Revenue management with dynamic pricing in competitive market

Abstract

In this study, we formulate the seasonal product pricing problem as a dynamic programming model analytically and discuss some structural properties of the optimal policy and the optimal value function. We consider discrete time dynamic pricing model where a seller needs to sell multiple items over a finite time horizon when the firms adjust their prices in accordance with the competition, on hand inventory and the time remaining in both monopolistic and oligopolistic market environment. Demands are Bernoulli process with probability lambda; for cases in which customer reservation prices follow normal distribution, we derive the optimal policy in a closed form. Upon arrival, a customer either purchases one unit of item if the posted price is lower than his/her reservation price, or leaves empty-handed and maybe wait for an appropriate posted price. After purchasing the item, some of the customers, who have bought an item, will return one unit of the item to the seller with binomial distribution for a full refund. We assume that a returned item can be resold to the future customers. The product's price needs to be adjusted dynamically to incorporate new demand information, to balance supply with demand over the sale horizon in order to maximize the expected total revenue when the sale horizon ends. We conduct numerical studies to develop insights on the sensitivity of the optimal policies to the various probability parameters and to evaluate the performance of expected revenue function under different arrival probability, price coefficient, cancelation probability and initial inventory levels in both monopolistic and oligopolistic market with full refund. The majority of research published in the literature, assumes that the market is monopolistic. Our nu- merical results show that, competition and cancelation are important issues to consider that affects the expected revenue.