A Combinatorial Benders Cut for the Integrated Production Scheduling and Distribution Problem

One of the most attractive topics for industry and researchers in industrial engineering is the integration of decisions in the supply chain. There are some advantages in the integrated decisions compared to different decisions, such as decreasing the cost of distribution and On-Time delivery. An integrated production scheduling and distribution problem is discussed in this study. The main contribution of this paper is to study this problem from a multi-agent viewpoint. In this case, each agent has a set of customers with their jobs, and each agent has a specific objective. Here, a two-agent problem is discussed in which the first agent objective is the minimization of the total tardiness for jobs of the first agent and the second agent objective is to minimize the total cost of the distribution. For this problem, a mixed-integer linear programming formulation is developed. Due to the complexity of the original problem and its specific structure, a combinatorial Benders decomposition approach decomposes it to the master problem and sub-problem. It means some modifications have been applied to the classic version of Benders method. The results show the excellent performance of the algorithm in comparison with another exact method .