A multi-objective simulated annealing to solve an identical parallel machine scheduling problem with deterioration effect and resources consumption constraints

Abstract

Production systems are subject to machine deterioration and resource consumption constraints. The deterioration increases the processing time which leads to an increase in resource consumption. In this study, we investigate and model the behavior of a parallel machine scheduling problem with respect to the processing time. The machine is subject to deterioration and includes two resource consumption constraints. The first resource R1 controls the processing time so that additional amounts of R1 decrease the processing time. The second R2 is controlled by the actual processing time so that R2 consumption is a linear function of the actual processing time. The increment of R1 consumption leads to processing time and so R2 decrement. Solving this problem consists in finding the optimal schedule that will minimize both makespan and resources cost. This paper provides a mathematical programming model. In fact, due to the deterioration effect and the two resource consumptions, solving such a problem may be very difficult and requires a large computational time. In this paper, we introduce a multi objective simulated annealing (MOSA) in order to solve the combinatorial optimization problem related to finding the best combination (machine, job, position, R1). Literally the best jobs assignment and resources allocation so that makespan and resources cost are minimized. In order to improve the quality of the results we also developed a 2-steps algorithm by decomposing the original problem into two sub problems: an assignment problem and a resources allocation problem. Some simulations were performed to analyze the performances of the two algorithms. The results show that the 2-steps algorithm is very efficient and outperforms MOSA.