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Inventory control with and without deliveries in several pieces

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  • Christian Larsen

    (Aarhus University)

Abstract

An inventory system is operated as a base stock system under a compound Poisson demand process. Besides having inventory and backorder costs, also a cost is incurred for each order that is delivered in several pieces to the customer (irrespective of whether some items in the order are delivered on time, or whether they are all delivered late but at different times). The possible split deliveries are assumed to happen automatically, meaning that there cannot at the same time be a positive on-hand inventory and a positive backlog. We develop a mathematical cost expression for this system to be optimized, denoted Model 1. We compare Model 1 to another model, denoted Model 2, where it is forbidden to make any of these split deliveries; thus at the same time, there can be a positive on-hand inventory and a positive backlog. We compare Model 2 to the standard textbook model, denoted Model 0, where split deliveries occur automatically and are costless. Thereby, we address a claim made by Zipkin (Foundations of inventory management. McGraw-Hill, Boston, 2000). We also examine the threshold value for the delivery split cost, which makes Model 1 and 2 perform equally well, and we examine how this threshold value depends on the other common parameters of the models.

Suggested Citation

  • Christian Larsen, 2017. "Inventory control with and without deliveries in several pieces," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 607-622, March.
    • Handle: RePEc:spr:orspec:v:39:y:2017:i:2:d:10.1007_s00291-016-0466-7
    DOI: 10.1007/s00291-016-0466-7
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    References listed on IDEAS

    as
    1. C Larsen & A Thorstenson, 2008. "A comparison between the order and the volume fill rate for a base-stock inventory control system under a compound renewal demand process," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(6), pages 798-804, June.
    2. Larsen, C. & Thorstenson, A., 2014. "The order and volume fill rates in inventory control systems," International Journal of Production Economics, Elsevier, vol. 147(PA), pages 13-19.
    3. Forsberg, Rolf, 1995. "Optimization of order-up-to-S policies for two-level inventory systems with compound Poisson demand," European Journal of Operational Research, Elsevier, vol. 81(1), pages 143-153, February.
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