Modeling and solving the distributed and flexible job shop scheduling problem with WIPs supply planning and bounded processing times

In this paper, for the first time in the literature, we integrated production scheduling decisions and WIPs planningdecisions in a distributed environment. We study the distributed and flexible job shop scheduling problem (DFJSP)which involves the scheduling of jobs (products) in a distributed manufacturing environment, under the assumptionthat the shop floor of each factory/cell is configured as a flexible job shop. It is also assumed that the work-in-process(WIP) parts can be bought from the market instead of manufacturing them in-house, and they also can be sold in themarket instead of processing their remaining operations and selling the end products. Moreover, the processing timesof the operations can be decreased by paying a cost. However, there are a lower limit and an upper limit for theprocessing time of each operation. We formulate this general problem as a mixed integer linear programming (MILP)model. A fast heuristic algorithm is also developed to obtain good solutions in very short time. The algorithm is testedon some problem instances in order to evaluate its performance. Computational results show that the proposedheuristic is a computationally efficient and practical approach.