Robust pricing and production with information partitioning and adaptation

• Main Authors: Perakis, Georgia, Sim, Melvyn, Tang, Qinshen, Xiong, Peng
• Other Authors: Nanyang Business School
• Format: Article
• Language: English
• Published: 2022
• Subjects: Business::Operations management::Supply chain management; Business::Operations management::Production management; Multi-Item; Pricing; Retail Analytics; Clustering; Distributionally Robust Optimization
• Online Access: https://hdl.handle.net/10356/160160
• Institution: Nanyang Technological University

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.