The newsvendor problem with normal, worst-case and binomial distribution of demand: Managerial implications with examples

Abstract

The paper examines the newsvendor problem with demand distributions commonly used in the literature. Optimal order convergence is checked numerically. An important contribution is that the expected profits differ considerably in nominal and relative terms when the profit-loss ratio is low valued while the demand variability is at least moderate. Missed expected profit reaches even 10% of total order cost for a mark-up that equals to the worst case break even one. The optimal order quantities are compared to counterparts derived from sales data. The main managerial implication indicates that the normal distribution solution outperforms distribution-free solutions in predicting the maximal expected profit under empirical demand. Therefore, the MaxiMin solution is recommended to be used in practice to simplify the maximal expected profit calculus and for break-even mark-up evaluation. However, it should not be used to solve the optimal order quantity because the worst-case distribution asymmetry is determined by the profit-to-loss ratio and can be contradictory to the asymmetry of sales data. Moreover, the normal distribution optimum bounded with 0.8 service level commitment shows negative expected profit under mark-up from the range of 5-20% while demand variability is low or moderate proportionally to mark-up.