Exact solutions and heuristics for multi-product inventory pricing problem

Abstract

We study the multi-product inventory pricing problem under stochastic and price sensitive demand. We have initial inventory of m resources whose different combinations form n products. Products are perishable and need to be sold by a deadline. Demand for each product is modeled as a non-homogeneous Poisson process whose intensity is a function of the current price of the product itself. The aim is to set the price of each product over the selling period to maximize the expected revenue. This problem is faced in various industries including retail, airlines, automobile, apparel, hotels and car rentals. Our contributions are twofold. First, we provide a closed form solution for the special case of exponential price response where the elasticity parameter of the demand function of all products are equal. Second, we develop two classes of dynamic pricing heuristics: one using the value approximation approach of dynamic programming and the other using the deterministic version of the problem. Our numerical analysis indicates that dynamic pricing yields significantly higher revenues compared to fixed price policies. One of the dynamic pricing heuristics based on the deterministic problem provides around 5−15% additional revenue compared to fixed price policies. Moreover, two value approximation heuristics that we suggest result in at most ∼ 0.5% and ∼ 3.4% gaps in the expected revenue compared to the optimal dynamic pricing policy for general form of exponential price response. These additional revenues can have a profound effect on the profitability of firms, so dynamic pricing should be preferred over fixed price policies in practice.