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

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.