Output Rate Variation Problem: Some Heuristic Paradigms and Dynamic Programming

  • Gyan Bahadur ThapaEmail author
  • Sergei Silvestrov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 179)


The output rate variation problem stands as one of the important research directions in the area of multi-level just-in-time production system. In this short survey, we present the mathematical models of the problem followed by consideration of its NP-hardness. We further carry out the brief review of heuristic approaches that are devised to solve the problem. The dynamic programming approach and pegging assumption are also briefly discussed. The pegging assumption reduces the multi-level problem into weighted single-level problem. A couple of the open problems regarding ORVP are listed at the end.


Just-in-time Objectives Constraints Heuristics Dynamic programming 


  1. 1.
    Bautista, J., Companys, R., Corominas, A.: Heuristics and exact algorithms for solving the Monden problem. Eur. J. Oper. Res. 88, 101–113 (1996)CrossRefzbMATHGoogle Scholar
  2. 2.
    Dhamala, T.N., Kubiak, W.: A brief survey of just-in-time sequencing for mixed-model systems. Int. J. Oper. Res. 2(2), 38–47 (2005)zbMATHGoogle Scholar
  3. 3.
    Dhamala, T.N., Thapa, G.B., Yu, H.: An efficient frontier for sum deviation just-in-time sequencing problem in mixed-model systems via apportionment. Int. J. Autom. Comput. 9(1), 87–97 (2012)CrossRefGoogle Scholar
  4. 4.
    Duplaga, E., Bragg, D.: Mixed-model assembly line sequencing heuristics for smoothing component parts usage: a comparative analysis. Int. J. Prod. Res. 36(8), 2209–2224 (1998)CrossRefzbMATHGoogle Scholar
  5. 5.
    Fliedner, M., Boysen, N., Scholl, A.: Solving symmetric mixed-model multi-level just-in-time scheduling problems. Discret. Appl. Math. 158, 222–231 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., New York, USA (1979)zbMATHGoogle Scholar
  7. 7.
    Garey, M.R., Johnson, D.S.: Complexity results for multiprocessor scheduling under resource constraints. SIAM J. Comput. 4(4), 397–411 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Goldstein, T., Miltenburg, J.: The effects of pegging in the scheduling of just-in-time production systems, Working paper, 294, Faculty of Business, McMaster University, Hamilton, Ontario (1998)Google Scholar
  9. 9.
    Khashouie, G.M.: Sequencing Mixed-model Assembly Lines in Just-in-time Production Systems, Department of Systems Engineering, Brunel University, UK (2003)Google Scholar
  10. 10.
    Korgaonker, M.G.: Just in Time Manufacturing. Macmillan India Ltd. (1992)Google Scholar
  11. 11.
    Kotani, S., Ito, T., Ohno, K.: Sequencing problem for a mixed-model assembly line in the Toyota production system. Int. J. Prod. Res. 42(23), 4955–4974 (2004)CrossRefzbMATHGoogle Scholar
  12. 12.
    Kubiak, W.: Completion Time Variance Minimization on Single Machine is Difficult, Working paper, 92-6, Memorial University of Newfoundland (1992)Google Scholar
  13. 13.
    Kubiak, W.: Minimizing variation of production rates in just-in-time systems: a survey. Eur. J. Oper. Res. 66, 259–271 (1993)CrossRefzbMATHGoogle Scholar
  14. 14.
    Kubiak, W., Sethi, S.: A note on level schedules for mixed-model assembly lines in just-in-time production systems. Manag. Sci. 37(1), 121–122 (1991)CrossRefzbMATHGoogle Scholar
  15. 15.
    Kubiak, W., Sethi, S.: Optimal just-in-time schedules for flexible transfer lines. Int. J. Flex. Manuf. Syst. 6, 137–154 (1994)CrossRefGoogle Scholar
  16. 16.
    Kubiak, W., Steiner, G., Yeomans, J.: Optimal level schedules for mixed-model multi-level just-in-time assembly systems. Ann. Oper. Res. 69, 241–259 (1997)CrossRefzbMATHGoogle Scholar
  17. 17.
    Lenstra, J.K., Rinnooy, A.H.G.: Computational complexity of discrete optimization problems. Ann. Discret. Math. 4, 121–140 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Miltenburg, J., Sinnamon, G.: Scheduling mixed-model multi-level just-in-time production systems. Int. J. Prod. Res. 27(9), 1487–1509 (1989)CrossRefGoogle Scholar
  19. 19.
    Miltenburg, J., Steiner, G., Yeomans, J.: A dynamic programming algorithm for scheduling mixed-model just-in-time production systems. Math. Comput. Model. 13(3), 57–66 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Monden, Y.: Toyota Production System; Practical Approach to Production Management. Industrial Engineering and Management Press, Norcross, GA (1983)Google Scholar
  21. 21.
    Okamura, K., Yamashina, H.: A heuristic algorithm for the assembly line model-mix sequencing problem to minimize the risk of stopping the conveyor. Int. J. Prod. Res. 17, 233–241 (1979)CrossRefGoogle Scholar
  22. 22.
    Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice Hall of India (2003)Google Scholar
  23. 23.
    Steiner, G., Yeomans, J.: Optimal level schedules in mixed-model multi-level JIT assembly systems with pegging. Eur. J. Oper. Res. 95, 38–52 (1996)CrossRefzbMATHGoogle Scholar
  24. 24.
    Sumichrast, R., Russell, R.: Evaluating mixed-model assembly line sequencing heuristics for just-in-time production systems. J. Oper. Manag. 9(3), 371–390 (1990)CrossRefGoogle Scholar
  25. 25.
    Sumichrast, R., Russell, R., Taylor, B.: A comparative analysis of sequencing procedures for mixed-model assembly lines in a just-in-time production system. Int. J. Prod. Res. 30(1), 199–214 (1992)CrossRefzbMATHGoogle Scholar
  26. 26.
    Thapa, G.B.: Computational complexity and integer programming. Mathematical Sciences and Applications, Kathmandu University, Nepal 60–70 (2006)Google Scholar
  27. 27.
    Thapa, G. B.: Optimization of Just-in-time Sequencing Problems and Supply Chain Logistics, Ph.D. Thesis, Division of Applied Mathematics, Mälardalen University, Sweden (2015)Google Scholar
  28. 28.
    Thapa, G.B., Dhamala, T.N.: Just-in-time sequencing in mixed-model production systems relating with fair representation in apportionment theory. Nepali Math. Sci. Rep. 29(1&2), 29–68 (2009)Google Scholar
  29. 29.
    Thapa, G.B., Silvestrov, S.: Heuristics for single-level just-in-time sequencing problem. J. Inst. Sci. Technol. 18(2), 125–131 (2013)Google Scholar
  30. 30.
    Thapa, G.B., Silvestrov, S.: Supply chain logistics in multi-level just-in-time production sequencing problems. J. Inst. Eng. 11(1), 91–100 (2015)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Pulchowk Campus, Institute of EngineeringTribhuvan UniversityKathmanduNepal
  2. 2.Division of Applied Mathematics, School of Education, Culture and CommunicationMälardalen UniversityVästeråsSweden

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