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, 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 challenges in the stochastic 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 allow us to reformulate the problem as a mixed-integer linear optimization problem that we can solve to optimality using commercial solvers. Both the numerical experiments and case study demonstrate that, with only a few number of clusters, the cluster-adapted markdown policy and the partitioned-moment-based ambiguity set can improve mean profit over the empirical model---when applied to most out-of-sample tests.Ministry of Education (MOE)Nanyang Technological UniversitySubmitted/Accepted versionThe research was conducted while Qinshen Tang was visiting in Sloan School of Management at the Massachusetts Institute of Technology and was partly financed by NUS Business School, FY2018 Ph.D. Exchange Fellowship. This paper was supported by Nanyang Technological University [Start-Up Grant 020022-00001], and the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Grant MOE-2019-T3-1- 010)