Single machine due-date scheduling of jobs with decreasing start-time dependent processing times

We study the problem of scheduling jobs whose processing times are decreasing functions of their starting times. We consider the case of a single machine and a common decreasing rate for the processing times. 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(nlogn) time algorithm to solve this problem.