A note on due-date assignment and single-machine scheduling with deteriorating jobs

In this note, we study a single–machine scheduling problem with deteriorating jobs whose processing times are an increasing function of their start times. The objective is to determine the optimal due–date and schedule simultaneously to minimize the total of due–date, earliness and tardiness penalties. We give a concise analysis of the problem and provide a polynomial time algorithm to solve the problem. Moreover, the algorithm can be easily applied to the ‘mirror’ scheduling problem in which the actual processing time of a job is a decreasing function of its starting time.