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Just-in-Time Scheduling with Equal-Size Jobs

  • Ameur SoukhalEmail author
  • Nguyen Huynh Toung
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 60)

Abstract

This chapter deals with common due date scheduling problem on single and parallel machines in which job processing times are identical. The objective is to minimize the total weighted earliness–tardiness. According to the common due date, two cases are considered. In the first case, the due date is given which involves that the common due date is enough early (restrictive version) or not (non-restrictive version) to constraint the optimal solution. In this case, there is no cost related to its value. The second case deals with unknown due date which is a decision variables. It means that the decision maker not only takes sequencing and scheduling decisions to minimize the total weighted earliness–tardiness but also determines the optimal value of due date which is specified as controllable parameter.

Keywords

Schedule Problem Completion Time Idle Time Single Machine Schedule Problem Identical Parallel Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Ahuja, R.K., Orlin, J.B.: A fast and simple algorithm for the maximum flow problem. Operations Research 37, 748–759 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Alidaee, B., Panwalkar, S.S.: Single stage minimum absolute lateness problem with a common due date on non-identical machines. Journal of the Operational Research Society 44(1), 29–36 (1993)zbMATHGoogle Scholar
  3. 3.
    Bagchi, U., Sullivan, R.S., Chang, Y.L.: Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties about a common due-date. Naval Research Logistics 34(5), 739–751 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Baker, K.R., Scudder, G.D.: Sequencing with earliness and tardiness penalties: a review. Operations Research 38, 22–36 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Baptiste, P., Brucker, P.: Scheduling equal processing time jobs. In JY Leung (Ed.): Handbook of scheduling: algorithms, models and performance analysis, CRC Press, Boca Raton, FL, USA (2004)Google Scholar
  6. 6.
    Bruno, J., Coffman, Jr.E.G., Sethi, R.: Scheduling independent tasks to reduce mean finishing time. Communicaiton of the ACM 17, 382–387 (1974)Google Scholar
  7. 7.
    Cheng, T.C.E., Chen, Z.L.: Parallel-machine scheduling problems with earliness and tardiness penalties. Journal of the Operational Research Society 45, 685–695 (1994)zbMATHGoogle Scholar
  8. 8.
    Cole, R., Ost, K., Schirra, S.: Edge-coloring bipartite multigraphs in O(ElogD) time. Combinatorica 21, 5–12 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    De, P., Ghosh, J.B., Wells, C.E.: Due-date assignment and early/tardy scheduling on identical parallel machines. Naval Research Logistics 41(1), 17–32 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the Association for Computing Machinery 19, 248–264 (1972)zbMATHCrossRefGoogle Scholar
  11. 11.
    Emmons, H: Scheduling to a common due-date on parallel uniform processors. Naval Research Logistics Quarterly 34, 803–810 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Garey, M.R., Tarjan, R.E., Wilfong, G.T.: One-processor scheduling with assymmetric earliness and tardiness penalties. Mathematics of Operations Research 13, 330–348 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum-flow problem. Journal of the Association for Computing Machinery 35, 921–940 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Gordon, V., Proth, J.M., Chu, C.: A survey of the state-of-art of common due date assignment and scheduling research. European Journal of Operational Research 139, 1–25 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Gordon, V. S., Proth, J.-M., Strusevich, V. A.: Scheduling with due date assignment. In Handbook of scheduling, J.Y.T Leung eds., CRC Press, Boca Raton, FL, USA (2004)Google Scholar
  16. 16.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5, 287–326 (1979)Google Scholar
  17. 17.
    Hall, N.G., Kubiak, W., Sethi, S.P.: Earliness-tardiness scheduling problem, II: Deviation of completion times about a restrictive common due date. Operations Research 39, 847–856 (1991)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Hall, N.G., Posner, M.E.: Earliness-tardiness scheduling problem, I: Weighted deviation of completion times about a common due date. Operations Research 39,836–846 (1991)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Hoogeveen, J.A., Van de Velde, S.L.: Scheduling around a small common due date. European Journal of Operational Research 55(2), 237–242 (1991)zbMATHCrossRefGoogle Scholar
  20. 20.
    Hoogeveen, J.A., Oosterhout, H., Van de Velde, S.L.: New lower and upper bounds for scheduling around a small common due date. Operations research 42(1), 102–110 (1994)zbMATHCrossRefGoogle Scholar
  21. 21.
