Halkos, George and Kevork, Ilias (2012): Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand.

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Abstract
This paper considers the classical Newsvendor model, also known as the Newsboy problem, with the demand to be fully observed and to follow in successive inventory cycles one of the Exponential, Rayleigh, and LogNormal distributions. For each distribution, appropriate estimators for the optimal order quantity are considered, and their sampling distributions are derived. Then, through MonteCarlo simulations, we evaluate the performance of corresponding exact and asymptotic confidence intervals for the true optimal order quantity. The case where normality for demand is erroneously assumed is also investigated. Asymptotic confidence intervals produce higher precision, but to attain equality between their actual and nominal confidence level, samples of at least a certain size should be available. This size depends upon the coefficients of variation, skewness and kurtosis. The paper concludes that having available data on the skewed demand for enough inventory cycles enables (i) to trace nonnormality, and (ii) to use the right asymptotic confidence intervals in order the estimates for the optimal order quantity to be valid and precise.
Item Type:  MPRA Paper 

Original Title:  Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand 
Language:  English 
Keywords:  Inventory Control; Newsboy Problem; Skewed Demand; Exact and Asymptotic Confidence Intervals; MonteCarlo Simulations 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General M  Business Administration and Business Economics; Marketing; Accounting > M1  Business Administration > M11  Production Management C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C44  Operations Research; Statistical Decision Theory C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General D  Microeconomics > D2  Production and Organizations > D24  Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity 
Item ID:  36205 
Depositing User:  G.E. Halkos 
Date Deposited:  26. Jan 2012 23:12 
Last Modified:  12. Feb 2013 18:47 
References:  Agrawal N., Smith, SA. (1996). Estimating Negative Binomial Demand for Retail Inventory Management with Unobservable Lost Sales. Naval Research Logistics 43: 839–861. Areeratchakul N, AbdelMalek L. (2006). An approach for solving the Multiproduct Newsboy Problem. International Journal of Operations Research, 3: 219227. Balakrishnan N, Cohen AC. (1991). Order Statistics and Inference Estimation Methods, San Diego: Academic Press. Benzion U, Cohen Y, Peled R, Sharit T. (2008). Decision Making and the newsvendor problem: an experimental study. Journal of the Operational Research Society 59: 12811287. Bell PC. (2000). Forecasting Demand Variation when there are Stockouts. Journal of the Operational Research Society 51: 358–363. Casimir RJ. (2002). The value of information in the multiitem newsboy problem. Omega 30: 45–50. Chen LH, Chen YC. (2009). A newsboy problem with a simple reservation arrangement. Computers and Industrial Engineering 56: 157160 Chen LH, Chen YC. (2010). A multipleitem budgetconstraint newsboy problem with a reservation policy. Omega 38: 431–9. Choi S, Ruszczynski A. (2008). A RiskAverse Newsvendor with Law Invariant Coherent Measures of Risk. Operations Research letters, 36: 7782. Conrad SA. (1976). Sales Data and the Estimation of Demand. Operational Research Quarterly, 27: 123–127. Dominey MJG, Hill RM. (2004). Performance of Approximations for Compound Poisson Distributed Demand in the Newsboy Problem. International Journal of Production Economics, 92: 145155. Dutta P, Chakraborty D, Roy AR. (2005). A single period inventory model with fuzzy random variable demand. Mathematical and Computer Modeling, 41: 915922. Geng W, Zhao X, Gao D. (2010). A SinglePeriod Inventory System with a General SShaped Utility and Exponential Demand. Journal of Systems Science and Systems Engineering, 19: 227236. Grubbstrom, RW. (2010). The Newsboy Problem when Customer Demand is a Compound Renewal Process. European Journal of Operational Research, 203: 134142 Hill RM. (1997). Applying Bayesian Methodology with a Uniform Prior to the Single Period Inventory Model. European Journal of Operational Research 98: 555–562. Huang D, Zhou H, Zhao QH. (2011). A competitive multipleproduct newsboy problem with partial product substitution. Omega 39: 302312. Jammernegg W, Kischka P. (2009). Risk Preferences and Robust Inventory Decisions. International Journal of Production Economics, 118: 269274. Jiang H, Netessine S, Savin S. (2012). Robust newsvendor competition under asymmetric information. Forthcoming in Operations Research, DOI 10.128. Johnson, NL., Kotz, S., and Bakakrishnan, N., 1994. Continuous Univariate Distributions. 2nd Edition. Wiley New York. Judge GG, Hill RC, Griffiths WE, Lutkerpohl H, Lee TC. (1988). Introduction to the Theory and Practice of Econometrics. 2nd Edition. John Wiley & Sons. Kevork IS. (2010). Estimating the optimal order quantity and the maximum expected profit for singleperiod inventory decisions. Omega 38: 218–27. Khouja M. (1996). A note on the Newsboy Problem with an Emergency Supply Option. Journal of the Operational Research Society 47: 15301534. Khouja M. (1999). The singleperiod (newsvendor) problem: literature review and suggestions for future research. Omega 27:537–53. Knight, K., 1999. Mathematical Statistics. Taylor & Francis Ltd. Law AM. (2007). Simulation Modeling and Analysis, 4th Edition, McGraw Hill. Lau H. (1997). Simple Formulas for the Expected Costs in the Newsboy Problem: an educational note. European Journal of Operational Research 100: 557–61. Lau AH, Lau H. (2002). The effects of reducing demand uncertainty in a manufacturerretailer channel for singleperiods products. Computers & Operations Research, 29: 15831602. Lee CM, Hsu SL, (2011). The effect of advertising on the distributionfree newsboy problem. International Journal of Production Economics 129: 217224. Matsuyama K. (2006). The multiperiod newsboy problem. European Journal of Operational Research 171: 170188. Mostard J, De Koster R, Teunter R. (2005). The DistributionFree Newsboy Problem with Resalable Returns. International Journal of Production Economics, 97: 329342. Nahmias S. (1994). Demand Estimation in Lost Sales Inventory Systems. Naval Research Logistics 41: 739–757. Olivares M, Terwiesch C, Cassorla L. (2008). Structural Estimation of the Newsvendor Model: An Application to Reserving Operating Room Time. Management Science, 54: 41–55. Rider AD, Van der Laan E, Salomon M. (1998). How Larger Demand Variability May Lead to Lower Costs in the Newsvendor Problem. Operations Research 46: 934936. SalazarIbarra J. (2005). The newsboy Model: Change in risk and price. The Geneva Risk and Insurance Review 30: 99109. Schweitzer ME., Cachon GP. (2000). Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence. Management Science, 46:. 404–420. Silver, E.A., D.F Pyke, and R. Peterson (1998). Inventory management and Production Planning and Scheduling (3rd ed). John Wiley & Sons, New York, NY Su RH, Pearn WL (2011). Product selection for newsboytype products with normal demands and unequal costs. International Journal of Production Economics 132: 214222. Wang CX and Webster S. (2009). The lossaverse newsvendor problem. Omega 37: 93–105. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/36205 