The distribution-free newsvendor problem with balking and penalties for balking and stockout

This paper investigates the ordering policy for the newsvendor problem with customer balking and penalties for balking and stockout. Our analysis is based on the assumption that only the mean and the variance of the demand distribution are known. In contrast to the existing research, we provide a new tradeoff tool as a replacement of the traditional one to weigh the holding cost and the goodwill cost segment: the balking penalty cost and the stockout penalty cost. Specifically, in addition to the stockout penalty, we also introduce the balking penalty, provide a new proof of the optimality of robust ordering policy to guarantee that the lower bound of expected profit obtained by us is tight, and get an robust optimal order quantity which is an exact solution but not an approximate one as before. Numerical experiments are conducted to illustrate the effect of penalties for balking and stockout.