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On Asymptotic Optimality of Permutation Schedules in Stochastic Flow Shops and Assembly Lines

In: Operations Research Proceedings 2004

Author

Listed:
  • Roman Koryakin

    (Sovolev Institure of Mathematics of SB RAS)

Abstract

For the stochastic flow shop problem with m machines, n jobs and operation processing times being independent identically distributed random variables, we consider permutation schedules — those in which each machine processes the jobs in the same order. For fixed m and increasing n, the asymptotic behavior of an arbitrary permutation schedule length is researched. Let T be the makespan of that schedule. Considering the maximum machine load L as a lower bound of the makespan, we show that for a wide class of operation processing time distributions the average-case ratio T/L converges to 1. Thus, an arbitrary permutation flow shop schedule is asymptotically optimal with n → ∞, and one can construct such schedule in a linear time. The same result is derived for the stochastic assembly line problem with m machines and n jobs.

Suggested Citation

  • Roman Koryakin, 2005. "On Asymptotic Optimality of Permutation Schedules in Stochastic Flow Shops and Assembly Lines," Operations Research Proceedings, in: Hein Fleuren & Dick Hertog & Peter Kort (ed.), Operations Research Proceedings 2004, pages 200-206, Springer.
    • Handle: RePEc:spr:oprchp:978-3-540-27679-1_25
    DOI: 10.1007/3-540-27679-3_25
    as

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