Single machine scheduling with discretely controllable processing times

Authors:
Zhi-Long Chen;Qing Lu;Guochun Tang
Affiliations:
Department of Civil Engineering & Operations Research, Princeton University, Princeton, NJ 08544, USA;Department of Decision Sciences, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511, Singapore;Department of Management, Shanghai Second Polytechnic University, Shanghai 200041, People's Republic of China
Venue:
Operations Research Letters
Year:
1997

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Abstract

In the field of machine scheduling problems with controllable processing times, it is often assumed that the possible processing time of a job can be continuously controlled, i.e. it can be any number in a given interval. In this paper, we introduce a discrete model in which job processing times are discretely controllable, i.e. the possible processing time of a job can only be controlled to be some specified lengths. Under this discrete model, we consider a class of single machine problems with the objective of minimizing the sum of the total processing cost and the cost measured by a standard criterion. We investigate most common criteria, e.g. makespan, maximum tardiness, total completion time, weighted number of tardy jobs, and total earliness-tardiness penalty. The computational complexity of each problem is analyzed, and pseudo-polynomial dynamic programming algorithms are proposed for hard problems.