Integrated production and outbound distribution scheduling problem with multiple facilities/vehicles and perishable items

Abstract

Integrated production and distribution operations are crucial and necessary for companies to outperform their competitors. In this paper, we study an integrated problem includes heterogeneous facilities and capacitated vehicles. Our goal is to produce and distribute products in batches that meet customer demands at the lowest possible cost. We first give the formal definition of the problem, then propose a Mixed Integer Programming (MIP) formulation and strengthen with several polynomial size valid inequalities. Furthermore, we develop Memetic Algorithm (MA) and finally present 2592 test instances to illustrate the efficiency of both MA and MIP formulation. The optimal or feasible solutions for 1283 of 2592 test instances are obtained by the proposed MIP formulation. MA finds optimal or near optimal solutions for all these instances. When comparing the best solutions obtained by MA with the solutions of the MIP formulation, MA produces a superior result. Besides that, the time to obtain for optimal solutions are approximately 9 min and for all test instances approximately 82 min using MIP formulation. The time needed to solve all test instances with MA is only 3 sec. These findings clearly demonstrate the speed and accuracy of MA in producing results. These results also demonstrate that, it is possible to achieve solutions that are either equal or very close to those found by the MIP formulation, in an extremely short computation time with MA.