Robust Pricing and Production with Information Partitioning and Adaptation

51 Pages Posted: 4 Jan 2019 Last revised: 23 Mar 2020

See all articles by Georgia Perakis

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Melvyn Sim

National University of Singapore (NUS) - NUS Business School

Qinshen Tang

Nanyang Technological University (NTU) - Nanyang Business School

Peng Xiong

National University of Singapore (NUS)

Date Written: December 21, 2018

Abstract

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.

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

Suggested Citation

Perakis, Georgia and Sim, Melvyn and Tang, Qinshen and Xiong, Peng, Robust Pricing and Production with Information Partitioning and Adaptation (December 21, 2018). Available at SSRN: https://ssrn.com/abstract=3305039 or http://dx.doi.org/10.2139/ssrn.3305039

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-565
Cambridge, MA 02142
United States

Melvyn Sim

National University of Singapore (NUS) - NUS Business School ( email )

1 Business Link
Singapore, 117592
Singapore

Qinshen Tang (Contact Author)

Nanyang Technological University (NTU) - Nanyang Business School ( email )

Singapore, 639798
Singapore

Peng Xiong

National University of Singapore (NUS) ( email )

1E Kent Ridge Road
NUHS Tower Block Level 7
Singapore, 119228
Singapore

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
299
Abstract Views
1,215
rank
112,693
PlumX Metrics