Operational Data Analytics for Decision Making in Supply Chains

We study the data-integrated decision making in supply chains, using the newsvendor problem as a running example. In the data-integrated newsvendor problem, the demand is random and potentially a stochastic function of a set of covariates. We progressively develop the operational data analytics (ODA) framework for different levels of knowledge of the demand function. The two pillars of the ODA framework are a data-integration model and a validation model. The data-integration model consists of a class of functions, called operational statistics. Each operational statistic maps the available data to the operational decisions. The validation model finds, among the set of candidate operational statistics, the one that leads to the highest actual profit (or lowest actual cost), which is unknown because of the unknown demand function.

Chapter 2 studies the price-setting newsvendor problem in which the price-demand relationship is described by some parametric model with unknown parameters. This ODA framework generates a uniformly optimal ordering quantity decision. Moreover, it also leads to a consistent estimate of the profit function, with which we optimize the pricing decision. The derived quantity and price decisions demonstrate robust profit performance even when the sample size is very small in relation to the demand variability. Compared with the conventional approach with which the unknown parameters are estimated and then the decisions are optimized, the ODA framework produces significantly superior performance in the mean, standard deviation, and minimum of the profit.

Chapter 3 investigates the contextual newsvendor problem where the demand is linear in the covariates. With a linear demand, we show that an appropriate decision must satisfy certain equivariant property in the sense that any decision outside of the set of equivariant class of operational statistics is inadmissible. Furthermore, in the parametric setting where the demand distribution family is known, a uniformly optimal ODA solution within the equivariant class can be derived. When the demand distribution is unknown, we identify subclasses of data-integration models through constant projection or adaptive boosting of some candidate solutions. The resulting nonparametric ODA solution is consistent and shows superior empirical performance against existing solutions. Moreover, boosting results in improved small sample performance that is insensitive to the choice of candidate solution.

Chapter 4 presents the most general case with high-dimensional covariates and a general nonlinear demand function. Recognizing that many demand models have alternative low-dimensional linear representations, we extend the ODA framework by applying covariate transformations. Under a high-dimensional linear demand model, our ODA solution generalizes the estimation-and-then-optimization solution based on the principal component regression and best subset selection. Under a nonlinear demand, we utilize the neural network feature extraction and embed the ODA solution into a linearized neural network. We rigorously analyze the statistical properties of the proposed solutions, establishing convergence rates that align with minimax benchmarks.

Our ODA framework, building on the inherent characteristics of the contextual newsvendor problem, highlights the importance of understanding structural properties in data-integrated decision making.