An interactive possibilistic programming approach for multiple objective supply chain master planning.

*(English)*Zbl 1168.90352Summary: Providing an efficient production plan that integrates the procurement and distribution plans into a unified framework is critical to achieving competitive advantage. In this paper, we consider a supply chain master planning model consisting of multiple suppliers, one manufacturer and multiple distribution centers. We first propose a new multi-objective possibilistic mixed integer linear programming model (MOPMILP) for integrating procurement, production and distribution planning considering various conflicting objectives simultaneously as well as the imprecise nature of some critical parameters such as market demands, cost/time coefficients and capacity levels. Then, after applying appropriate strategies for converting this possibilistic model into an auxiliary crisp multi-objective linear model (MOLP), we propose a novel interactive fuzzy approach to solve this MOLP and finding a preferred compromise solution. The proposed model and solution method are validated through numerical tests. Computational results indicate that the proposed fuzzy method outperforms other fuzzy approaches and is very promising not only for solving our problem, but also for any MOLP model especially multi-objective mixed integer models.

##### MSC:

90B06 | Transportation, logistics and supply chain management |

90C11 | Mixed integer programming |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

##### Keywords:

possibilistic programming; supply chain master planning; mixed-integer linear programs; compromise solution
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\textit{S. A. Torabi} and \textit{E. Hassini}, Fuzzy Sets Syst. 159, No. 2, 193--214 (2008; Zbl 1168.90352)

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