A Multiobjective Bilevel Program for Production-Distribution Planning in a Supply Chain

Production-distribution planning problems in a supply chain are complex and generally involve several decision makers. If there is a principal firm which controls the integrated production-distribution process or multiple firms assumed to collaborate in order to achieve common goals, then standard mathematical programs with one or multiple objectives can be used to address them. However, very often production-distribution planning problems involve decision makers at two distinct levels with a hierarchical relationship between them. This might be systems in which a principal firm, at the upper-level of the decision process, controls the distribution centers and seeks to minimize transportation costs from the suppliers to the warehouses and from these to the retailers. At the lower-level, each manufacturing plant, on receiving the order of the company, seeks to minimize its operating costs. This paper addresses these systems and proposes bilevel optimization to model them. If a single firm controls the manufacturing plants, the resulting model is a linear bilevel optimization program. When manufacturing plants have more objectives to consider than just operating costs, a linear/linear multiobjective bilevel program is proposed to model the system. In both cases, the optimal solution is achieved at an extreme point of the constraint region.