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A general solution for the newsboy model with random order size and possibly a cutoff transaction size

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  • H Shore

    (Ben-Gurion University of the Negev)

Abstract

In a recent paper, Dekker et al developed a solution procedure for the newsboy problem with a cutoff transaction size (CTS), such that customers with orders larger than the cutoff value are satisfied in an alternative way, against additional cost. A compound Poisson demand with discrete order sizes is assumed, and a computational procedure developed to identify the optimal solution. In this paper, we discard all distributional assumptions, and, given that order size is random, only the first three moments of the arrival rate and the order size are specified. A general optimal solution is developed, using Shore's piece-wise linear approximations. For cases where a CTS exists, the derived optimal solution is extended to also identify the optimal CTS. The new solution approach requires minimal distributional information, and its merits relative to current approaches are discussed and numerically demonstrated. The new methodology, based on a ‘Calculus of moments’ combined with a distributional approximation, may be easily extended to other computationally intractable problems.

Suggested Citation

  • H Shore, 2004. "A general solution for the newsboy model with random order size and possibly a cutoff transaction size," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(11), pages 1218-1228, November.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:11:d:10.1057_palgrave.jors.2601637
    DOI: 10.1057/palgrave.jors.2601637
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    References listed on IDEAS

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    1. Haim Shore, 1982. "Simple Approximations for the Inverse Cumulative Function, the Density Function and the Loss Integral of the Normal Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 108-114, June.
    2. Shore, Haim, 1999. "Optimal solutions for stochastic inventory models when the lead-time demand distribution is partially specified," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 477-485, March.
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    Citations

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    Cited by:

    1. D J Robb & E A Silver, 2006. "Inventory management under date-terms supplier trade credit with stochastic demand and leadtime," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 692-702, June.
    2. Silver, Edward A. & Robb, David J., 2008. "Some insights regarding the optimal reorder period in periodic review inventory systems," International Journal of Production Economics, Elsevier, vol. 112(1), pages 354-366, March.
    3. U Benzion & Y Cohen & R Peled & T Shavit, 2008. "Decision-making and the newsvendor problem: an experimental study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1281-1287, September.

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