Mixed binary integer programming formulations for the flow shop scheduling problems. A case study: ISD projects scheduling

In this paper, we consider a flow shop scheduling problem under different conditions. The model is formulated in a form of mixed binary integer programming. The primary goal of this paper is to develop operation schedules that specify the completion time of operations. The objective function of our model is formulated as a minimization of the makespan, the weighted mean flow-time or the weighted mean tardiness. There are several constraints which are involved in our modeling such as the due dates of jobs, the jobs ready times, etc. For these objective functions and constraints, seven mixed binary integer programming models are proposed. We demonstrate the implementation of our proposed models using different numerical examples. As a case study, we apply the proposed models for an information systems development (ISD) center to schedule the ISD projects using some real data.