An inverse newsvendor model to set the optimal number of customers in a capacitated environment

The inverse newsvendor problem is a variant of the traditional newsvendor problem where the decision of interest is to select the number of customers that could be served in the available capacity, measured in units of time. In essence, the traditional newsvendor problem maps demand into capacity, whereas with the inverse newsvendor problem capacity is mapped into demand. First, we provide an analysis of the problem under the assumptions of normally and exponentially distributed service times. We also numerically show that approximations of the lognormal and the gamma distributions to the normal distribution are relevant and valid. For normally distributed service times, we take into accounts both identical and nonidentical distributions. We propose three heuristics to decide who to be served rather than the number of customers when service times are nonidentically and normally distributed. We conduct extensive numerical studies to show the efficacy of the heuristics.