Production scheduling of a parallel machine system with sequence dependent set-up times

This study tackles a difficult scheduling problem involving unrelated parallel machines with set-up times that vary with the sequence. Notably, the machines vary in their production rates, resulting in variable processing durations for the same task on different machines. Furthermore, the capacity of these computers to process jobs varies, as they handle different subsets of the whole work set. The set-up time also varies depending on the machine and the jobs that are processed on it.Four mixed-integer programming (MIP) models are developed to reflect distinct parts of the problem. Three of these models are concerned with minimizing makespan, overall tardiness, and the number of tardy jobs. The fourth model is specifically designed to generate compromise solutions, providing a more sophisticated approach to optimization. The study uses the AUGEMEN method to develop a set of Pareto Optimal Solutions, which is then supplemented by the Max-Min approach to select an optimal solution from the compromised set. This study involves an unrelated parallel machine scheduling problem. Set-up times are sequence-dependent. Unrelated machines have different production rates,providing different processing times on the same job on different machines. In addition, they are different regarding the capacity to process jobs, i.e., unrelated machines can process different subsets of all jobs. Moreover, set-up time is different based on the machine and the jobs to be processed on the machine. Four mixed integer programming models are developed to represent the problems and three of them have the objective function of minimizing the makespan, total tardiness, and the number of tardy jobs, respectively. The last model is used to obtain the compromised solutions. Applying the AUGEMEN method, it provides the set of Pareto Optimal Solutions. Along with the Max-Min method to be able to select one of the compromised solutions in the Optimal Solutions.Recognizing the computational constraints given by large-scale problem instances in real systems, the study proposes a dynamic dispatching rule-based heuristic method. This algorithm uses four single dispatching rules that have been deliberately tuned to account for both machine- and sequence-dependent set-up time. These criteria include shortest completion time (SCT), shortest completion time based on longest processing time (SC-LPT), earliest due date (SC-EDD), and minimum slack (SCMinSlack). This novel technique seeks to give effective solutions for addressing the complexities inherent in large-scale scheduling difficulties in actual systems.