The classical newsvendor model under normal demand with large coefficients of variation

In the classical newsvendor model, when demand is represented by the normal distribution singly truncated at point zero, the standard optimality condition does not hold. Particularly, we show that the probability not to have stock-out during the period is always greater than the critical fractile which depends upon the overage and the underage costs. For this probability we derive the range of its values. Writing the safety stock coefficient as a quantile function of both the critical fractile and the coefficient of variation we obtain appropriate formulae for the optimal order quantity and the maximum expected profit. These formulae enable us to study the changes of the two target inventory measures when the coefficient of variation increases. For the optimal order quantity, the changes are studied for different values of the critical fractile. For the maximum expected profit, its changes are examined for different combinations of the critical fractile and the loss of goodwill. The range of values for the loss of goodwill ensures that maximum expected profits are positive. The sizes of the relative approximation error which result in by using the normal distribution to compute the optimal order quantity and the maximum expected profit are also investigated. This investigation is extended to different values of the critical fractile and the loss of goodwill. The results indicate that it is naïve to suggest for the coefficient of variation a maximum flat value under which the normal distribution approximates well the target inventory measures.