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Financially Optimal Inventory Policies With Non-Linear Replenishment Costs

Author

Listed:
  • JIANG ZHANG

    (Department of Management, Marketing, and Decision Sciences, School of Business, Adelphi University, Garden City, New York 11530, USA)

  • MATTHEW J. SOBEL

    (Department of Operations, Weatherhead School of Management, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA)

Abstract

We model the inventory decisions of a firm that maximizes its market value, namely, the expected present value of the time stream of dividends issued to its shareholders. The firm is single-product and equity-owned, it orders products from an outside supplier, its only short-term borrowing is for solvency if necessary, and it issues dividends to its shareholders while facing financial and market risks (uncertain demand). The distinguishing features of the model are the financial criterion, hence joint selection of operational and financial decisions, and non-linear replenishment costs. If the non-linearity is due to a setup cost, we show that an(s, S)replenishment policy is optimal. The analysis isnota straightforward variant of Scarf's argument. If the non-linearity is due to bilinear smoothing costs, we show that the optimal replenishment policy has the same form as in the traditional smoothing cost model. These seem to be the first instances in which the optimization of a model with a financial criterion andnon-linearreplenishment costs yields policies having the same forms as in the corresponding cost minimization problems.

Suggested Citation

  • Jiang Zhang & Matthew J. Sobel, 2010. "Financially Optimal Inventory Policies With Non-Linear Replenishment Costs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(04), pages 477-492.
    • Handle: RePEc:wsi:apjorx:v:27:y:2010:i:04:n:s0217595910002806
    DOI: 10.1142/S0217595910002806
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    Cited by:

    1. Xiaoyan Qian & Tava Lennon Olsen, 2020. "Operational and Financial Decisions Within Proportional Investment Cooperatives," Manufacturing & Service Operations Management, INFORMS, vol. 22(3), pages 545-561, May.
    2. Lode Li & Martin Shubik & Matthew J. Sobel, 2013. "Control of Dividends, Capital Subscriptions, and Physical Inventories," Management Science, INFORMS, vol. 59(5), pages 1107-1124, May.

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