Bilevel model for production–distribution planning solved by using ant colony optimization

This paper addresses a hierarchical production–distribution planning problem. There are two different decision makers controlling the production and the distribution processes, respectively, that do not cooperate because of different optimization strategies. The distribution company, which is the leader of the hierarchical process, controls the allocation of retailers to each depot and the routes which serve them. In order to supply items to retailers, the distribution company orders from the manufacturing company the items which have to be available at the depots. The manufacturing company, which is the follower of the hierarchical process, reacts to these orders deciding which manufacturing plants will produce them. A bilevel program is proposed to model the problem and an ant colony optimization based approach is developed to solve the bilevel model. In order to construct a feasible solution, the procedure uses ants to compute the routes of a feasible solution of the associated multi-depot vehicle route problem. Then, under the given data on depot needs, the corresponding production problem of the manufacturing company is solved. Global pheromone trail updating is based on the leader objective function, which involves costs of sending items from depots to retailers and costs of acquiring items from manufacturing plants and unloading them into depots. A computational experiment is carried out to analyze the performance of the algorithm.