The Comparison of the Integer Programming Models for Solving the Stage Shop Scheduling Problem

The development and extending the classic models for approaching the real world conditions are always in consideration of researchers. For this reason, many efforts are made for generalization of the job shop scheduling problem. The stage shop scheduling problem is defined as a generalization of the mixed shop and a special case of the general shop. In a stage shop, each job includes several stages and each stage contains one or more operations. A stage is a subset of the set of the operations of a job so that these operations can be processed in any arbitrary order. In other words, the process of the operations of a stage cannot be initiated unless all the operations of the previous stage are completed. In this paper, two mixed integer programming models are presented for each of the problems "the stage shop scheduling with total weighted tardiness criterion" and "the stage shop scheduling with makespan criterion" (totally four models) and then the models are compared. For the comparison of the efficiency of the proposed models, some problem instances are generated. The computational results show that the second model is more efficient.