Due-date assignment and single machine scheduling with deteriorating jobs

We study a scheduling problem with deteriorating jobs, that is, jobs whose processing times are an increasing function of their start times. We consider the case of a single machine and linear job-independent deterioration. The problem is to determine an optimal combination of the due-date and schedule so as to minimize the sum of due-date, earliness and tardiness penalties. We give an O(n log n) time algorithm to solve this problem.