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.