Data-Driven Robust Production Planning

This chapter discusses a two-stage production planning problem with demand ambiguity, which can be seen as a distributionally robust facility location. The first stage regards a product service to offer. The second stage involves production planning. The problem is cast in a data-driven decision-making setting. Historical information is considered for demand and related covariates. An econometric model is developed to predict the demand, leveraging seemingly unrelated regression estimated with feasible generalized least squares. A predictive ambiguity set is constructed to harness the prediction model with the empirical covariates and residuals. A decision-dependent two-stage distributionally robust optimization (DRO) model is built, taking advantage of the econometric model and predictive ambiguity set. The problem is reformulated as an empirical counterpart under the predicted demand distribution regularized by a perceived shortage cost as the shadow price for ambiguity aversion. Exploiting this structure, ambiguity-averse operational properties are analyzed, including risk exposure. Numerical results demonstrate the effectiveness of the modeling framework proposed.