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Derivation of confidence intervals of service measures in a base-stock inventory control system with low-frequent demand

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Abstract

We explore a base-stock system with backlogging where the demand process is a compound renewal process and the compound element is a delayed geometric distribution. For this setting it is proven in [4] that the long-run average service measures order fill rate (OFR) and volume fill rate (VFR) are equal in values. In [4] it is also demonstrated that although equal ex ante one will ex post observe differences as actual sample paths are different. By including a low-frequency assumption in the model, we are able to derive mathematical expressions of the confidence intervals one will get if OFR and VFR are estimated in a simulation using the regenerative method. Through numerical examples we show that of the two service measures it is OFR that can be estimated most accurately. However, simulation results show that the opposite conclusion holds if we instead consider finitehorizon service measures, namely per-cycle variants of OFR and VFR.

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  • Larsen, Christian, 2008. "Derivation of confidence intervals of service measures in a base-stock inventory control system with low-frequent demand," CORAL Working Papers L-2008-03, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbls:2008-003
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    1. J. B. Ward, 1978. "Determining Reorder Points When Demand is Lumpy," Management Science, INFORMS, vol. 24(6), pages 623-632, February.
    2. Douglas J. Thomas, 2005. "Measuring Item Fill-Rate Performance in a Finite Horizon," Manufacturing & Service Operations Management, INFORMS, vol. 7(1), pages 74-80, September.
    3. Chen, Frank Y. & Krass, Dmitry, 2001. "Inventory models with minimal service level constraints," European Journal of Operational Research, Elsevier, vol. 134(1), pages 120-140, October.
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    1. Kjeldsen, Karina Hjortshøj, 2008. "Classification of routing and scheduling problems in liner shipping," CORAL Working Papers L-2008-06, University of Aarhus, Aarhus School of Business, Department of Business Studies.

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