The Flow Shop Problem with Random Operation Processing Times

Roman A. Koryakin () and Sergey V. Sevastyanov ()
Additional contact information
Roman A. Koryakin: Sobolev Institute of Mathematics
Sergey V. Sevastyanov: Sobolev Institute of Mathematics

A chapter in Operations Research Proceedings 2005, 2006, pp 697-702 from Springer

Abstract: Summary We consider the classical flow shop problem with m machines, n jobs and the minimum makespan objective. The problem is treated in stochastic formulation, where all operation processing times are random variables with distribution from a given class F. We present a polynomial time algorithm with absolute performance guarantee C max(S) − L ≤ 1.5(m − 1)p + o(1) that holds with high probability (Frieze, 1998) for n → ∞, where L is a trivial lower bound on the optimum (equal to the maximum machine load) and p is the maximum operation processing time. Class F includes distributions with regularly varying tails. The algorithm presented is based on a new algorithm for the compact vector summation problem and constructs a permutation schedule. The new absolute guarantee is superior to the best-known absolute guarantee for the considered problem (C max(S) − L ≤ (m − 1)(m − 2 + 1/(m − 2))p; Sevastyanov, 1995) that holds for all possible inputs of the flow shop problem.

Keywords: Feasible Schedule; Machine Load; Flow Shop Problem; Stochastic Formulation; Small Vector (search for similar items in EconPapers)
Date: 2006
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-540-32539-0_109

Ordering information: This item can be ordered from
http://www.springer.com/9783540325390

DOI: 10.1007/3-540-32539-5_109

Access Statistics for this chapter

More chapters in Operations Research Proceedings from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().