Halkos, George and Kevork, Ilias (2012): Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand.
Download (351kB) | Preview
In this paper we consider the classical newsvendor model with profit maximization. When demand is fully observed in each period and follows either the Rayleigh or the exponential distribution, appropriate estimators for the optimal order quantity and the maximum expected profit are established and their distributions are derived. Measuring validity and precision of the corresponding generated confidence intervals by respectively the actual confidence level and the expected half-length divided by the true quantity (optimal order quantity or maximum expected profit), we prove that the intervals are characterized by a very important and useful property. Either referring to confidence intervals for the optimal order quantity or the maximum expected profit, measurements for validity and precision take on exactly the same values. Furthermore, validity and precision do not depend upon the values assigned to the revenue and cost parameters of the model. To offer, therefore, a-priori knowledge for levels of precision and validity, values for the two statistical criteria, that is, the actual confidence level and the relative expected half-length are provided for different combinations of sample size and nominal confidence levels 90%, 95% and 99%. The values for the two criteria have been estimated by developing appropriate Monte-Carlo simulations. For the relative-expected half-length, values are computed also analytically.
|Item Type:||MPRA Paper|
|Original Title:||Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand|
|Keywords:||Inventory Control; Classical newsvendor model; Exponential and Rayleigh Distributions; Confidence Intervals; Monte-Carlo 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
|Depositing User:||G.E. Halkos|
|Date Deposited:||06. Feb 2012 12:22|
|Last Modified:||13. Feb 2013 07:28|
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, Abdel-Malek L. (2006). An approach for solving the Multi-product Newsboy Problem. International Journal of Operations Research, 3: 219-227.
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: 1281-1287.
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 multi-item newsboy problem. Omega 30: 45–50.
Chen LH, Chen YC. (2009). A newsboy problem with a simple reservation arrangement. Computers and Industrial Engineering 56: 157-160.
Chen LH, Chen YC. (2010). A multiple-item budget-constraint newsboy problem with a reservation policy. Omega 38: 431–439.
Cohen, AC, Whitten, BJ. (1988). Parameter estimation in reliability and life span models, New York, Marcel Dekker.
Conrad SA. (1976). Sales Data and the Estimation of Demand. Operational Research Quarterly, 27: 123–127.
Dutta P, Chakraborty D, Roy AR. (2005). A single period inventory model with fuzzy random variable demand. Mathematical and Computer Modeling, 41: 915-922.
Geng W, Zhao X, Gao D. (2010). A Single-Period Inventory System with a General S-Shaped Utility and Exponential Demand. Journal of Systems Science and Systems Engineering, 19: 227-236.
Grubbstrom, RW. (2010). The Newsboy Problem when Customer Demand is a Compound Renewal Process. European Journal of Operational Research, 203: 134-142.
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 multiple-product newsboy problem with partial product substitution. Omega 39: 302-312.
Jammernegg W, Kischka P. (2009). Risk Preferences and Robust Inventory Decisions. International Journal of Production Economics, 118: 269-274.
Jawitz, J.W. (2004). Moments of truncated continuous univariate distributions. Advances in Water Resources, 27: 269-281.
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.
Kevork IS. (2010). Estimating the optimal order quantity and the maximum expected profit for single-period 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: 1530-1534.
Khouja M. (1999). The single-period (news-vendor) problem: literature review and suggestions for future research. Omega 27:537–53.
Knight, K., 1999. Mathematical Statistics. Taylor & Francis Ltd.
Lapin, LL. (1994). Quantitative methods for business decision with cases. 6th edition, Duxbury Press, An International Thomson Publishing Company.
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 manufacturer-retailer channel for single-periods products. Computers & Operations Research, 29: 1583-1602.
Lee CM, Hsu SL, (2011). The effect of advertising on the distribution-free newsboy problem. International Journal of Production Economics 129: 217-224.
Matsuyama K. (2006). The multi-period newsboy problem. European Journal of Operational Research 171: 170-188.
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.
Pandey, BN, and Singh, J. (1977). A note on estimation of variance in exponential density. Sankya, B, 39: 294-298.
Salazar-Ibarra J. (2005). The newsboy Model: Change in risk and price. The Geneva Risk and Insurance Review 30: 99-109.
Schweitzer ME, Cachon GP. (2000). Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence. Management Science, 46:. 404–420.
Silver, EA, Pyke, DF, Peterson, R. (1998). Inventory management and Production Planning and Scheduling (3rd ed). John Wiley & Sons, New York, NY.
Singh, HP, and Chander, V. (2008). Estimating the variance of an exponential distribution in the presence of large true observations. Austrian Journal of Statistics, 37: 207-216.
Su RH, Pearn WL (2011). Product selection for newsboy-type products with normal demands and unequal costs. International Journal of Production Economics 132: 214-222.
Wang CX and Webster S. (2009). The loss-averse newsvendor problem. Omega 37: 93–105.