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

61 Pages Posted: 25 Mar 2019 Last revised: 28 Jul 2021

See all articles by Hanzhang Qin

Hanzhang Qin

National University of Singapore (NUS)

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 multiperiod 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 a product 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, which depends on the price in each period. In reality, the demand functions or random noise distributions are usually difficult to know exactly, whereas past demand data are relatively easy to collect. We propose a data-driven approximation algorithm that uses pre-collected demand data to solve the joint pricing and inventory control problem. We assume that the retailer does not know the noise distributions or the true demand functions; instead, we assume either she has access to demand hypothesis sets and the true demand functions can be represented by nonnegative combinations of candidate functions in the demand hypothesis sets, or the true demand function is generalized linear. We assume that the retailer does not know the noise distributions or true demand functions; instead, we assume that she has access only to demand hypothesis sets, while the true demand function is a nonnegative combination of the candidate demand functions in the demand hypothesis set or the true demand function is generalized linear. We prove the algorithm's sample complexity bound: the number of data samples needed in each period 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. In a numerical study, we demonstrate the construction of demand hypothesis sets from data, and show that the proposed data-driven algorithm solves the dynamic problem effectively and significantly improves the optimality gaps over the baseline algorithms.

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)

National University of Singapore (NUS) ( email )

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

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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