Halkos, George and Kevork, Ilias (2012): Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand.

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Abstract
Three estimation policies for the optimal order quantity of the classical newsvendor model under exponential demand are evaluated in the current paper. According to the principle of the first estimation policy, the corresponding estimator is obtained replacing in the theoretical formula which gives the optimal order quantity the parameter of exponential distribution with its maximum likelihood estimator. The estimator of the second estimation policy is derived in such a way as to ensure that the requested critical fractile is attained. For the third estimation policy, the corresponding estimator is obtained maximizing the apriori expected profit with respect to a constant which has been included into the form of the estimator. Three statistical measures have been chosen to perform the evaluation. The actual critical fractile attained by each estimator, the mean square error, and the range of deviation of estimates from the optimal order quantity, when the probability to take such a range is the same for the three estimation policies. The behavior of the three statistical measures is explored under different combinations of sample sizes and critical fractiles. With small sample sizes, no estimation policy predominates over the others. The estimator which attains the closest actual critical fractile to the requested one, this estimator has the largest mean square and the largest range of deviation of estimates from the optimal order quantity. On the contrary, with samples over 40 observations, the choice is restricted among the estimators of the first and third estimation policy. To facilitate this choice, at different sample sizes, we offer the required values of the critical fractile which determine which estimation policy eventually should be applied.
Item Type:  MPRA Paper 

Original Title:  Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand 
Language:  English 
Keywords:  Classical newsvendor model; Exponential distribution; Demand estimation; Actual critical fractile; Mean square error of estimators 
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 D  Microeconomics > D2  Production and Organizations > D24  Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity 
Item ID:  39650 
Depositing User:  G.E. Halkos 
Date Deposited:  25. Jun 2012 14:21 
Last Modified:  21. Feb 2013 01:52 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/39650 