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On the relationship between cost and service models for general inventory systems

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  • G. J. Van Houtum
  • W. H. M. Zijm

Abstract

In this paper, we present a systematic overview of possible relations between cost and service models for fairly general single‐ and multi‐stage inventory systems. In particular, we relate various types of penalty costs in pure cost models to equivalent types of service measures in service models. We show how an optimal policy for a service model may be obtained from cost‐optimal policies in a related pure cost model. Pure cost models have been studied extensively in the literature. By our results it seems possible to transform many of the known optimal solutions for pure cost models to service models, which are more appropriate from a practical point of view. A number of examples are discussed to show the generality and the possibly far reaching consequences of the results.

Suggested Citation

  • G. J. Van Houtum & W. H. M. Zijm, 2000. "On the relationship between cost and service models for general inventory systems," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(2), pages 127-147, July.
    • Handle: RePEc:bla:stanee:v:54:y:2000:i:2:p:127-147
    DOI: 10.1111/1467-9574.00132
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    Cited by:

    1. (Ai-Chih) Chang, Jasmine & Lu, Haibing & (Junmin) Shi, Jim, 2019. "Stockout risk of production-inventory systems with compound Poisson demands," Omega, Elsevier, vol. 83(C), pages 181-198.
    2. Klosterhalfen, Steffen T. & Willems, Sean P. & Dittmar, Daniel, 2023. "Safety stock placement in supply chains with expediting," European Journal of Operational Research, Elsevier, vol. 307(2), pages 745-757.
    3. Topan, E. & Eruguz, A.S. & Ma, W. & van der Heijden, M.C. & Dekker, R., 2020. "A review of operational spare parts service logistics in service control towers," European Journal of Operational Research, Elsevier, vol. 282(2), pages 401-414.
    4. Bora Kat & Zeynep Avṣar, 2011. "Using aggregate fill rate for dynamic scheduling of multi-class systems," Annals of Operations Research, Springer, vol. 182(1), pages 87-117, January.
    5. Wong, H. & van Houtum, G.J. & Cattrysse, D. & Oudheusden, D. Van, 2006. "Multi-item spare parts systems with lateral transshipments and waiting time constraints," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1071-1093, June.
    6. Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.
    7. Geert-Jan van Houtum & Alan Scheller-Wolf & Jinxin Yi, 2007. "Optimal Control of Serial Inventory Systems with Fixed Replenishment Intervals," Operations Research, INFORMS, vol. 55(4), pages 674-687, August.
    8. Taher Ahmadi & Zümbül Atan & Ton Kok & Ivo Adan, 2020. "Time-based service constraints for inventory systems with commitment lead time," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 355-395, June.
    9. Klosterhalfen, Steffen T. & Holzhauer, Falk & Fleischmann, Moritz, 2018. "Control of a continuous production inventory system with production quantity restrictions," European Journal of Operational Research, Elsevier, vol. 268(2), pages 569-581.
    10. Bijvank, Marco & Vis, Iris F.A., 2012. "Lost-sales inventory systems with a service level criterion," European Journal of Operational Research, Elsevier, vol. 220(3), pages 610-618.
    11. Knofius, N. & van der Heijden, M.C. & Zijm, W.H.M., 2019. "Consolidating spare parts for asset maintenance with additive manufacturing," International Journal of Production Economics, Elsevier, vol. 208(C), pages 269-280.
    12. Yuanguang Zhong & Zhichao Zheng & Mabel C. Chou & Chung-Piaw Teo, 2018. "Resource Pooling and Allocation Policies to Deliver Differentiated Service," Management Science, INFORMS, vol. 64(4), pages 1555-1573, April.
    13. Tarim, S. Armagan & Kingsman, Brian G., 2004. "The stochastic dynamic production/inventory lot-sizing problem with service-level constraints," International Journal of Production Economics, Elsevier, vol. 88(1), pages 105-119, March.
    14. Jim Shi, 2022. "Optimal continuous production-inventory systems subject to stockout risk," Annals of Operations Research, Springer, vol. 317(2), pages 777-804, October.

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