Due-date assignment and parallel-machine scheduling with deteriorating jobs

Abstract

In this paper we study the problem of scheduling n deteriorating jobs on m identical parallel machines. Each job's processing time is a nondecreasing function of its start time. The problem is to determine an optimal combination of the due-date and schedule so as to minimize the sum of the due-date, earliness and tardiness penalties. We show that this problem is NP-hard, and we present a heuristic algorithm to find near-optimal solutions for the problem. When the due-date penalty is 0, we present a polynomial time algorithm to solve it.

Keywords:

• deteriorating jobs
• parallel-machine scheduling
• due-date

Acknowledgements

This research was supported in part by The Hong Kong Polytechnic University under grant number G-YW81. LY Kang was also supported by the National Natural Science Foundation of China(10571117).