A generalized single product and single-period inventory problem with non-linear parameters

Abstract : In this paper, we extend the study of the classical single-period newsboy inventory problem by considering costs that are non-linear functions of the decision variable. We assume that the demand probability density function is known to the decision maker. We prove that, under some much more relaxed conditions, the total expected profit function remains concave and classical optimization methods can thus be used to obtain the global optimal solution. After that, we provide numerical examples for illustrative purpose.