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A two‐echelon inventory model with purchases, dispositions, shipments, returns and transshipments

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  • Bruce Hoadley
  • Daniel P. Heyman

Abstract

This paper presents a one‐period two‐echelon inventory model with one warehouse in the first echelon and n warehouses in the second echelon. At the beginning of the period the stock levels at all facilities are adjusted by purchasing or disposing of items at the first echelon, returning or shipping items between the echelons and transshipping items within the second echelon. During the period, demands (which may be negative) are placed on all warehouses in the second echelon and an attempt is made to satisfy shortages either by an expedited shipment from the first echelon to the second echelon or an expedited transshipment within the second echelon. The decision problem is to choose an initial stock level at the first echelon (by a purchase or a disposition) and an initial allocation so as to minimize the initial stock movement costs during the period plus inventory carrying costs and system shortage costs at the end of the period. It is shown that the objective function takes on one of four forms, depending on the relative magnitudes of the various shipping costs. All four forms of the objective function are derived and proven to be convex. Several applications of this general model are considered. We also consider multi‐period extensions of the general model and an important special case is solved explicitly.

Suggested Citation

  • Bruce Hoadley & Daniel P. Heyman, 1977. "A two‐echelon inventory model with purchases, dispositions, shipments, returns and transshipments," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(1), pages 1-19, March.
    • Handle: RePEc:wly:navlog:v:24:y:1977:i:1:p:1-19
    DOI: 10.1002/nav.3800240102
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    Cited by:

    1. Mohammad Ali Nasiri Khalili & Mostafa Kafaei Razavi & Morteza Kafaee Razavi, 2016. "An Optimized Mathematical Model for Items Supplies Planning of a Logistic System," Modern Applied Science, Canadian Center of Science and Education, vol. 10(10), pages 133-133, October.
    2. Ting Qu & Tianxiang Huang & Duxian Nie & Yelin Fu & Lin Ma & George Q. Huang, 2022. "Joint Decisions of Inventory Optimization and Order Allocation for Omni-Channel Multi-Echelon Distribution Network," Sustainability, MDPI, vol. 14(10), pages 1-23, May.
    3. Topan, E. & van der Heijden, M.C., 2020. "Operational level planning of a multi-item two-echelon spare parts inventory system with reactive and proactive interventions," European Journal of Operational Research, Elsevier, vol. 284(1), pages 164-175.
    4. 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.
    5. Gerrits, B. & Topan, E. & van der Heijden, M.C., 2022. "Operational planning in service control towers – heuristics and case study," European Journal of Operational Research, Elsevier, vol. 302(3), pages 983-998.
    6. Naderi, Siamak & Kilic, Kemal & Dasci, Abdullah, 2020. "A deterministic model for the transshipment problem of a fast fashion retailer under capacity constraints," International Journal of Production Economics, Elsevier, vol. 227(C).

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