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Service Differentiation

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

Abstract

As in Chaps.  2 and 3, we analyze a multi-item, single-location inventory model. In this chapter, we assume that the installed base consists of machines of the same machine type, but these machine are classified in multiple machine groups, each with their own target for the aggregate mean waiting time. We again assume that emergency shipments are being used when stockouts occur. For the inventory control of the spare parts, we assume critical level policies. We apply Dantzig-Wolfe decomposition, which gives both a Dantzig-Wolfe heuristic and a corresponding lower bound for the optimal costs, and we describe exact solution procedures for the underlying, single-item inventory problem. In a computational experiment, we show that the Dantzig-Wolfe heuristic performs well, and we compare the use of critical level policies to a so-called round-up policy. The latter comparison is also made in a case study at ASML.

Keywords

Critical Level Spare Part Fill Rate Demand Rate Restrict Master Problem 
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.
    Alvarez, E.M., Van der Heijden, M.C., Zijm, W.H.M.: The selective use of emergency shipments for service-contract differentiation. Int. J. Prod. Econ. 143, 518–526 (2013) Google Scholar
  2. 2.
    Barbour, A.D.: Networks of queues and the method of stages. Adv. Appl. Probab. 8, 584–591 (1976) Google Scholar
  3. 3.
    Baskett, F., Chandy, K.M., Muntz, R.R., Palacios, F.G.: Open, closed, and mixed networks of queues with different classes of customers. J. Assoc. Comput. Mach. 22, 248–260 (1975) Google Scholar
  4. 4.
    Cohen, M.A., Kleindorfer, P.R., Lee, H.L.: Near-optimal service constrained stocking policies for spare parts. Oper. Res. 37, 104–117 (1989) Google Scholar
  5. 5.
    Cohen, M.A., Kleindorfer, P.R., Lee, H.L., Pyke, D.F.: Multi-item service constrained (s, S) policies for spare parts logistics systems. Nav. Res. Logist. 39, 561–577 (1992)CrossRefGoogle Scholar
  6. 6.
    Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8, 101–111 (1960) Google Scholar
  7. 7.
    Dekker, R., Hill, R.M., Kleijn, M.J., Teunter, R.H.: On the (S − 1, S) lost sales inventory model with priority demand classes. Nav. Res. Logist. 49, 593–610 (2002) Google Scholar
  8. 8.
    Deshpande, V., Cohen, M.A., Donohue, K.: A threshold inventory rationing policy for service-differentiated demand classes. Manag. Sci. 49, 683–703 (2003) Google Scholar
  9. 9.
    De Véricourt, F., Karaesmen, F., Dallery, Y.: Optimal stock allocation for a capacitated supply system. Manag. Sci. 48, 1486–1501 (2002) Google Scholar
  10. 10.
    Enders, P., Adan, I.J.B.F., Scheller-Wolf, A.A., Van Houtum, G.J.: Inventory rationing for a system with heterogeneous customer classes. Flex. Serv. Manuf. J. 26, 344–386 (2014) Google Scholar
  11. 11.
    Gnedenko, B.V., Kovalenko, I.N.: Introduction to Queueing Theory. Israel Program for Scientific Translations, Jerusalem (1968) Google Scholar
  12. 12.
    Ha, A.Y.: Inventory rationing in a make-to-stock production system with several demand classes and lost sales. Manag. Sci. 43, 1093–1103 (1997) Google Scholar
  13. 13.
    Karush, W.: A queueing model for an inventory problem. Oper. Res. 5, 693–703 (1957) Google Scholar
  14. 14.
    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
  15. 15.
    Kranenburg, A.A., Van Houtum, G.J.: Service differentiation in spare parts inventory management. J. Oper. Res. Soc. 59, 946–955 (2008)1 Google Scholar
  16. 16.
    Melchiors, P., Dekker, R., Kleijn, M.J.: Inventory rationing in an (s, Q) inventory model with lost sales and two demand classes. J. Oper. Res. Soc. 51, 111–122 (2000) Google Scholar
  17. 17.
    Miller, B.: A queueing reward system with several customer classes. Manag. Sci. 16, 234–245 (1969) Google Scholar
  18. 18.
    Möllering, K.T., Thonemann, U.W.: An optimal critical level policy for inventory systems with two demand classes. Nav. Res. Logist. 55, 632–642 (2008) Google Scholar
  19. 19.
    Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley-Interscience, New York (1994) Google Scholar
  20. 20.
    Topkis, D.M.: Optimal ordering and rationing policies in a nonstationary dynamic inventory model with n demand classes. Manag. Sci. 15, 160–176 (1968) Google Scholar
  21. 21.
    Van Jaarsveld, W.L.: Maintenance centered service parts inventory control. Ph.D. thesis, Erasmus University (2013). http://repub.eur.nl/dissertations
  22. 22.
    Veinott, A.F.: Optimal policy in a dynamic, single product, non-stationary inventory model with several demand classes. Oper. Res. 13, 761–778 (1965) Google Scholar
  23. 23.
    Wolff, R.W.: Stochastic Modeling and the Theory of Queues. Prentice-Hall International, London (1989) 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

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