Advertisement

Basic Multi-Item, Single-Location Inventory Model

  • Geert-Jan van Houtum
  • Bram Kranenburg
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 227)

Abstract

Chapter  2 is devoted to basic multi-item, single-location inventory models for spare parts. These models constitute the basis for all other chapters. We start with a basic model with backordered demands and a service level constraint in terms of the aggregate mean number of backordered demands. This measure is directly related to system availability. For the minimization of the investment in spare parts under this service level constraint, we formulate a greedy heuristic, which is shown to generate efficient solutions for a directly related two-objective optimization problem. Next, we discuss Lagrangian relaxation and Dantzig-Wolfe decomposition as alternative optimization techniques, we explain the item approach, and we show how to deal with alternative service measures. Finally, we describe a variant of the model with emergency shipments and an aggregate mean waiting time constraint, and multiple other extensions are given.

References

  1. 1.
    Axsäter, S.: Inventory Control, 2nd edn. Springer, New York (2006) Google Scholar
  2. 2.
    Bijvank, M., Vis, I.F.A.: Lost-sales inventory theory: a review. Eur. J. Oper. Res. 215, 1–13 (2011) Google Scholar
  3. 3.
    Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8, 101–111 (1960) Google Scholar
  4. 4.
    Everett, H. III: Generalized lagrange multiplier method for solving problems of optimum allocation of resources. Oper. Res. 11, 399–417 (1963) Google Scholar
  5. 5.
    Feeney, G.J., Sherbrooke, C.C.: The (s − 1, s) inventory policy under compound Poisson demand. Manag. Sci. 12, 391–411 (1966) Google Scholar
  6. 6.
    Fisher, M.L.: The Lagrangian relaxation method for solving integer programming problems. Manag. Sci. 27, 1–18 (1981) Google Scholar
  7. 7.
    Fisher, M.L.: An application oriented guide to Lagrangian relaxation. Interfaces 15, 10–21 (1985) Google Scholar
  8. 8.
    Fox, B.: Discrete optimization via marginal analysis. Manag. Sci. 13, 210–216 (1966) Google Scholar
  9. 9.
    Karush, W.: A queueing model for an inventory problem. Oper. Res. 5, 693–703 (1957) Google Scholar
  10. 10.
    Kranenburg, A.A.: Spare parts inventory control under system availability constraints. Ph.D. thesis, Eindhoven University of Technology (2006).http://w3.tue.nl/en/services/library/digilib/publications_from_tue/dissertations/
  11. 11.
    Kranenburg, A.A., Van Houtum, G.J.: Cost optimization in the (S − 1, S) lost sales inventory model with multiple demand classes. OR Lett. 35, 493–502 (2007) Google Scholar
  12. 12.
    Little, J.D.C.: A proof of the queuing formula L = λ W. Oper. Res. 9, 383–387 (1961) Google Scholar
  13. 13.
    Palm, C.: Analysis of the Erlang traffic formula for busy-signal arrangements. Ericsson Technics 4, 204–212 (1938) Google Scholar
  14. 14.
    Porteus, E.L.: Foundations of Stochastic Inventory Theory. Stanford University Press, Stanford (2002) Google Scholar
  15. 15.
    Rustenburg, W.D.: A system approach to budget-constrained spare parts management. Ph.D. thesis, Eindhoven University of Technology (2000). http://w3.tue.nl/en/services/library/digilib/publications_from_tue/dissertations/
  16. 16.
    Rustenburg, W.D., Van Houtum, G.J., Zijm, W.H.M.: Spare parts management at complex technology-based organizations: an agenda for research. Int. J. Prod. Econ. 71, 177–193 (2001) Google Scholar
  17. 17.
    Sherbrooke, C.C.: METRIC: a multi-echelon technique for recoverable item control. Oper. Res. 16, 122–141 (1968)Google Scholar
  18. 18.
    Sherbrooke, C.C.: Optimal Inventory Modeling of Systems: Multi-echelon Techniques. Kluwer Academic, Boston/Dordrecht/London (2004)Google Scholar
  19. 19.
    Thonemann, U.W., Brown, A.O., Hausman, W.H.: Easy quantification of improved spare parts inventory policies. Manag. Sci. 48, 1213–1225 (2002) Google Scholar
  20. 20.
    Van Houtum, G.J., Hoen, K.M.R.: Single-location, multi-item inventory models for spare parts. Lecture notes, Eindhoven University of Technology (2008) Google Scholar
  21. 21.
    Van Jaarsveld, W., Dekker, R.,: Spare parts stock control for redundant systems using reliability centered maintenance data. Reliab. Eng. Syst. Saf. 96, 1576–1586 (2011) Google Scholar
  22. 22.
    Wong, H., Kranenburg, A.A., Van Houtum, G.J., Cattrysse, D.: Efficient heuristics for two-echelon spare parts inventory systems with an aggregate mean waiting time constraint per local warehouse. OR Spectr. 29, 699–722 (2007) Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Geert-Jan van Houtum
    • 1
  • Bram Kranenburg
    • 2
  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Consultants in Quantitative Methods CQM B.V.EindhovenThe Netherlands

Personalised recommendations