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The impact of the number of parallel warehouses on total inventory

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  • Bernhard Fleischmann

    (Augsburg University)

Abstract

In the strategic design of a distribution system, the right number of stock points for the various products is an important question. In the past decade, a strong trend in the consumer goods industry led to centralizing the inventory in a single echelon consisting of a few parallel warehouses or even a single distribution center for a Europe-wide distribution system. Centralizing inventory is justified by the reduction in total stock which mostly overcompensates the increasing transportation cost. The effect of centralization is usually described by the “Square Root Law”, stating that the total stock increases with the square root of the number of stock points. However, in the usual case where the warehouses are replenished in full truck loads and where a given fill rate has to be satisfied, the Square Root Law is not valid. This paper explores that case. It establishes functional relationships between the demand to be served by a warehouse and the necessary safety and cycle stock for various demand settings and control policies, using an approximation of the normal loss function and its inverse. As a consequence, the impact of the number of parallel warehouses on the total stock can be derived. The results can be used as tools in network design models.

Suggested Citation

  • Bernhard Fleischmann, 2016. "The impact of the number of parallel warehouses on total inventory," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 899-920, October.
    • Handle: RePEc:spr:orspec:v:38:y:2016:i:4:d:10.1007_s00291-016-0442-2
    DOI: 10.1007/s00291-016-0442-2
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    References listed on IDEAS

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    1. Bernhard Fleischmann & Herbert Kopfer & Christopher Sürie, 2015. "Transport Planning for Procurement and Distribution," Springer Texts in Business and Economics, in: Hartmut Stadtler & Christoph Kilger & Herbert Meyr (ed.), Supply Chain Management and Advanced Planning, edition 5, chapter 12, pages 225-240, Springer.
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    Cited by:

    1. Dariusz Milewski, 2020. "Total Costs of Centralized and Decentralized Inventory Strategies—Including External Costs," Sustainability, MDPI, vol. 12(22), pages 1-16, November.
    2. Straubert, Christian, 2024. "A continuous approximation location-inventory model with exact inventory costs and nonlinear delivery lead time penalties," International Journal of Production Economics, Elsevier, vol. 268(C).
    3. Darmawan, Agus & Wong, Hartanto & Thorstenson, Anders, 2021. "Supply chain network design with coordinated inventory control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    4. Thomas Wensing & Michael G. Sternbeck & Heinrich Kuhn, 2018. "Optimizing case-pack sizes in the bricks-and-mortar retail trade," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 913-944, October.
    5. Holzapfel, Andreas & Potoczki, Tobias & Kuhn, Heinrich, 2023. "Designing the breadth and depth of distribution networks in the retail trade," International Journal of Production Economics, Elsevier, vol. 257(C).
    6. Holzapfel, Andreas & Kuhn, Heinrich & Sternbeck, Michael G., 2018. "Product allocation to different types of distribution center in retail logistics networks," European Journal of Operational Research, Elsevier, vol. 264(3), pages 948-966.

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