Semi-online scheduling with combined information on two identical machines in parallel

Qian Cao () and Guohua Wan ()
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Qian Cao: Shanghai University of Electric Power
Guohua Wan: Shanghai Jiao Tong University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 13, 686-695

Abstract: Abstract This paper is concerned with a semi-online scheduling problem with combined information on two identical parallel machines to minimize the makespan, where all the jobs have processing times in the interval $$[1,\,t]$$ [ 1 , t ] $$(t\ge 1)$$ ( t ≥ 1 ) and the jobs arrive in non-increasing order of their processing times. The objective is to minimize the makespan. For $$t\ge 1$$ t ≥ 1 , we obtain a lower bound $$\max _{N=1,2,3,\ldots }\left\{ \min \{\frac{4N+3}{4N+2}\,,\frac{Nt+N+1}{2N+1}\}\right\} $$ max N = 1 , 2 , 3 , … min { 4 N + 3 4 N + 2 , N t + N + 1 2 N + 1 } and show that the competitive ratio of the $$LS$$ L S algorithm achieves the lower bound.

Keywords: Scheduling; Semi-online; Identical parallel machines; Combined information (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-014-9778-1

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