrid approach combining group fuzzy entropy and cloud technique for the order of preference by similarity to the ideal solution theory. Clean Technol Environ Policy. 2020;22:493–512.
Fuzzy Information and Engineering – Taylor & Francis
Published: Apr 2, 2020
Keywords: Cellular manufacturing system; cell formation; inter/intra-cell layout; Pareto-based algorithms; hybrid meta-heuristic algorithm
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.