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Supply chain integration has become one of the most attractive topics for researchers in recent years. One of the advantages of this integration is in improving overall profit in comparison to separate decisions. In this study, an integrated scheduling and distribution problem is investigated. One of the contributions of this paper is to study this problem from a multi-agent viewpoint. In this case, each agent has a set of jobs with its own objective and compete with each other to acquire supply chain resources. Here, a two-agent problem is discussed where the objectives of the agents are the minimization of the total tardiness and the total cost of distribution. A mathematical formulation and two heuristics based on decomposition approaches are presented. In the first approach, a modified Benders decomposition is presented. Also, some valid inequalities are introduced to increase the convergence speed of this algorithm. In the second approach, a decomposition and cutting approach is developed. The results represent the good performance of both algorithms in comparison to other exact methods.

Two heuristic methods based on decomposition to the integrated multi-agent supply chain scheduling and distribution problem