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Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions

  • Kevork, Ilias S.

The paper considers the classical single-period inventory model, also known as the Newsboy Problem, with the demand normally distributed and fully observed in successive inventory cycles. The extent of applicability of such a model to inventory management depends upon demand estimation. Appropriate estimators for the optimal order quantity and the maximum expected profit are developed. The statistical properties of the two estimators are explored for both small and large samples, analytically and through Monte-Carlo simulations. For small samples, both estimators are biased. The form of distribution of the optimal order quantity estimator depends upon the critical fractile, while the distribution of the maximum expected profit estimator is always left-skewed. Small samples properties of the estimators indicate that, when the critical fractile is set over a half, the optimal order quantity is underestimated and the maximum expected profit is overestimated with probability over 50%, whereas the probability of overestimating both quantities exceeds again 50% when the critical fractile is below a half. For large samples, based on the asymptotic properties of the two estimators, confidence intervals are derived for the corresponding true population values. The validity of confidence intervals using small samples is tested by developing appropriate Monte-Carlo simulations. In small samples, these intervals attain acceptable confidence levels, but with high unit shortage cost, for the case of maximum expected profit, significant reductions in their precision and stability are observed.

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Article provided by Elsevier in its journal Omega.

Volume (Year): 38 (2010)
Issue (Month): 3-4 (June)
Pages: 218-227

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Handle: RePEc:eee:jomega:v:38:y:2010:i:3-4:p:218-227
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  1. Wang, Charles X. & Webster, Scott, 2009. "The loss-averse newsvendor problem," Omega, Elsevier, vol. 37(1), pages 93-105, February.
  2. Maurice E. Schweitzer & Gérard P. Cachon, 2000. "Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence," Management Science, INFORMS, vol. 46(3), pages 404-420, March.
  3. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
  4. Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.
  5. Lau, Hon-Shiang & Hing-Ling Lau, Amy, 1996. "Estimating the demand distributions of single-period items having frequent stockouts," European Journal of Operational Research, Elsevier, vol. 92(2), pages 254-265, July.
  6. Berk, Emre & Gurler, Ulku & Levine, Richard A., 2007. "Bayesian demand updating in the lost sales newsvendor problem: A two-moment approximation," European Journal of Operational Research, Elsevier, vol. 182(1), pages 256-281, October.
  7. David Goldsman & Lee Schruben, 1984. "Asymptotic Properties of Some Confidence Interval Estimators for Simulation Output," Management Science, INFORMS, vol. 30(10), pages 1217-1225, October.
  8. Chahar, Kiran & Taaffe, Kevin, 2009. "Risk averse demand selection with all-or-nothing orders," Omega, Elsevier, vol. 37(5), pages 996-1006, October.
  9. Hill, Roger M., 1997. "Applying Bayesian methodology with a uniform prior to the single period inventory model," European Journal of Operational Research, Elsevier, vol. 98(3), pages 555-562, May.
  10. Hon-Shiang Lau, 1997. "Simple formulas for the expected costs in the newsboy problem: An educational note," European Journal of Operational Research, Elsevier, vol. 100(3), pages 557-561, August.
  11. Wu, Jun & Li, Jian & Wang, Shouyang & Cheng, T.C.E., 2009. "Mean-variance analysis of the newsvendor model with stockout cost," Omega, Elsevier, vol. 37(3), pages 724-730, June.
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