Dynamic Pricing with Money Back Guarantees

47 Pages Posted: 10 Apr 2019

See all articles by Ningyuan Chen

Ningyuan Chen

University of Toronto at Mississauga - Department of Management; University of Toronto - Rotman School of Management

Yan Liu

School of Management, University of Science and Technology of China

Date Written: March 21, 2019

Abstract

Money back guarantees (MBGs), which allow customers to return products that do not meet their expectations, are widely used in the retail industry. In this paper, we study a retailer's MBG policy with dynamic pricing of a limited inventory. A key decision for the retailer is to decide whether to offer MBGs. When the product can be returned instantly, we find that the optimal MBG is a simple threshold policy: given the inventory level, it is optimal to offer an MBG if and only if the remaining selling time is longer than a threshold. Moreover, the threshold is increasing in the inventory level. We also address the problem of dynamic pricing with positive return times. Due to its complexity, we analyze the associated fluid model, which has an infinite number of constraints. We consider a series of relaxations that have a nested structure and use the Lagrangian approach to explicitly solve these relaxed problems. This allows us to develop an iterative approach that is guaranteed to solve the fluid model in finite iterations. Our numerical analysis shows that the deterministic solution is asymptotically optimal for the stochastic system.

Keywords: Revenue Management, Dynamic Pricing, Money Back Guarantee, Product Return

Suggested Citation

Chen, Ningyuan and Liu, Yan, Dynamic Pricing with Money Back Guarantees (March 21, 2019). Available at SSRN: https://ssrn.com/abstract=3357337 or http://dx.doi.org/10.2139/ssrn.3357337

Ningyuan Chen

University of Toronto at Mississauga - Department of Management ( email )


Canada

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Yan Liu (Contact Author)

School of Management, University of Science and Technology of China ( email )

Hefei, Anhui
China

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