Scheduling linear deteriorating jobs with an availability constraint on a single machine

Authors:
Min Ji;Yong He;T. C. E. Cheng
Affiliations:
College of Computer Science and Information Engineering, Zhejiang Gongshang University, Hangzhou, PR China and Department of Mathematics, State Key Lab of CAD & CG, Zhejiang University, Hangzhou, ...;Department of Mathematics, State Key Lab of CAD & CG, Zhejiang University, Hangzhou, PR China;Department of Logistics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
Venue:
Theoretical Computer Science
Year:
2006

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Abstract

We consider a single machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time and the machine is subject to an availability constraint. We consider the non-resumable case. The objectives are to minimize the makespan and the total completion time. We show that both problems are NP-hard and present pseudopolynomial time optimal algorithms to solve them. Furthermore, for the makespan problem, we present an optimal approximation algorithm for the on-line case, and a fully polynomial time approximation scheme for the off-line case. For the total completion time problem, we provide a heuristic and evaluate its efficiency by computational experiments.