Multiobjective bilevel optimization for production-distribution planning problems using hybrid genetic algorithm

Currently, the production-distribution planning problems are usually modeled as single-objective bilevel programming problems. However, many real world production-distribution planning problems involve several objectives simultaneously for decision makers at two different levels when the production and the distribution processes are considered. In this paper, a multiobjective bilevel production-distribution planning model with equilibrium between supply and demand is set up, in which the distribution company is the leader who controls the distributing process with the aims to minimize its overall cost, and the manufacturer is the follower who controls the production process with the aims to minimize its overall cost and storage cost. So in the proposed model, the leader has one objective and the follower has two objectives. To solve the model efficaciously, the lower level problem (follower's problem) is transformed into an equivalent single-objective programming problem by a weighted aggregation method. As a result, the multiobjective bilevel optimization problem is transformed into a single-objective bilevel optimization problem. To solve the transformed problem efficiently, a uniform design scheme is applied to generate some representative weight vectors and initial population. Thereafter, a uniform design based crossover and exponential mutation are designed, and a local search scheme is applied. Based on all these, a hybrid genetic algorithm is proposed. Finally, two real word problems are solved successfully by the proposed algorithm, and the effectiveness and efficiency of the proposed algorithm are also tested by other test problems.