Integrating Dynamic Pricing with Inventory Decisions Under Lost Sales

Forthcoming in Management Science

43 Pages Posted: 29 Mar 2016 Last revised: 15 Feb 2019

See all articles by Qi Feng

Qi Feng

Purdue University - Krannert School of Management

Sirong Luo

Shanghai University of Finance and Economics

J. George Shanthikumar

Purdue University - Krannert School of Management

Date Written: November 9, 2019

Abstract

Inventory-based pricing under lost sales is an important, yet notoriously challenging problem in the operations management literature. The vast existing literature on this problem focuses on identifying optimality conditions for a simple management policy, while restricting to special classes of demand functions and to the special case of single-period or long-term stationary settings. In view of the existing developments, it seems unlikely to find general, easy-to-verify conditions for a tractable optimal policy in a possibly nonstationary environment. Instead, we take a different approach to tackle this problem. Specifically, we refine our analysis to a class of intuitively appealing policies, under which the price is decreasing in the post-order inventory level. Using properties of stochastic functions, we show that, under very general conditions on the stochastic demand function, the objective function is concave along such price paths, leading to a simple base stock list price policy. We identify the upper and lower boundaries for a candidate set of decreasing price paths and show that any decreasing path outside of this set is always dominated by some inside the set in terms of profit performance. The boundary policies can be computed efficiently through a single-dimensional search. An extensive numerical analysis suggests that choosing boundary policies yields close-to-optimal profit—in most instances, one of the boundary policies indeed generates the optimal profit, even when they are not, the profit loss is very marginal.

Keywords: Stochastic function; Monotone policy; Inventory-pricing problem; Lost sales

Suggested Citation

Feng, Qi and Luo, Sirong and Shanthikumar, J. George, Integrating Dynamic Pricing with Inventory Decisions Under Lost Sales (November 9, 2019). Forthcoming in Management Science, Available at SSRN: https://ssrn.com/abstract=2755995

Qi Feng (Contact Author)

Purdue University - Krannert School of Management ( email )

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

Sirong Luo

Shanghai University of Finance and Economics ( email )

777 Guoding Road
Shanghai, P.R.China, 200433
China

J. George Shanthikumar

Purdue University - Krannert School of Management ( email )

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

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
133
Abstract Views
965
rank
250,587
PlumX Metrics