Approximation algorithms for parallel machine scheduling with linear deterioration

Authors:
Ming Liu;Feifeng Zheng;Shijin Wang;Yinfeng Xu
Affiliations:
School of Economics & Management, Tongji University, Shanghai, 200092, PR China;Glorious Sun School of Business and Management, Donghua University, Shanghai, 200092, PR China;School of Economics & Management, Tongji University, Shanghai, 200092, PR China;School of Management, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

This paper deals with a parallel machine scheduling problem. Different from fixed processing time assumption in the classical scheduling, a job's processing time is a simple linear increasing function of its starting time. The aim is makespan minimization, and our focus is on the case with an arbitrary number of parallel machines. We prove that LIST rule is (1+b"m"a"x)^m^-^1^m-approximation where m is the number of machines and b"m"a"x is the maximum deteriorating rate of job. We then propose one heuristic LDR (Largest deteriorating Rate first). The heuristic is proved by (1+b"m"i"n)^m^-^1^m-approximation where b"m"i"n is the minimum deteriorating rate. We further show that this ratio is tight when m=2,3 and 4.