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Unbiased estimation of maximum expected profits in the Newsvendor Model: a case study analysis

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  • Halkos, George
  • Kevork, Ilias

Abstract

In the current paper we study a real life inventory problem whose operating conditions match to the principles of the classical newsvendor model. Applying appropriate tests to the available sample of historical demand data, we get the sufficient statistical evidences to support that daily demand is stationary, uncorrelated, and normally distributed. Given that at the start of each day, the selling price, the purchasing cost per unit, and the salvage value are known, and do not change through the whole period under investigation, we derive exact and asymptotic prediction intervals for the daily maximum expected profit. To evaluate their performance, we derive the analytic form of three accuracy information metrics. The first metric measures the deviation of the estimated probability of no stock-outs during the day from the critical fractile. The other two metrics relate the validity and precision of the two types of prediction interval to the variability of estimates for the ordered quantity. Both theoretical and empirical analysis demonstrates the importance of implications of the loss of goodwill to the adopted inventory policy. Operating the system at the optimal situation, this intangible cost element determines the probability of no stock-outs during the day, and assesses the precision of prediction intervals. The rising of the loss of goodwill leads to smaller estimates for the daily maximum expected profit and to wider prediction intervals. Finally, in the setting of the real life newsvendor problem, we recommend the asymptotic prediction interval since with samples over 25 observations this type of interval has higher precision and probability to include the daily maximum expected profit almost equal to the nominal confidence level.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40724.

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Date of creation: 17 Aug 2012
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Handle: RePEc:pra:mprapa:40724

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Keywords: Newsvendor model; Loss of goodwill; Target inventory measures; Prediction interval; Accuracy information metric;

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  1. Severini,Thomas A., 2005. "Elements of Distribution Theory," Cambridge Books, Cambridge University Press, number 9780521844727, April.
  2. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand," MPRA Paper 39650, University Library of Munich, Germany.
  3. Feng, Tianjun & Keller, L. Robin & Zheng, Xiaona, 2011. "Decision making in the newsvendor problem: A cross-national laboratory study," Omega, Elsevier, vol. 39(1), pages 41-50, January.
  4. R. H. Hayes, 1969. "Statistical Estimation Problems in Inventory Control," Management Science, INFORMS, vol. 15(11), pages 686-701, July.
  5. Mostard, Julien & Teunter, Ruud & de Koster, René, 2011. "Forecasting demand for single-period products: A case study in the apparel industry," European Journal of Operational Research, Elsevier, vol. 211(1), pages 139-147, May.
  6. Janssen, Elleke & Strijbosch, Leo & Brekelmans, Ruud, 2009. "Assessing the effects of using demand parameters estimates in inventory control and improving the performance using a correction function," International Journal of Production Economics, Elsevier, vol. 118(1), pages 34-42, March.
  7. Halkos, George & Kevork, Ilias, 2012. "Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand," MPRA Paper 36460, University Library of Munich, Germany.
  8. Kevork, Ilias S., 2010. "Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions," Omega, Elsevier, vol. 38(3-4), pages 218-227, June.
  9. Mostard, Julien & Teunter, Ruud, 2006. "The newsboy problem with resalable returns: A single period model and case study," European Journal of Operational Research, Elsevier, vol. 169(1), pages 81-96, February.
  10. Marcelo Olivares & Christian Terwiesch & Lydia Cassorla, 2008. "Structural Estimation of the Newsvendor Model: An Application to Reserving Operating Room Time," Management Science, INFORMS, vol. 54(1), pages 41-55, January.
  11. George Halkos & Ilias Kevork, 2005. "A comparison of alternative unit root tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(1), pages 45-60.
  12. Silver, Edward A. & Rahnama, Mina Rasty, 1987. "Biased selection of the inventory reorder point when demand parameters are statistically estimated," Engineering Costs and Production Economics, Elsevier, vol. 12(1-4), pages 283-292, July.
  13. Syntetos, Aris A. & Nikolopoulos, Konstantinos & Boylan, John E., 2010. "Judging the judges through accuracy-implication metrics: The case of inventory forecasting," International Journal of Forecasting, Elsevier, vol. 26(1), pages 134-143, January.
  14. 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.
  15. Uri Ben-Zion & Yuval Cohen & Ruth Peled & TAL SHAVIT, 2007. "Decision-Making and the Newsvendor Problem – An Experimental Study," Working Papers 0711, Ben-Gurion University of the Negev, Department of Economics.
  16. Halkos, George & Kevork, Ilias, 2012. "The classical newsvendor model under normal demand with large coefficients of variation," MPRA Paper 40414, University Library of Munich, Germany.
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