Comparing Mixed-Integer and Constraint Programming for the No-Wait Flow Shop Problem with Due Date Constraints

Abstract

The impetus for this research was examining a flow shop problem in which tasks were expected to be successively carried out with no time interval (i.e., no wait time) between them. For this reason, they should be completed by specific dates or deadlines. In this regard, the efficiency of the models was evaluated based on makespan. To solve the NP-Hard problem, we developed two mathematical models. Once we solved our problem using Mixed-Integer Programming Model (henceforth MIPM) and then, we applied a Constraint Programming Model (CPM); finally, we compared the optimality of the presented results.