Scheduling linearly deteriorating jobs on multiple machines

This paper investigates the scheduling problems in which the job processing times do not remain constant but are increasing linear functions of their starting times. Two deteriorating scheduling models, Model 1 and Model 2, for multiple machines are considered, with the goal being to minimize the makespan. In this paper, we propose an efficient heuristic for Model 1 and prove that the ratio of the makespan obtained by the heuristic to the optimal makespan is bounded. For Model 2, three heuristics, including a probabilistic heuristic, are proposed for minimizing the makespan. Numerical results are provided to show the efficiency of the approaches in this paper.