Just-in-time on single machine scheduling problem with deteriorating jobs

One single machine scheduling problem with deteriorating jobs is studied,which means the jobs whose processing times are an increasing liner function of their start times,and the different job deterioration are inequality for all jobs. The problem is to determine an optimal common due-date and schedule so as to minimize the sum of due-date,earliness and tardiness penalties. An O(nlogn) time algorithm is given to solve this problem.