Data-Driven Approximation Schemes for Joint Pricing and Inventory Control Models

45 Pages Posted: 25 Mar 2019

See all articles by Hanzhang Qin

Hanzhang Qin

Massachusetts Institute of Technology (MIT) - Center for Computational Engineering

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Li Wang

Massachusetts Institute of Technology (MIT) - Operations Research Center

Date Written: March 18, 2019

Abstract

We study the classic multi-period joint pricing and inventory control problem in a data-driven setting.

In this problem, a retailer makes periodic decisions on the prices and inventory levels of an item that she wishes to sell. The retailer's objective is to maximize the expected profit over a finite horizon, by matching the inventory level with a random demand that depends on the price in each period. In reality, the demand functions or the distribution of the random noise are usually difficult to know exactly, whereas past demand data are relatively easy to collect.

We propose a data-driven approximation algorithm, which uses the past demand data to solve the joint pricing and inventory control problem. We assume the retailer does not know the noise distributions or the true demand functions; instead she only has access to demand hypothesis sets that contain the true demand functions. We prove the algorithm's sample complexity bound, the number of data samples needed to guarantee a near-optimal profit, is O(T6ε −2 log T), where T is the number of periods and ε is the absolute difference between the expected profit of the data-driven policy and the expected optimal profit. A simulation study suggests that the data-driven algorithm solves the dynamic program effectively.

Keywords: dynamic pricing, inventory control, revenue management, approximation algorithm, data-driven optimization, dynamic programming

JEL Classification: C61

Suggested Citation

Qin, Hanzhang and Simchi-Levi, David and Wang, Li, Data-Driven Approximation Schemes for Joint Pricing and Inventory Control Models (March 18, 2019). Available at SSRN: https://ssrn.com/abstract=3354358 or http://dx.doi.org/10.2139/ssrn.3354358

Hanzhang Qin (Contact Author)

Massachusetts Institute of Technology (MIT) - Center for Computational Engineering ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

MA
United States

Li Wang

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

77 Massachusetts Avenue
Bldg. E40-103
Cambridge, MA 02139
United States

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