TY - JOUR

T1 - Newsvendor-type models with decision-dependent uncertainty

AU - Lee, Soonhui

AU - Homem-De-Mello, Tito

AU - Kleywegt, Anton J.

PY - 2012/10

Y1 - 2012/10

N2 - Models for decision-making under uncertainty use probability distributions to represent variables whose values are unknown when the decisions are to be made. Often the distributions are estimated with observed data. Sometimes these variables depend on the decisions but the dependence is ignored in the decision maker's model, that is, the decision makermodels these variables as having an exogenous probability distribution independent of the decisions, whereas the probability distribution of the variables actually depend on the decisions. It has been shown in the context of revenue management problems that such modeling error can lead to systematic deterioration of decisions as the decision maker attempts to refine the estimates with observed data. Many questions remain to be addressed. Motivated by the revenue management, newsvendor, and a number of other problems, we consider a setting in which the optimal decision for the decision maker's model is given by a particular quantile of the estimated distribution, and the empirical distribution is used as estimator. We give conditions under which the estimation and control process converges, and showthat although in the limit the decision maker's model appears to be consistent with the observed data, the modeling error can cause the limit decisions to be arbitrarily bad.

AB - Models for decision-making under uncertainty use probability distributions to represent variables whose values are unknown when the decisions are to be made. Often the distributions are estimated with observed data. Sometimes these variables depend on the decisions but the dependence is ignored in the decision maker's model, that is, the decision makermodels these variables as having an exogenous probability distribution independent of the decisions, whereas the probability distribution of the variables actually depend on the decisions. It has been shown in the context of revenue management problems that such modeling error can lead to systematic deterioration of decisions as the decision maker attempts to refine the estimates with observed data. Many questions remain to be addressed. Motivated by the revenue management, newsvendor, and a number of other problems, we consider a setting in which the optimal decision for the decision maker's model is given by a particular quantile of the estimated distribution, and the empirical distribution is used as estimator. We give conditions under which the estimation and control process converges, and showthat although in the limit the decision maker's model appears to be consistent with the observed data, the modeling error can cause the limit decisions to be arbitrarily bad.

KW - Data-driven optimization

KW - Newsvendor model

KW - Stochastic approximation

UR - http://www.scopus.com/inward/record.url?scp=84867278770&partnerID=8YFLogxK

U2 - 10.1007/s00186-012-0396-3

DO - 10.1007/s00186-012-0396-3

M3 - Article

AN - SCOPUS:84867278770

SN - 1432-2994

VL - 76

SP - 189

EP - 221

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

IS - 2

ER -