TY - JOUR

T1 - Controlling risk and demand ambiguity in newsvendor models

AU - Rahimian, Hamed

AU - Bayraksan, Güzin

AU - Homem-de-Mello, Tito

N1 - Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2019/12/16

Y1 - 2019/12/16

N2 - We use distributionally robust optimization (DRO) to model a general class of newsvendor problems with unknown demand distribution. The goal is to find an order quantity that minimizes the worst-case expected cost among an ambiguity set of distributions. The ambiguity set consists of those distributions that are not far—in the sense of the total variation distance—from a nominal distribution. The maximum distance allowed in the ambiguity set (called level of robustness) places the DRO between the risk-neutral stochastic programming and robust optimization models. An important problem a decision maker faces is how to determine the level of robustness—or, equivalently, how to find an appropriate level of risk-aversion. We answer this question in two ways. Our first approach relates the level of robustness and risk to the regions of demand that are critical (in a precise sense we introduce) to the optimal cost. Our second approach establishes new quantitative relationships between the DRO model and the corresponding risk-neutral and classical robust optimization models. To achieve these goals, we first focus on a single-product setting and derive explicit formulas and properties of the optimal solution as a function of the level of robustness. Then, we demonstrate the practical and managerial relevance of our results by applying our findings to a healthcare problem to reserve operating room time for cardiovascular surgeries. Finally, we extend some of our results to the multi-product setting and illustrate them numerically.

AB - We use distributionally robust optimization (DRO) to model a general class of newsvendor problems with unknown demand distribution. The goal is to find an order quantity that minimizes the worst-case expected cost among an ambiguity set of distributions. The ambiguity set consists of those distributions that are not far—in the sense of the total variation distance—from a nominal distribution. The maximum distance allowed in the ambiguity set (called level of robustness) places the DRO between the risk-neutral stochastic programming and robust optimization models. An important problem a decision maker faces is how to determine the level of robustness—or, equivalently, how to find an appropriate level of risk-aversion. We answer this question in two ways. Our first approach relates the level of robustness and risk to the regions of demand that are critical (in a precise sense we introduce) to the optimal cost. Our second approach establishes new quantitative relationships between the DRO model and the corresponding risk-neutral and classical robust optimization models. To achieve these goals, we first focus on a single-product setting and derive explicit formulas and properties of the optimal solution as a function of the level of robustness. Then, we demonstrate the practical and managerial relevance of our results by applying our findings to a healthcare problem to reserve operating room time for cardiovascular surgeries. Finally, we extend some of our results to the multi-product setting and illustrate them numerically.

KW - Calibration of level of robustness

KW - Distributionally robust optimization

KW - Inventory

KW - Newsvendor problem

KW - Operating room time reservation problem

UR - http://www.scopus.com/inward/record.url?scp=85068478873&partnerID=8YFLogxK

U2 - 10.1016/j.ejor.2019.06.036

DO - 10.1016/j.ejor.2019.06.036

M3 - Article

AN - SCOPUS:85068478873

SN - 0377-2217

VL - 279

SP - 854

EP - 868

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 3

ER -