Two machine flow shop scheduling problem with weighted WIP costs

This paper considers two new machine flow shop scheduling problems where the objective is to minimize the total WIP (work-in-process) cost. In this type of problems, the unit time WIP cost increases or decreases as a job passes through a series of stages in the production process. We first introduce this relatively new class of flow shop scheduling problems. Then, we establish the complexity of several problems with different types of job restrictions and weighted cost characteristics. For some tractable cases, we propose optimal solution procedures. Finally, a heuristic is introduced for a class of problem instances, and we find upper bounds on the relative errors.