Dynamic Pricing of Limited Inventories When Customers Negotiate

Ross School of Business Paper No. 1159

Forthcoming in Operations Research

34 Pages Posted: 16 Aug 2011 Last revised: 20 Apr 2012

See all articles by Chia-Wei Kuo

Chia-Wei Kuo

National Taiwan University - Department of Business Administration

Hyun-Soo Ahn

University of Michigan, Stephen M. Ross School of Business

Goker Aydin

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering

Date Written: August 1, 2010

Abstract

Although take-it-or-leave-it pricing is the main mode of operation for many retailers, a number of retailers discreetly allow price negotiation when some haggle-prone customers ask for a bargain. At these retailers, the posted price, which itself is subject to dynamic adjustments in response to the pace of sales during the selling season, serves two important roles: (i) it is the take-it-or-leave-it price to many customers who do not bargain, and (ii) it is the price from which haggle-prone customers negotiate down. In order to effectively measure the benefit of dynamic pricing and negotiation in such a retail environment, one must take into account the interactions among inventory, dynamic pricing, and negotiation. The outcome of the negotiation (and the final price a customer pays) depends on the inventory level, the remaining selling season, the retailer's bargaining power, and the posted price. We model the retailer's dynamic pricing problem as a dynamic program, where the revenues from both negotiation and posted pricing are embedded in each period. We characterize the optimal posted price and the resulting negotiation outcome as a function of inventory and time. We also show that negotiation is an effective tool to achieve price discrimination, particularly when the inventory level is high and/or the remaining selling season is short even when implementing negotiation is costly.

Keywords: inventory, production, dynamic programming, marketing, pricing

JEL Classification: D4, D11, C78

Suggested Citation

Kuo, Chia-Wei and Ahn, Hyun-Soo and Aydin, Goker, Dynamic Pricing of Limited Inventories When Customers Negotiate (August 1, 2010). Ross School of Business Paper No. 1159, Forthcoming in Operations Research, Available at SSRN: https://ssrn.com/abstract=1910617 or http://dx.doi.org/10.2139/ssrn.1910617

Chia-Wei Kuo (Contact Author)

National Taiwan University - Department of Business Administration ( email )

1 Sec. 4, Roosevelt Road
Taipei 106, 106
Taiwan

Hyun-Soo Ahn

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan St
R5456
Ann Arbor, MI 48109-1234
United States

Goker Aydin

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering ( email )

1205 Beal Avenue
Ann Arbor, MI 48109
United States

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