Mixed Integer Programming model for flexible job-shop scheduling problem (FJSP) to minimize makespan and total machining time

In manufacturing-related industries, scheduling of resources and tasks play an important role in improving efficiency and productivity as well as reducing costs. Job-shop scheduling problem (JSP) concerns with the problem whereby there is only one machine that can process one type of operation. The flexible job-shop scheduling problem (FJSP) is an extension of the job shop scheduling problem. FJSP allows an operation to be processed by any machine out of a set of alternative machines. Thus, the objectives of this research are to analyze the production schedules and operations of the machines in FJSSP, to formulate a Mixed Integer Goal Programming (MIGP) model to solve FJSP; and to propose an optimal production job shop scheduling strategies based on the solution model. The MIGP model formulated is to solve FJSP with two objective functions, which are to minimize the makespan and the total machining. The model was solved by implementing the pre-emptive goal programming approach and using the Microsoft Excel Solver Add-Ins. Data from benchmark problem instances for the general FJSP with total flexibility as in [1] has been used in the computational experiments. Optimal solutions were found for the FJSP involved. The results obtained proved that the proposed solution approach gives competitive results as compared to the metaheuristics approaches.