Journal Articles

Dynamic Pricing of Limited Inventories when Customers Negotiate

2011, Operations Research

C. Kuo, H. Ahn, Goker Aydin


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.

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.


Kuo, C., H. Ahn, and G. Aydin (2011), "Dynamic Pricing of Limited Inventories when Customers Negotiate," Operations Research, Vol. 59, No. 4, July/August, pp. 882-897.

Kelley School of Business

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