Heuristics for parallel machine scheduling with deterioration effect

Authors:
Ming Liu;Feifeng Zheng;Yinfeng Xu;Lu Wang
Affiliations:
School of Economomics & Management Tongji University, Shanghai, P.R. China;School of Management, Xi'an JiaoTong University, Xi'an, Shaanxi and The State Key Lab for Manufacturing Systems Engineering, Xi'an, Shaanxi and Ministry of Education Key Lab for Intelligent Networ ...;School of Management, Xi'an JiaoTong University, Xi'an, Shaanxi and The State Key Lab for Manufacturing Systems Engineering, Xi'an, Shaanxi and Ministry of Education Key Lab for Intelligent Networ ...;Shanghai Vocational School of CAAC, Shanghai, P.R. China
Venue:
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Year:
2011

Citing 6
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Abstract

This paper considers one parallel machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the makespan, and our focus is on the case with an arbitrary number of parallel machines. We prove that LIST rule is (1 + bmax)m-1/m -approximation where m is the number of machines and bmax is the maximum deteriorating rate of job. We then propose one heuristic LDR (Largest deteriorating Rate first). The heuristic is proved (1 + bmin)m-1/m -approximation where bmin is the minimum deteriorating rate. We further show that this ratio is tight when m = 2,3 and 4.