Multi-cut Benders decomposition approach to collaborative scheduling

This paper considers the scheduling of jobs with deadlines across a distributed production network involving cost minimisation among distributed factories with parallel machines. This problem has two sub-problems: (1) assigning a job to an appropriate factory according to the four features, namely the original factory of jobs that ordered it, transportation time between different factories, speed of machines and production costs in each factory, and (2) scheduling jobs in each factory. With respect to such property, the problem can be decomposed into an assignment and single factory scheduling sub-problems. The proposed approach first formulates the problem as a mixed integer linear program and then reformulates it using a Benders decomposition (BD) approach as an assignment sub-problem and as a single factory scheduling sub-problem. Since it is assumed that each job has its factory that initially ordered to it, for better balancing of the jobs completion times according to the speed and cost of each factory, jobs can be shifted between factories. This movement has a transportation time which is explicitly considered and integrated in a proposed model. To show that the BD-based approach is computationally powerful exact solution algorithm and is capable to solve medium-size problems, the performance of the proposed algorithm is examined by applying it to several test problems.