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.