A fuzzy multi-objective multi-follower linear Bi-level programming problem to supply chain optimization

In todayʹs world, many planning problems include a hierarchical decision structure with independent and often conflicting objectives. Therefore, the optimization of supply chains with hierarchical structure is essential. In this paper, we investigate a fuzzy multi-objective multi-products supply chain optimization problem in a bi-level structure with one level corresponding to a manufacturer planning problem, while the other to K distribution centers problem. In our model, customer demand and supply chain costs are considered uncertain and will be modeled with use of fuzzy sets. We first describe how different kinds of problems can be modeled as bi-level programming problems. Then, this fuzzy model is first converted into an equivalent crisp model by using ?-cut method in each level, and then by applying extended Kuhn–Tucker approach, we have a linear multi-objective programming problem. Fuzzy goal programming technique is applied to solve the multi-objective linear programming problem to obtain a set of Pareto-optimal solutions. Finally, a numerical example is illustrated to demonstrate the feasibility of the proposed approach.