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Mathematical optimization offers a valuable approach to tackle Industry scheduling problems. By formulating the scheduling challenge as a mathematical problem, mathematical optimization enables efficient and effective decision-making processes. Mathematical optimization is particularly beneficial in complex scheduling scenarios, such as in networked manufacturing environments, where multiple jobs and resources need to be coordinated. By leveraging optimization models and algorithms, it becomes possible to generate optimal process plans, considering factors like job dependencies, resource availability, and timing constraints. Through mathematical optimization, organizations can achieve improved efficiency, reduced lead times, and enhanced utilization of resources. Rigorous mathematical formulations and optimization techniques enables to surpass traditional manual planning methods and brings forth powerful computational capabilities. By optimizing various scheduling objectives, from minimizing makespan to maximizing resource utilization, mathematical optimization provides organizations with valuable insights and actionable plans. The purpose of this study is to discuss scheduling solutions for multiple jobs in a networked manufacturing setting based on mathematical optimization process. The study analyses a solver-based approach to generate the optimal process plans for multiple jobs and compare it with a more traditional game-theoretic approach. The objectives aim to develop two solver-based model using Z3 and Gurobi to generate optimal process plans; implement a game-theoretic model to solve for the same set of scheduling problems, and compare the computational time, solution quality, and efficiency of both approaches. To achieve this, the methodology will start with the problem definition. Multiple jobs are to be scheduled on a set of parallel machines. Each job has predefined processing times, deadlines, and priorities. The objective is to minimize the total completion time and maximize machine utilization while meeting all deadlines.
Silva et al. (Wed,) studied this question.