This paper deals with multi-factory parallel job scheduling in which independent factories try to satisfy market demand by cooperating with each other. In parallel job scheduling, unlike classical scheduling, jobs require a pre-specified job-dependent number of machines simultaneously when being processed. In the research, although it is assumed that the factories operate separately, in some cases, due to a large number of orders in one factory, some jobs may be sent to other factories to minimize the total completion time of jobs taking into account transportation time. In other words, in this system, it is assumed that each factory, after satisfying the demand of its region, can cooperate with other factories in order to achieve a better objective function for the production network. In the first step of the proposed approach, after associating the scheduling system with a constrained graph, a semidefinite programming rounding and a heuristic are proposed to color the graph in small and large-size instances, respectively. Finally, in the first step, it is shown that the problem under study can be reduced to a parallel machine scheduling problem. Given the heterogeny of factories, in the next step, mixed-integer linear programming, as well as two heuristic algorithms, are proposed. The comparison results of the proposed algorithm, imperialist competitive algorithm and the non-cooperative local scheduling algorithm show that the two-phase cooperative distributed algorithm is quite efficient.
