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Two-Echelon System

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

Abstract

Chapter  6 is devoted to a multi-item, two-echelon spare parts inventory system. The system consists of a central warehouse and multiple local warehouses, and there is a target for the aggregate mean waiting time per local warehouse. We describe an exact recursion for the evaluation of a given basestock policy, leading to an exact evaluation method, and we give approximate evaluation methods based on two-moment and one-moment fits, respectively. Next, we describe a greedy heuristic and the Dantzig-Wolfe heuristic, together with the Dantzig-Wolfe lower bound on the optimal total costs. Both heuristics can be combined with a local search, which gives four heuristics in total. The quality of the heuristics, all based on exact evaluations, is tested in a computational experiment. The greedy heuristic (without local search) performs most satisfactorily. It is accurate, easy to implement, and the computational requirements are limited. Its computational efficiency can be increased by using approximate evaluation based on two-moment fits. That results in a good feasible algorithm for real-life cases with many SKU’s and local warehouses.

References

  1. 1.
    Adan, I.J.B.F., Van Eenige, M.J.A., Resing, J.A.C.: Fitting discrete distributions on the first two moments. Probab. Eng. Inf. Sci. 9, 623–632 (1996) Google Scholar
  2. 2.
    Axsäter, S.: Simple solution procedures for a class of two-echelon inventory systems. Oper. Res. 38, 64–69 (1990)CrossRefGoogle Scholar
  3. 3.
    Axsäter, S.: Continuous review policies for multi-level inventory systems with stochastic demand. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P.H. (eds.) Logistics of Production and Inventory, Chap. 10. North-Holland, New York (1993)Google Scholar
  4. 4.
    Caggiano, K.E., Jackson, P.L., Muckstadt, J.A., Rappold, J.A.: Optimizing service parst inventory in a multiechelon, multi-item supply chain with time-based customer service-level agreements. Oper. Res. 55, 303–318 (2007) Google Scholar
  5. 5.
    Caglar, D., Li, C.L., Simchi-Levi, D.: Two-echelon spare parts inventory system subject to a service constraint. IIE Trans. 36, 655–666 (2004) Google Scholar
  6. 6.
    Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8, 101–111 (1960) Google Scholar
  7. 7.
    Graves, S.C.: A multi-echelon inventory model for a repairable item with one-for-one replenishment. Manag. Sci. 31, 1247–1256 (1985) Google Scholar
  8. 8.
    Hopp, W.J., Zhang, R.Q., Spearman, M.L.: An easily implementable hierarchical heuristic for a two-echelon spare parts distribution system. IIE Trans. 31, 977–988 (1999) Google Scholar
  9. 9.
    Kruse, K.C.: An exact N echelon inventory model: the simple Simon method. U.S. Army Research Office, Technical Report TR 79-2 (1979) Google Scholar
  10. 10.
    Muckstadt, J.A., Thomas, L.J.: Are multi-echelon inventory methods worth implementing in systems with low-demand-rate items? Manag. Sci. 26, 483–494 (1980) Google Scholar
  11. 11.
    Özkan, E., Van Houtum, G.J., Serin, Y.: A new approximate evaluation method for two-echelon inventory systems with emergency shipments. Ann. Oper. Res. 224, 147–169 (2015) Google Scholar
  12. 12.
    Palm, C.: Analysis of the Erlang traffic formula for busy-signal arrangements. Ericsson Tech. 4, 204–212 (1938) Google Scholar
  13. 13.
    Rustenburg, W.D., Van Houtum, G.J., Zijm, W.H.M.: Exact and approximate analysis of multi-echelon, multi-indenture spare parts systems with commonality. In: Shanthikumar, J.G., Yao, D.D., Zijm, W.H.M. (eds.) Stochastic Modeling and Optimization of Manufacturing Systems and Supply Chains, pp. 143–176. Kluwer Academic, Boston/Dordrecht/London (2003) Google Scholar
  14. 14.
    Sherbrooke, C.C.: METRIC: A multi-echelon technique for recoverable item control. Oper. Res. 16, 122–141 (1968) Google Scholar
  15. 15.
    Sherbrooke, C.C.: Optimal inventory modeling of systems: multi-echelon techniques. Kluwer Academic, Boston/Dordrecht/London (2004)Google Scholar
  16. 16.
    Simon, R.M.: Stationary properties of a two-echelon inventory model for low demand items. Oper. Res. 19, 761–773 (1971) Google Scholar
  17. 17.
    Slay, F.M.: VARI-METRIC: an approach to modeling multi-echelon resupply when the demand process is Poisson with a Gamma prior. Report AF301-3, Logistics Management Institute, Washington, DC (1984) Google Scholar
  18. 18.
    Stenius, O., Karaarslan, A.G., Marklund, J., De Kok, A.G.: Exact analysis of divergent inventory systems with time-based shipment consolidation and compound Poisson demand. Working paper, Lund University (2014) Google Scholar
  19. 19.
    Topan, E., Bayindir, Z.P., Tan, T.: An exact solution procedure for multi-item two-echelon spare parts inventory control problem with batch ordering in the central warehouse. Oper. Res. Lett. 38, 454–461 (2010) Google Scholar
  20. 20.
    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)1 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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