Two-machine decentralized flow shop scheduling problem with inter-factory batch delivery system

Technological advancement, the emergence of more complex production systems, and the need for greater manufacturer competition have caused production systems to shift from a centralized environment to a decentralized one. Researchers have paid more attention to distributed flow shop scheduling problems and investigated various features and issues related to them in recent years. However, special types of these problems, in which the network structure is serial and inter-factory transportation is significant, have received less attention. This study investigated the two-machine decentralized flow shop scheduling problem, in which inter-factory transportation is handled by a batch delivery system. The goal was to simultaneously reduce the costs of makespan and batch delivery. A mixed-integer linear programming model capable of solving small-size instances in a logical running time was presented to better describe the problem. Then, in order to solve large-size instances in a logical running time, a fast branch and bound algorithm with a heuristic method were developed to obtain the appropriate upper bound as well as the tight lower bounds at each node. The computational results indicated that the B&B algorithm performed very well in terms of problem-solving running time. The findings also demonstrated that the heuristic method can solve the most complex instances by 100 jobs with less than 13% error.