Matheuristic approaches for parallel machine scheduling problem with time-dependent deterioration and multiple rate-modifying activities

•We consider a parallel machine scheduling with time-dependent deterioration and multiple rate-modifying activities.•The deterioration is a linear function of a gap between starting time of job and the ending time of the previous RMA.•We developed a mixed integer programming model for the problem to find the optimal solution.•A novel simulated annealing algorithm embedding a mathematical model with an adjustment heuristic is provided. The study considers a parallel machine scheduling (PMS) problem with time-dependent deterioration and multiple rate-modifying activities (RMAs). The objective of the problem is to simultaneously determine the number and positions of RMAs and a schedule of jobs on parallel machines to minimize the makespan. In order to determine an optimal solution, a mixed integer linear programming (MILP) model for the PMS problem is introduced. Subsequently, novel metaheuristic algorithms embedding a mathematical model are developed based on matheuristic approaches to effectively handle large-sized problems. The matheuristic approaches decompose the original problem into sub-problems by determining partial decision variables from each iteration in simulated annealing (SA) and genetic algorithm (GA). Subsequently, the rest of the decision variables are optimally determined by using a mathematical model for the sub-problems with partial decision variables predetermined. In order to enhance the performance of SA and GA, an adjustment heuristic is proposed based on an optimality property for the problem. The performance of the proposed algorithms is evaluated by conducting numerical experiments based on randomly generated examples, and subsequently the behavior of the algorithms is discussed.