Proposing a mathematical model of parallel machine scheduling with the aim of minimizing the task completion time and energy cost using a meta-heuristic algorithm.

This research proposes and solves a mathematical problem of parallel machine scheduling to minimize the total completion time and energy cost. This research aims to design and optimize a multi-objective mathematical model by minimizing energy consumption and total completion time for the parallel machine scheduling problem in Semnan Polyethylene Factory. First, the mathematical model of the problem is provided, and then the solution method is investigated using the epsilon constraint method in the GAMS optimization software and the meta-heuristic imperialist competitive algorithm (ICA). The mathematical model is validated using GAMS software and the constraint epsilon method and a real problem is implemented in large dimensions regarding the case study of the polyethylene factory in Semnan province using the meta-heuristic ICA. Finally, the performance of the ICA is measured in terms of the RPI index for small dimensions and the MID index for examples with large dimensions. Numerical results show that the value of the index for distance from the ideal point in the ICA is lower than that of the index obtained from solving the problem in GAMS. With these interpretations, it can be concluded that the ICA has a better performance than GAMS for optimizing the parallel machine scheduling problem in this research. According to the obtained answers, it can be concluded that with the increase in the time to do a task, the time to complete all tasks also increases and the cost of energy remains constant. While the cost of doing the task and the price of the electricity signal increase, energy costs increase and the time to complete tasks remains constant.