Journal of Combinatorial Optimization

, Volume 8, Issue 1, pp 13–28 | Cite as

Flow Shop Scheduling Problems Under Machine–Dependent Precedence Constraints

  • A.A. Gladky
  • Y.M. Shafransky
  • V.A. Strusevich

Abstract

The paper considers the flow shop scheduling problems to minimize the makespan, provided that an individual precedence relation is specified on each machine. A fairly complete complexity classification of problems with two and three machines is obtained.

flow shop precedence constraints complexity polynomial-time algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.R. Garey, D.S. Johnson, and R. Sethi, “The complexity of flowshop and jobshop scheduling,” Math. Oper. Res., vol. 1, pp. 117–129, 1976.Google Scholar
  2. V.S. Gordon and Y.M. Shafransky, “Optimal sequencing under series-parallel precedence constraints,” Doklady Akademii Nauk BSSR, vol. 22, pp. 244–247, 1978 (in Russian).Google Scholar
  3. L.A. Hall and D.B. Shmoys, “Jackson's rule for single machine scheduling: Making a good heuristic better,” Math. Oper. Res., vol. 17, pp. 22–35, 1992.Google Scholar
  4. S.M. Johnson, “Optimal two-and three-stage production schedules with setup times included,” Naval Res. Log. Quart., vol. 1, pp. 61–68, 1954.Google Scholar
  5. E.L. Lawler, “Optimal sequencing of a single machine subject to precedence constraints,” Manag. Sci., vol. 19, pp. 544–546, 1973.Google Scholar
  6. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys, “Sequencing and scheduling: Algorithms and complexity,” in Handbooks in Operations Research and Management Science, Logistics of Production and Inventory, S.C. Graves, A.H.G. Rinnooy Kan, and P.H. Zipkin (Eds.), North-Holland, Amsterdam et al., 1993, vol. 4, pp. 445–522.Google Scholar
  7. J.K. Lenstra, A.H.G. Rinnooy Kan, and P. Brucker, “Complexity of machine scheduling problems,” Ann. Discr. Math., vol. 1, pp. 343–362, 1977.Google Scholar
  8. C.L. Monma, “The two-machine maximum flow time problem with series parallel precedence constraints: An algorithm and extensions,” Oper. Res., vol. 27, pp. 792–797, 1979.Google Scholar
  9. C.L. Monma, “Sequencing to minimize the maximum job cost,” Oper. Res., vol. 28, pp. 942–951, 1980.Google Scholar
  10. C.L. Monma and J.B. Sidney, “Sequencing with series-parallel precedence constraints,” Math. Oper. Res., vol. 4, pp. 215–234, 1979.Google Scholar
  11. Y.M. Shafransky and V.A. Strusevich, “The open shop scheduling problem with a given sequence of jobs on one machine,” Naval Res. Log., vol. 45, pp. 705–731, 1998.Google Scholar
  12. J.B. Sidney, “The two-machine maximum flow time problem with series parallel precedence relation,” Oper. Res., vol. 27, pp. 782–791, 1979.Google Scholar
  13. V.A. Strusevich, “Shop scheduling problems under precedence constraints,” Ann. Oper. Res., vol. 69, pp. 351–377, 1997.Google Scholar
  14. V.S. Tanaev, V.S. Gordon, and Y.M. Shafransky, Scheduling Theory: Single-Stage Systems, Kluwer Academic Publishers: Dordrecht et al., 1994.Google Scholar
  15. V.S. Tanaev, Y.N. Sotskov, and V.A. Strusevich, Scheduling Theory: Multi-Stage Systems, Kluwer Academic Publishers: Dordrecht et al., 1994.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • A.A. Gladky
    • 1
  • Y.M. Shafransky
    • 1
  • V.A. Strusevich
    • 2
  1. 1.National Academy of Sciences of BelarusInstitute of Engineering CyberneticsMinskRepublic of Belarus
  2. 2.School of Computing and Mathematical SciencesUniversity of GreenwichLondonUK

Personalised recommendations