Journal of Heuristics

, Volume 5, Issue 1, pp 5–28 | Cite as

A 3/2 Algorithm for Two-Machine Open Shop with Route-Dependent Processing Times

  • V. A. Strusevich
  • A. J. A. van de Waart
  • R. Dekker
Article

Abstract

This paper considers the problem of minimizing the schedule length of a two-machine shop in which not only can a job be assigned any of the two possible routes, but also the processing times depend on the chosen route. This problem is known to be NP-hard. We describe a simple approximation algorithm that guarantees a worst-case performance ratio of 2. We also present some modifications to this algorithm that improve its performance and guarantee a worst-case performance ratio of 3/2.

approximation open shop scheduling heuristics worst-case analysis 

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References

  1. Adiri, I., and N. Amit. (1983). “Route-Depended Open-Shop Scheduling,” IIE Transactions 15, 231–234.Google Scholar
  2. Chen, B., and V. A. Strusevich. (1993). “Approximation Algorithms for Three Machine Open Shop Scheduling,” ORSA Journal on Computing 5, 321–326.Google Scholar
  3. Gonzalez, T., and S. Sahni. (1976). “Open Shop Scheduling to Minimize Finish Time,” Journal of the Association for Computing Machinery 23, 665–679.Google Scholar
  4. Jackson, J. R. (1956). “An Extension of Johnson' Results on Job Lot Scheduling,” Naval Research Logistics Quarterly 3, 201–203.Google Scholar
  5. Johnson, S. M. (1954). “Optimal Two-and Three-Stage Production Schedules with Set-Up Times Included,” Naval Research Logistics Quarterly 1, 61–68.Google Scholar
  6. Karp, R. M. (1972). “Reducibility Among the Combinatorial Problems.” In R. E. Miller and J.W. Thatcher (eds.), Complexity of Computer Computation, pp. 85–103. New York: Plenum Press.Google Scholar
  7. Lawler, E. L., J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys. (1993). “Sequencing and Scheduling: Algorithms and Complexity.” In S. C. Graves, A. H. G. Rinnooy Kan, and P. Zipkin (eds.), Handbooks in Operations Research and Management Science, Vol. 4: Logistics of Production and Inventory, pp. 445–522. Amsterdam: North-Holland.Google Scholar
  8. Potts, C. N. (1985). “Analysis of a Linear Programming Heuristic for Scheduling Unrelated Parallel Machines.” Discrete Applied Mathematics 10, 155–164.Google Scholar
  9. Sevast'janov, S. V., and G. J. Woeginger. (1998). “Makespan Minimization in Open Shops: A Polynomial Time Approximation Scheme.” Report SFB68, TU Graz, Austria, to appear in Mathematical Programming 82, 191–198.Google Scholar
  10. Shmoys, D. B., C. Stein, and J. Wein. (1994). “Improved Approximation Algorithms for Shop Scheduling Problems.” SIAM Journal on Computing 23, 617–632.Google Scholar
  11. Tanaev, V. S., Y. N. Sotskov, and V. A. Strusevich. (1994). Scheduling Theory: Multi-Stage Systems. Dordrecht: Kluwer Academic Publishers.Google Scholar
  12. Williamson, D. P., L.A. Hall, J. A. Hoogeveen, C. A. J. Hurkens, J. K. Lenstra, S.V. Sevast'janov, and D. B. Shmoys. (1997). “Short Shop Schedules.” Operations Research 45, 288–294.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • V. A. Strusevich
    • 1
  • A. J. A. van de Waart
    • 2
  • R. Dekker
    • 2
  1. 1.University of GreenwichLondonU.K.
  2. 2.Erasmus UniversityRotterdamThe Netherlands

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