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

38 Pages Posted: 27 Aug 2021

See all articles by Qi Feng

Qi Feng

Mitchell E. Daniels, Jr School of Business, Purdue University

J. George Shanthikumar

Purdue University - Krannert School of Management

Date Written: August 23, 2021

Abstract

Uncertainties involved in decision making often impose challenges to our ability of modeling and analyzing the reality. The purpose of this paper 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.

Keywords: Stochastic orders, parametric stochastic orders, stochastic functions, inventory control, dynamic pricing

Suggested Citation

Feng, Qi and Shanthikumar, J. George, Applications of Stochastic Orders and Stochastic Functions in Inventory and Pricing Problems (August 23, 2021). Available at SSRN: https://ssrn.com/abstract=3911402 or http://dx.doi.org/10.2139/ssrn.3911402

Qi Feng (Contact Author)

Mitchell E. Daniels, Jr School of Business, Purdue University ( email )

403 Mitch Daniels Blvd.
West Lafayette, IN 47907
United States

J. George Shanthikumar

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

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