Heuristics for Parallel Machine Scheduling with Deterioration Effect

This paper considers one parallel machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the makespan, and our focus is on the case with an arbitrary number of parallel machines. We prove that LIST rule is (1 + bmax)m-1/m -approximation where m is the number of machines and bmax is the maximum deteriorating rate of job. We then propose one heuristic LDR (Largest deteriorating Rate first). The heuristic is proved (1 + bmin)m-1/m -approximation where bmin is the minimum deteriorating rate. We further show that this ratio is tight when m = 2,3 and 4.