The effect of machine availability on the worst-case performance of LPT

Authors:
Hark-Chin Hwang;Kangbok Lee;Soo Y. Chang
Affiliations:
Department of Industrial Engineering, Chosun University, 375 Susuk-Dong, Dong-Gu, Gwangju 501-709, Republic of Korea;Department of Industrial Engineering, Division of Electrical and Computer Engineering, Pohang University of Science and Technology, Hyoja Dong San 31, Namgu, Pohang, 790-784 Kyungbuk, Republic of ...;Department of Industrial Engineering, Division of Electrical and Computer Engineering, Pohang University of Science and Technology, Hyoja Dong San 31, Namgu, Pohang, 790-784 Kyungbuk, Republic of ...
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

We consider the makespan minimization parallel machine scheduling problem where each machine may be unavailable for a known time interval. For this problem, we investigate how the worst-case behavior of the longest processing time first algorithm (LPT) is affected by the availability of machines. In particular, for given m machines, we analyze the cases where arbitrary number, @l, ranging from one to m-1, machines are unavailable simultaneously. Then, we show that the makespan of the schedule generated by LPT is never more than the tight worst-case bound of 1+12@?m/(m-@l)@? times the optimum makespan.