The distribution-free newsboy problem: Extensions to the shortage penalty case

In the classical newsboy problem, no cost is assumed if the ordered quantity is less than the demand. However, in reality failure to meet demand is always associated with a penalty. The aim of this work is to extend the analysis of the distribution-free newsboy problem to the case when shortage cost is taken into consideration. The analysis is based on the assumption that only the mean and variance of demand are known, but its particular probability distribution is not. A model is presented for determining both an optimal order quantity and a lower bound on the profit under the worst possible distribution of the demand. The following cases are considered: the single product case, the fixed ordering cost case, the random yield case, and the resource-constrained multi-product case.