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Joint Pricing and Production: A Fusion of Machine Learning and Robust Optimization

Georgia Perakis(georgiap***at***mit.edu)
Melvyn Sim(dscsimm***at***nus.edu.sg)
Qinshen Tang(qinshen.tang***at***gmail.com)
Peng Xiong(xiongpengnus***at***gmail.com)

Abstract: We integrate machine learning with distributionally robust optimization to address a two-period problem for the joint pricing and production of multiple items. First, we generalize the additive demand model to capture both cross-product and cross-period effects as well as the demand dependence across periods. Next, we apply K-means clustering to the demand residual mapping based on historical data and then construct a K-means ambiguity set on that residual while specifying only the mean, the support, and the mean absolute deviation. Finally, we investigate the joint pricing and production problem by proposing a K-means adaptive markdown policy and an affine recourse approximation; the latter allows us to reformulate the problem as an approximate but more tractable mixed-integer linear programming problem. Both the case study and our simulation demonstrate that, with only a few clusters, the K-means adaptive markdown policy and ambiguity set can increase expected profits by 1.12% on average and by as much as 2.22%---as compared with the empirical model---when applied to most out-of-sample tests.

Keywords: multi-item, pricing, inventory control, K-means clustering, distributionally robust optimization

Category 1: Applications -- OR and Management Sciences

Category 2: Robust Optimization


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Entry Submitted: 12/31/2019
Entry Accepted: 01/01/2019
Entry Last Modified: 12/31/2019

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