This paper considers a distributed production network scheduling that involves heterogeneous factories with the parallel machine. Although, each factory has its own local customers as a production agent, for better load balancing of machines in the production network, the jobs can transfer among factories. In order to make the problem more realistic, in addition to considering the ability of factories in processing of jobs, the capacity constraints of factories are also included in the scheduling. The aim of this paper is to maximize the profits of jobs such that each job is assigned to precisely one factory subject to their deadlines. To solve this problem, based on the decomposition algorithm, for the first time, an efficient decomposition-based branch and cut algorithm is designed. In this regard, first, the problem is formulated as a mixed-integer linear program (MILP), then using the Benders decomposition structure and after reformulating as an assignment subproblem and single factory scheduling subproblems, a branch and cut algorithm is proposed. Finally, the obtained results of the proposed algorithm, the original MILP, and non-cooperative local scheduling, all solved by CPLEX, are compared.
