Applications of Stochastic Orders and Stochastic Functions in Inventory and Pricing Problems

Uncertainties involved in decision making often impose challenges to our ability of modeling and analyzing the reality. The purpose of this study is to demonstrate how one can go beyond the conventional optimization thinking, via taking a stochastic viewpoint, to push the boundaries of the analysis. We review the basic notions of stochastic orders and stochastic functions, with which the conventional (deterministic) way of modeling can be generalized. Based on the orders among distribution functions associated with random variables, we can treat the input-output relationship as stochastic functions in our models. This viewpoint, leads to extended functional properties in the stochastic sense. Taking the existing models involving inventory and pricing decisions, we show how the stochastic notions are powerful in simplifying and generalizing the analysis, as well as generating new insights.