Abstract

In this chapter dynamic lot sizing problems with random demands are discussed. Several approaches to handle uncertainty are presented. Single-item problems as well as multi-item lot sizing problems with limited capacities of a scarce resource are considered. Thereby the focus is on numerically tractable solution approaches.

References

  1. 1.
    Askin, R. (1981). A procedure for production lot sizing with probabilistic dynamic demand. AIIE Transactions13, 132–137.CrossRefGoogle Scholar
  2. 2.
    Banerjee, A., & Paul, A. (2005). Average fill rate and horizon length. Operations Research Letters33, 525–530.CrossRefGoogle Scholar
  3. 3.
    Bitran, G., & Yanasse, H. (1984). Deterministic approximations to stochastic production problems. Operations Research32, 999–1018.CrossRefGoogle Scholar
  4. 4.
    Bollapragada, S., & Morton, T. (1999). Simple heuristic for computing nonstationary (s, S) policies. Operations Research47, 576–584.CrossRefGoogle Scholar
  5. 5.
    Bookbinder, J., & Tan, J.-Y. (1988). Strategies for the probabilistic lot-sizing problem with service-level constraints. Management Science34, 1096–1108.CrossRefGoogle Scholar
  6. 6.
    Bradley, S., Hax, A., & Magnanti, T. (1977). Applied mathematical programming. Reading: Addison-Wesley.Google Scholar
  7. 7.
    Buschkühl, L., Sahling, F., Helber, S., & Tempelmeier, H. (2010). Dynamic capacitated lotsizing problems – a classification and review of solution approaches. OR Spectrum32(2), 231–261.CrossRefGoogle Scholar
  8. 8.
    Chen, F., & Krass, D. (2001). Inventory models with minimal service level constraints. European Journal of Operational Research134, 120–140.CrossRefGoogle Scholar
  9. 9.
    Chen, J., Lin, D., & Thomas, D. (2003). On the single item fill rate for a finite horizon. Operations Research Letters31, 119–123.CrossRefGoogle Scholar
  10. 10.
    Guan, Y., Ahmed, S., Miller, A., & Nemhauser, G. (2006). On formulations of the stochastic uncapacitated lot-sizing problem. Operations Research Letters34, 241–250.CrossRefGoogle Scholar
  11. 11.
    Helber, S., Sahling, F., & Schimmelpfeng, K. (2012). Dynamic capacitated lot sizing with random demand and dynamic safety stocks. OR Spectrum, 38, 75–105.Google Scholar
  12. 12.
    Herpers, S. (2009). Dynamische Losgrößenplanung bei stochastischer Nachfrage. Köln: Kölner Wissenschaftsverlag.Google Scholar
  13. 13.
    Iglehart, D. (1963). Dynamic programming and stationary analysis of inventory problems. In H. Scarf, D. Gilford, & M. Shelley (Eds.), Multistage inventory models and techniques. Stanford: Stanford University Press.Google Scholar
  14. 14.
    Lasserre, J., Bes, C., & Roubellat, F. (1985). The stochastic discrete dynamic lot size problem: An open-loop solution. Operations Research33, 684–689.CrossRefGoogle Scholar
  15. 15.
    Maes, J., & Van Wassenhove, L. (1986). A simple heuristic for the multi item single level capacitated lotsizing problem. OR Letters4, 265–273.Google Scholar
  16. 16.
    Manne, A. (1958). Programming of economic lot sizes. Management Science4, 115–135.CrossRefGoogle Scholar
  17. 17.
    Pochet, Y., & Wolsey, L. (2006). Production planning using mixed-integer programming. New York: Springer.Google Scholar
  18. 18.
    Rossi, R., Tarim, S., Hnich, B., & Prestwich, S. (2008). A global chance-constraint for stochastic inventory systems under service levels constraints. Constraints13, 490–517.CrossRefGoogle Scholar
  19. 19.
    Sahling, F., Buschkühl, L., Helber, S., & Tempelmeier, H. (2009). Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic. Computers & Operations Research36, 2546–2553.CrossRefGoogle Scholar
  20. 20.
    Scarf, H. (1959). The optimality of (S, s) policies in the dynamic inventory problem. In K. Arrow, S. Karlin, & P. Suppes (Eds.), Mathematical methods in the social sciences (pp. 196–202). Stanford: Stanford University Press.Google Scholar
  21. 21.
    Sox, C. (1997). Dynamic lot sizing with random demand and non-stationary costs. Operations Research Letters20, 155–164.CrossRefGoogle Scholar
  22. 22.
    Sox, C., Jackson, P., Bowman, A., & Muckstadt, J. (1999). A review of the stochastic lot scheduling problem. International Journal of Production Economics62, 181–200.CrossRefGoogle Scholar
  23. 23.
    Tarim, S., & Kingsman, B. (2004). The stochastic dynamic production/inventory lot-sizing problem with service-level constraints. International Journal of Production Economics88, 105–119.CrossRefGoogle Scholar
  24. 24.
    Tarim, S., & Kingsman, B. (2006). Modelling and computing \(({R}^{n},{S}^{n})\) policies for inventory systems with non-stationary stochastic demands. European Journal of Operational Research174, 581–599.CrossRefGoogle Scholar
  25. 25.
    Tempelmeier, H. (2007). On the stochastic uncapacitated dynamic single-item lotsizing problem with service level constraints. European Journal of Operational Research181, 184–194.CrossRefGoogle Scholar
  26. 26.
    Tempelmeier, H. (2011). A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint. Omega39, 627–633.CrossRefGoogle Scholar
  27. 27.
    Tempelmeier, H. (2011). Inventory management in supply networks – problems, models, solutions (2nd ed.). Norderstedt: Books on Demand.Google Scholar
  28. 28.
    Tempelmeier, H., & Herpers, S. (2010). ABCβ- a heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint. International Journal of Production Research48, 5181–5193.CrossRefGoogle Scholar
  29. 29.
    Tempelmeier, H., & Herpers, S. (2011). Dynamic uncapacitated lot sizing with random demand under a fillrate constraint. European Journal of Operational Research212(3), 497–507.CrossRefGoogle Scholar
  30. 30.
    Tempelmeier, H., & Hilger, T. (2013). Linear programming models for the stochastic dynamic capacitated lot sizing problem. Technical report, University of Cologne, Department of Supply Chain Management and Production, Cologne, Germany.Google Scholar
  31. 31.
    Thomas, D. (2005). Measuring item fill-rate performance in a finite horizon. Manufacturing & Service Operations Management7, 74–80.CrossRefGoogle Scholar
  32. 32.
    Tunc, H., Kilic, O., Tarim, S. A., & Eksioglu, B. (2011). The cost of using stationary inventory policies when demand is non-stationary. Omega39, 410–415.CrossRefGoogle Scholar
  33. 33.
    Vargas, V. (2009). An optimal solution for the stochastic version of the Wagner-Whitin dynamic lot-size model. European Journal of Operational Research198, 447–451.CrossRefGoogle Scholar
  34. 34.
    Wagner, H., & Whitin, T. (1958). Dynamic version of the economic lot size model. Management Science5, 89–96.CrossRefGoogle Scholar
  35. 35.
    Winands, E., Adan, I., & van Houtum, G. (2011). The stochastic economic lot scheduling problem: A survey. European Journal of Operational Research210, 1–9.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Supply Chain Management and ProductionUniversity of CologneCologneGermany

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