A hybrid imperialist competitive algorithm for integrated scheduling of production and distribution with vehicle routing

In this paper, integrated scheduling of production and distribution with vehicle routing problem is considered. A manufacturer with parallel production lines receives customer orders; after producing them, they are then delivered to the customers in batches by a fleet of vehicles. Unlike a direct delivery of products from the manufacturer to each customer, batch delivery reduces the transportation costs because of the maximum utilization of the vehicle capacities, but it may increase the holding and tardiness costs. The objective is to find an integrated schedule of production and distribution so as to minimize the setup, holding, distribution and tardiness costs. The problem is first formulated as a mixed integer linear programming model. In view of its NP-hardness, a procedure by incorporating dominance properties with imperialist competitive algorithm is then proposed to solve large-sized problem instances. To evaluate the performance of the proposed algorithm, several instances are generated and solved. Computational results demonstrate that the algorithm has a good performance for large problems.