##
**A possibilistic programming approach for closed-loop supply chain network design under uncertainty.**
*(English)*
Zbl 1230.90204

Summary: The design of closed-loop supply chain networks has attracted more attention in recent years according to business and environmental factors. The significance of accounting for uncertainty and risk in such networks spurs an interest to develop appropriate decision making tools to cope with uncertain and imprecise parameters in closed-loop supply chain network design problems. This paper proposes a bi-objective possibilistic mixed integer programming model to deal with such issues. The proposed model integrates the network design decisions in both forward and reverse supply chain networks, and also incorporates the strategic network design decisions along with tactical material flow ones to avoid the sub-optimalities led from separated design in both parts. To solve the proposed possibilistic optimization model, an interactive fuzzy solution approach is developed by combining a number of efficient solution approaches from the recent literature. Numerical experiments are conducted to demonstrate the significance and applicability of the developed possibilistic model as well as the usefulness of the proposed solution approach.

### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C29 | Multi-objective and goal programming |

### Keywords:

fuzzy mathematical programming; closed-loop supply chain network design; possibilistic programming; fuzzy multi-objective optimization
PDFBibTeX
XMLCite

\textit{M. S. Pishvaee} and \textit{S. A. Torabi}, Fuzzy Sets Syst. 161, No. 20, 2668--2683 (2010; Zbl 1230.90204)

Full Text:
DOI

### References:

[1] | Dullaert, W.; Braysy, O.; Goetschalckx, M.; Raa, B., Supply chain (re)design: support for managerial and policy decisions, European Journal of Transport and Infrastructure Research, 7, 2, 73-91 (2007) |

[2] | Meade, L.; Sarkis, J.; Presley, A., The theory and practice of reverse logistics, International Journal of Logistics Systems and Management, 3, 56-84 (2007) |

[3] | Petek, J.; Glavic, P., An integral approach to waste minimization in process industries, Resource, Conservation and Recycling, 17, 169-188 (1996) |

[4] | Fleischmann, M.; Bloemhof-Ruwaard, J. M.; Beullens, P.; Dekker, R., Reverse logistics network design, (Dekker, R.; Fleischmann, M.; Inderfurth, K.; Van Wassenhove, L. N., Reverse Logistics: Quantitative Models for Closed-loop Supply chains (2004), Springer: Springer Berlin), 65-94 |

[5] | Üster, H.; Easwaran, G.; Akçali, E.; Çetinkaya, S., Benders decomposition with alternative multiple cuts for a multi-product closed-loop supply chain network design model, Naval Research Logistics, 54, 890-907 (2007) · Zbl 1135.90362 |

[6] | Krikke, H. R.; Van Harten, A.; Schuur, P. C., Reverse logistic network re-design for copiers, OR Spektrum, 21, 381-409 (1999) · Zbl 0940.90011 |

[7] | Ko, H. J.; Evans, G. W., A genetic-based heuristic for the dynamic integrated forward/reverse logistics network for 3PLs, Computers & Operations Research, 34, 346-366 (2007) · Zbl 1113.90028 |

[8] | Du, F.; Evans, G. W., A bi-objective reverse logistics network analysis for post-sale service, Computers & Operations Research, 35, 2617-2634 (2008) · Zbl 1179.90033 |

[9] | Jayaraman, V.; Patterson, R. A.; Rolland, E., The design of reverse distribution networks: models and solution procedures, European Journal of Operational Research, 150, 128-149 (2003) · Zbl 1023.90501 |

[10] | Min, H.; Ko, C. S.; Ko, H. J., The spatial and temporal consolidation of returned products in a closed-loop supply chain network, Computers & Industrial Engineering, 51, 309-320 (2006) |

[11] | Pishvaee, M. S.; Kianfar, K.; Karimi, B., Reverse logistics network design using simulated annealing, International Journal of Advanced Manufacturing Technology, 47, 269-281 (2010) |

[12] | Lee, D.; Dong, M., A heuristic approach to logistics network design for end-of-lease computer products recovery, Transportation Research Part E, 44, 455-474 (2007) |

[13] | Wojanowski, R.; Verter, V.; Boyaci, T., Retail-collection network design under deposit-refund, Computers and Operations Research, 34, 324-345 (2007) · Zbl 1109.90014 |

[14] | Pishvaee, M. S.; Farahani, R. Z.; Dullaert, W., A memetic algorithm for bi-objective integrated forward/reverse logistics network design, Computers and Operation Research, 37, 1100-1112 (2010) · Zbl 1178.90060 |

[15] | El-Sayed, M.; Afia, N.; El-Kharbotly, N., A stochastic model for forward-reverse logistics network design under risk, Computers & Industrial Engineering, 58, 423-431 (2010) |

[16] | Klibi, W.; Martel, A.; Guitouni, A., The design of robust value-creating supply chain networks: a critical review, European Journal of Operational Research, 203, 283-293 (2010) · Zbl 1177.90054 |

[17] | Ho, C., Evaluating the impact of operating environments on MRP system nervousness, International Journal of Production Research, 27, 1115-1135 (1989) |

[18] | Listes, O.; Dekker, R., A stochastic approach to a case study for product recovery network design, European Journal of Operational Research, 160, 268-287 (2005) · Zbl 1134.90433 |

[19] | Salema, M. I.G.; Barbosa-Povoa, A. P.; Novais, A. Q., An optimization model for the design of a capacitated multi-product reverse logistics network with uncertainty, European Journal of Operational Research, 179, 1063-1077 (2007) · Zbl 1163.90371 |

