Just-in-Time Scheduling in Modern Mass Production Environment

  • Joanna JózefowskaEmail author
Part of the Springer Optimization and Its Applications book series (SOIA, volume 60)


The main goal of just-in-time production planing is the reduction of the in-process inventory level. This goal may be achieved by completing the items as close to their further processing (or shipment) dates as possible. In the mass production environment, it is too costly to define and control due dates for individual items. Instead, the model proposed in Toyota is applied that assumes monitoring the actual product rate of particular products. The objective is to construct schedules with minimum deviation from an ideal product rate. In the approach aimed at minimization of the Product Rate Variation, the control process concentrates on product types, not individual items. In this chapter, we discuss the PRV model and scheduling algorithms developed to solve this problem with two types of objectives: to minimize the total or maximum deviation from the ideal product rate. We present algorithms proposed in the context of the just-in-time production scheduling as well as in other areas, adopted later to solve the PRV problem. One of the most interesting problems discussed in this context is the apportionment problem. Originally, the PRV problem was defined as a single machine scheduling problem. We show that some algorithms can be generalized to solve the parallel-machine scheduling problem as well.


Schedule Problem Assembly Line Divisor Function Hamilton Method Divisor Method 
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.


  1. 1.
    Balinski, M., Ramirez, V.: Parametric methods of apportionment, rounding and production. Mathematical Social Sciences 37(2), 107–122 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Balinski, M., Shahidi, N.: A simple approach to the product rate variation problem via axiomatics. Operations Research Letters 22(4-5), 129–135 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Balinski, M., Young, H.: The quota method of apportionment. The American Mathematical Monthly 82(7), 701–730 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Balinski, M., Young, H.: Fair Representation: Meeting the Ideal of One Man, One Vote. Yale University Press (1982)Google Scholar
  5. 5.
    Bautista, J., Companys, R., Corominas, A.: A note on the relation between the product rate variation (prv) problem and the apportionment problem. Journal of the Operational Research Society 47(11), 1410–1414 (1996)zbMATHGoogle Scholar
  6. 6.
    Brauner, N., Crama, Y.: The maximum deviation just-in-time scheduling problem. Discrete Applied Mathematics 134, 25–50 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Garey, M.R., Tarjan, R.E., Wilfong, G.T.: One-processor scheduling with symmetric earliness and tardiness penalties. Mathematics of Operations Research 13, 330–348 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Inman, R.R., Bulfin, R.L.: Sequencing jit mixed-model assembly lines. Management Science 37, 901–904 (1991)zbMATHCrossRefGoogle Scholar
  9. 9.
    Józefowska, J.: Models and Algorithms for Computer and Manufacturing Systems. Springer, New York (2007)zbMATHGoogle Scholar
  10. 10.
    Józefowska, J., Józefowski, L., Kubiak, W.: Characterization of just in time sequencing via apportionment. In: H. Yan, G. Yin, Q. Zhang (eds.) Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, International Series in Operations Research & Management Science, vol. 94, pp. 175–200. Springer US (2006)Google Scholar
  11. 11.
    Józefowska, J., Józefowski, L., Kubiak, W.: Apportionment methods and the liu-layland problem. European Journal of Operational Research 193(3), 857–864 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Józefowska, J., Józefowski, L., Kubiak, W.: Dynamic divisor-based resource scheduling algorithm. In: Proceedings of the 12th International Workshop on Project Management and Scheduling. Tours, France (2010)Google Scholar
  13. 13.
    Kubiak, W.: Proportional Optimization and Fairness, International Series in Operations Research & Management Science, vol. 127. Springer, New York (2009)Google Scholar
  14. 14.
    Kubiak, W., Sethi, S.: A note on “level schedules for mixed-model assembly lines in just-in-time production systems”. Management Science 37(1), 121–122 (1991)zbMATHCrossRefGoogle Scholar
  15. 15.
    Kubiak, W., Sethi, S.P.: Optimal just-in-time schedules for flexible transfer lines. International Journal of Flexible Manufacturing Systems 6, 137–154 (1994)CrossRefGoogle Scholar
  16. 16.
    Miltenburg, J.: Level schedules for mixed-model assembly lines in just-in-time production systems. Management Science 35(2), 192–207 (1989)zbMATHCrossRefGoogle Scholar
  17. 17.
    Monden, Y.: Toyota Production Systems. Industrial Engineering and Management Press, Norcross (1983)Google Scholar
  18. 18.
    Okamura, K., Yamashina, H.: A heuristic algorithm for the assembly line model-mix sequencing problem to minimize the risk of stopping the conveyor. Journal of Production Research 17(3), 233–247 (1979)CrossRefGoogle Scholar
  19. 19.
    Steiner, G., Yeomans, S.: Level schedules for mixed-model, just-in-time processes. Management Science 39, 728–735 (1993)zbMATHCrossRefGoogle Scholar
  20. 20.
    Still, J.W.: A class of new methods for congressional apportionment. SIAM Journal on Applied Mathematics 37(2), 401–418 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Tijdeman, R.: The chairman assignment problem. Discrete Mathematics 32(3), 323–330 (1980)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Poznań University of TechnologyPoznańPoland

Personalised recommendations