Inventory-Based Dynamic Pricing with Costly Price Adjustment

33 Pages Posted: 13 Aug 2014 Last revised: 2 Dec 2014

See all articles by Wen Chen

Wen Chen

Providence College

Qi Feng

Purdue University - Krannert School of Management

Sridhar Seshadri

University of Illinois at Urbana Champaign; Indian School of Business

Date Written: December 1, 2014

Abstract

We study an average-cost stochastic inventory control problem in which the firm can replenish inventory and adjust price at anytime. We establish the optimality to change the price from low to high in each replenishment cycle as inventory is depleted. With costly price adjustment, scale economies of inventory replenishment are reflected in the cycle time instead of lot size -- An increased fixed ordering cost leads to an extended replenishment cycle but does not necessarily increase the order quantity. A reduced marginal cost of ordering calls for an increased order quantity, as well as speeding up product selling within a cycle. We derive useful properties of the profit function that allows for reducing computational complexity of the problem. For systems requiring short replenishment cycles, the optimal solution can be easily computed by applying these properties. For systems requiring long replenishment cycles, we further consider a relaxed problem that is computational tractable. Under this relaxation, the sum of fixed ordering cost and price adjustment cost is equal to (greater than, less than) the total inventory holding cost within a replenishment cycle when the inventory holding cost is linear (convex, concave) in the stock level. Moreover, under the optimal solution, the time-average profit is the same across all price segments when the inventory holding cost is accounted properly. Through a numerical study, we demonstrate that inventory-based dynamic pricing can lead to significant profit improvement compared with static pricing and limited price adjustment can yield a benefit that is close to unlimited price adjustment. To be able to enjoy the benefit of dynamic pricing, however, it is important to appropriately choose inventory levels at which the price is revised.

Keywords: Inventory Control, Dynamic Pricing, Costly Price Adjustment

Suggested Citation

Chen, Wen and Feng, Qi and Seshadri, Sridhar, Inventory-Based Dynamic Pricing with Costly Price Adjustment (December 1, 2014). Available at SSRN: https://ssrn.com/abstract=2479011 or http://dx.doi.org/10.2139/ssrn.2479011

Wen Chen

Providence College ( email )

United States

Qi Feng (Contact Author)

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

Sridhar Seshadri

University of Illinois at Urbana Champaign ( email )

1206 South Sixth Street
Champaign, IL 61820
United States

Indian School of Business ( email )

Hyderabad, Gachibowli 500 019
India

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