Minimizing the operational costs in a flexible flow shop scheduling problem with unrelated parallel machines

This paper investigates a flexible flow shop scheduling problem with the aim of minimizing the operational costs as a new objective function. In this production system, there are some unrelated parallel machines with different performances and different technology levels in the first stage and each other stage consists of a single machine. Setup times are assumed as sequence-dependent and are need when a machine starts to process a new job. Some of the parallel machines in the first stage are multifunctional and can do several processes on jobs. So, the jobs that are assigned to these machines do not need to be processed in some next stages. This problem is described with an example, and its parameters and decision variables are defined. Then a mathematical model based on mixed-integer linear programming (MIP) is developed to solve the problem in small-sized scales. As this problem is discussed in an Np-hard environment, the Genetic Algorithm (GA) is applied to solve the considered problem on practical-sized scales. Due to the result, the operational costs conflict with makespan as a common objective function in scheduling problems. Therefore, the supplementary analysis has been presented considering a restriction on the makespan.