[20] | Zadeh, L., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3-28 (1978) · Zbl 0377.04002 |

[21] | Dubois, D.; Fargier, H.; Fortemps, P., Fuzzy scheduling: modelling flexible constraints vs. coping with incomplete knowledge, European Journal of Operational Research, 147, 231-252 (2003) · Zbl 1037.90028 |

[22] | Selim, H.; Ozkarahan, I., A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach, International Journal of Advanced Manufacturing Technology, 36, 401-418 (2008) |

[23] | Wang, J.; Shu, Y. F., A possibilistic decision model for new product supply chain design, European Journal of Operational Research, 177, 1044-1061 (2007) · Zbl 1111.90331 |

[24] | Selim, H.; Araz, C.; Ozkarahan, I., Collaborative production-distribution planning in supply chain: a fuzzy goal programming approach, Transportation Research Part E, 44, 396-419 (2008) |

[25] | Torabi, S. A.; Hassini, E., An interactive possibilistic programming approach for multiple objective supply chain master planning, Fuzzy Sets and Systems, 159, 193-214 (2008) · Zbl 1168.90352 |

[26] | Shen, Z. M., Integrated supply chain design models: a survey and future research directions, Journal of Industrial and Management Optimization, 3, 1, 1-27 (2007) · Zbl 1166.90346 |

[27] | Bellman, R. E.; Zadeh, L. A., Decision making in a fuzzy environment, Management Science, 17, 141-164 (1970) · Zbl 0224.90032 |

[28] | Lai, Y. J.; Hwang, C. L., A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, 49, 121-133 (1992) |

[29] | Lai, Y. J.; Hwang, C. L., Possibilistic linear programming for managing interest rate risk, Fuzzy Sets and Systems, 54, 135-146 (1993) |

[30] | Mula, J.; Poler, R.; Garcia, J. P., MRP with flexible constraints: a fuzzy mathematical programming approach, Fuzzy Sets and Systems, 157, 74-97 (2006) · Zbl 1085.90062 |

[31] | Peidro, D.; Mula, J.; Poler, R.; Verdegay, J. L., Fuzzy optimization for supply chain planning under supply, demand and process uncertainties, Fuzzy Sets and Systems, 160, 2640-2657 (2009) · Zbl 1279.90206 |

[32] | Peidro, D.; Mula, J.; Jiménez, M.; Botella, M., A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment, European Journal of Operational Research, 205, 65-80 (2010) · Zbl 1187.90184 |

[33] | Jimenez, M., Ranking fuzzy numbers through the comparison of its expected intervals, International Journal of Uncertainty, Fuzziness and Knowledge Based Systems, 4, 4, 379-388 (1996) · Zbl 1232.03040 |

[34] | Jimenez, M.; Arenas, M.; Bilbao, A.; Rodriguez, M. V., Linear programming with fuzzy parameters: an interactive method resolution, European Journal of Operational Research, 177, 1599-1609 (2007) · Zbl 1102.90345 |

[35] | Wang, R. C.; Liang, T. F., Applying possibilistic linear programming to aggregate production planning, International Journal of Production Economics, 98, 328-341 (2005) |

[36] | Inuiguchi, M.; Ramik, J., Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem, Fuzzy Sets and Systems, 111, 3-28 (2000) · Zbl 0938.90074 |

[37] | Parra, M. A.; Terol, A. B.; Gladish, B. P.; Rodriguez Uria, M. V., Solving a multiobjective possibilistic problem through compromise programming, European Journal of Operational Research, 164, 748-759 (2005) · Zbl 1057.90056 |

[38] | Yager, R., A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24, 143-161 (1981) · Zbl 0459.04004 |

[39] | Dubois, D.; Prade, H., The mean value of a fuzzy number, Fuzzy Sets and Systems, 24, 279-300 (1987) · Zbl 0634.94026 |

[40] | Heilpern, S., The expected value of a fuzzy number, Fuzzy Sets and Systems, 47, 81-86 (1992) · Zbl 0755.60004 |

[41] | Gonzalez, A., A study of the ranking function approach through mean values, Fuzzy Sets and Systems, 35, 29-43 (1990) · Zbl 0733.90003 |

[42] | Fortemps, P.; Roubens, M., Ranking and defuzzification methods based on area compensation, Fuzzy Sets and Systems, 82, 319-330 (1996) · Zbl 0886.94025 |

[43] | Dubois, D.; Kerre, E.; Mesiar, R.; Prade, H., Fuzzy interval analysis, (Dubois, D.; Prade, H., Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series (2000), Kluwer: Kluwer Boston, MA), 483-581 · Zbl 0988.26020 |

[44] | Zimmermann, H. J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 45-55 (1978) · Zbl 0364.90065 |

[45] | Sakawa, M.; Yano, H.; Yumine, T., An interactive fuzzy satisfying method for multiobjective linear-programming problems and its application, IEEE Transactions on Systems, Man and Cybernetics, SMC-17, 654-661 (1987) |

[46] | Werners, B., Aggregation models in mathematical programming, (Mitra, G.; Greenberg, H. J.; Lootsma, F. A.; Rijckaert, M. J.; Zimmermann, H-J., Mathematical Models for Decision Support (1988), Springer: Springer Berlin, Heidelberg, New York), 295-305 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.