Robust Pricing and Production with Information Partitioning and Adaptation

We introduce a new distributionally robust optimization model to address a two-period, multi-item joint pricing and production problem, which can be implemented in a data-driven setting using historical demand and side information pertinent to the prediction of demands. Starting from an additive demand model we introduce a new partitioned-moment-based ambiguity set to characterize its residuals. Unlike the standard moment-based ambiguity set, as we increase the number of clusters of the information partition, we can adjust the level of robustness by varying the number of information clusters from being the most robust as the standard moment-based ambiguity set with one cluster to being the least robust as the empirical distribution. The partitioned-moment-based ambiguity set also addresses the key challenge in the dynamic optimization problem to determine how the second-period demand would evolve from the first-period information in a data-driven setting, without the need to impose additional assumptions on the distribution of demands such as independence. In addition, it also inspires a practicable non-anticipative policy that is adapted to the cluster. In particular, we investigate the joint pricing and production problem by proposing a cluster-adapted markdown policy and an affine recourse approximation, which allows us to reformulate the problem as a mixed-integer linear optimization problem that we can solve to optimality using commercial solvers. Both the case study and our simulation study demonstrate that, with only a few number of clusters, the cluster-adapted markdown policy and ambiguity set can improve mean profit over the empirical model---when applied to most out-of-sample tests