Combining possibilistic linear programming and fuzzy AHP for solving the multi-objective capacitated multi-facility location problem

The capacitated multi-facility location problem is a complex and imprecise decision-making problem which contains both quantitative and qualitative factors. In the literature, many objectives for optimizing many types of logistics networks are described: (i) minimization objectives such as cost, inventory, transportation time, environmental impact, financial risk and (ii) maximization objectives such as profit, customer satisfaction, and flexibility and robustness. However, only a few papers have considered quantitative and qualitative factors together with imprecise methodologies. Unlike traditional cost-based optimization techniques, the approach proposed here evaluates these factors together while considering various viewpoints. Decision-makers must deal both factors together to model complex structure of real-world applications. In this paper, a two-phase possibilistic linear programming approach and a fuzzy analytical hierarchical process approach have been combined to optimize two objective functions (“minimum cost” and “maximum qualitative factors benefit”) in a four-stage (suppliers, plants, distribution centers, customers) supply chain network in the presence of vagueness. The results and findings of this method are illustrated with a numerical example, and the advantages of this methodology are discussed in the conclusion.