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Controlling risk and demand ambiguity in newsvendor models

Journal Article · · European Journal of Operational Research
 [1];  [2];  [3]
  1. Northwestern Univ., Evanston, IL (United States); OSTI
  2. The Ohio State Univ., Columbus, OH (United States)
  3. Univ. Adolfo Ibañez, Santiago (Chile)
+ Show Author Affiliations
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.
Research Organization:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
1799668
Alternate ID(s):
OSTI ID: 1898701
Journal Information:
European Journal of Operational Research, Journal Name: European Journal of Operational Research Journal Issue: 3 Vol. 279; ISSN 0377-2217
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

99 GENERAL AND MISCELLANEOUS
calibration of level of robustness
distributionally robust optimization
inventory
newsvendor problem
operating room time reservation problem