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

Author

Listed:
  • Qian Cao

    (Shanghai University of Electric Power
    Shanghai Jiao Tong University)

  • Guohua Wan

    (Shanghai Jiao Tong University)

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.

Suggested Citation

  • Qian Cao & Guohua Wan, 2016. "Semi-online scheduling with combined information on two identical machines in parallel," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 686-695, February.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:2:d:10.1007_s10878-014-9778-1
    DOI: 10.1007/s10878-014-9778-1
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    Cited by:

    1. Leah Epstein, 2018. "A survey on makespan minimization in semi-online environments," Journal of Scheduling, Springer, vol. 21(3), pages 269-284, June.

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