    Hopcroft, J.E., Karp, R.M.: An n 5 ∕ 2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing 2, 225–231 (1973)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Huynh Tuong, N., Soukhal, A.: Due dates assignment and JIT scheduling with equal-size jobs. European Journal of Operational Research 205(2), 280-289 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Huynh Tuong, N., Soukhal, A.: Some new polynomial cases in just-in-time scheduling problems with multiple due dates. In Proceeding of the 6th International Conference on Research, Innovation & Vision for the Future in Computing & Communications Technologies (RIVF’08), Ho Chi Minh (Vietnam), 36–41 (2008)Google Scholar
  24. 24.
    Huynh Tuong, N., Soukhal, A.: Ordonnancement juste-à-temps sur une seule machine avec date de fin souhaitée commune. 9ème Congrés de la Société Française de Recherche Opérationnelle et d’Aide à la Décision (ROADEF’08), Febuary 25–27, Clermont-Ferrand (France), 146–148 (2008)Google Scholar
  25. 25.
    Huynh Tuong, N., Soukhal, A.: Polynomial cases and PTAS for just-in-time scheduling on parallel machines around a common due date. 11th International Workshop on Project Management and Scheduling (PMS’08), April 28-30, Istanbul (Turkey), 152–155 (2008)Google Scholar
  26. 26.
    Józefowska, J.: Just-in-time Scheduling : Models and Algorithms for Computer and Manufacturing Systems. Springer-Verlag New York Inc. (2007)Google Scholar
  27. 27.
    Jurisch, B., Kubiak, W., Józefowska, J.: Algorithms for minclique scheduling problems. Discrete Applied Mathematics 72, 115–139 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Kaminsky, P., Hochbaum, D.: Due date quotation models and algorithms. In Handbook of scheduling, J.Y.T Leung eds., CRC Press, Boca Raton, FL, USA (2004)Google Scholar
  29. 29.
    Kanet, J.J.: Minimizing the average deviation of job completion times about a common due date. Naval Research Logistics Quarterly 28, 643–651 (1981)zbMATHCrossRefGoogle Scholar
  30. 30.
    Kao, M.-Y., Lam, T.-W., Sung, W.-K., Ting, H.-F.: A decomposition theorem for maximum weight bipartite matchings. SIAM Journal on Computing 31, 18–26 (2002)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Kovalyov, M.Y.: Soft and negotiable release and due dates in supply chain scheduling. Rapport de projet ORDO-COO-OC de GDR RO (2006)Google Scholar
  32. 32.
    Kovalyov, M.Y., Kubiak, W.: A fully polynomial approximation scheme for the weighted earliness-tardiness problem. Operations Research 47, 757–761 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Kubiak, W., Lou, S., Sethi, S.: Equivalence of mean flow time problems and mean absolute deviation problems. Operations Research Letters 9, 371–374 (1990)zbMATHCrossRefGoogle Scholar
  34. 34.
    Kuhn, W.H.: The Hungarian Method for the assignment problem. Naval Research Logistics Quarterly 2, 83–97 (1955)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Mosheiov, G., Yovel, U.: Minimizing weighted earliness–tardiness and due date cost with unit processing–time jobs. European Journal of Operations Research 172, 528–544 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Mosheiov, G., Sarig, A.: Due-date assignment on uniform machines. European Journal of Operational Research 193(1), 49–58 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  37. 37.
    Panwalkar, S.S., Smith, M.L., Seidmann, A.: Common due-date assignment to minimize total penalty for the one machine scheduling problem. Operations Research 30, 391–399 (1982)zbMATHCrossRefGoogle Scholar
  38. 38.
    Smith, W.E.: Various optimizers for single-stage production. Naval Research Logistics Quarterly 3, 59–66 (1956)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Sourd, F.: New exact algorithms for one-machine earliness-tardiness scheduling. INFORMS Journal of Computing 21(1), 167–175 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Sun, H., Wang, G.: Parallel machine earliness and tardiness scheduling with proportional weights. Computers & Operations Research 30(5), 801–808 (2003)zbMATHCrossRefGoogle Scholar
  41. 41.
    T’kindt, V., Billaut, J.-C.: Multicriteria Scheduling: Theory, Models and Algorithms. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  42. 42.
    Webster, S.: The complexity of scheduling job families about a common due date. Operations Research Letters 20(2), 65–74 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    Xiao, W.-Q., Li, C.-L.: Approximation algorithms for common due date assignment and job scheduling on parallel machines. IIE Transactions 34(5), 467–477 (2002)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Yuan, J.: The NP-hardness of the single machine common due date weighted tardiness problem. Systems Science and Mathematical Sciences 5, 328–333 (1992)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Laboratoire d’InformatiqueUniversité François RabelaisToursFrance
  2. 2.Faculty of Computer Science and EngineeringUniversity of Technology of Ho Chi Minh CityHo Chi Minh CityVietnam

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