Dynamic pricing in continuous time with cancellation and refund policies

In this work, we study a continuous time dynamic pricing model with focus on the event of cancellation and return policies for perishable products. A number of products of the same kind have to be sold during a finite time horizon. The potential customers arrive in accordance with a Poisson process. Upon arrival, a customer either purchases one item if the current price is lower than his/her reservation price, or leaves the store without buying an item. Some customers, however, choose to return the product to the store after they buy the item and hope to obtain a refund. Any returned item is associated with a loss even though it is assumed that a returned item is in good condition and the store is able to sell it to a future customer during the remaining time horizon, because the store loses the opportunity to sell it earlier with a higher price. Our study mainly focuses on which refund policy a store should adopt: full refund without any penalty or partial refund with a penalty. We formulate the problem using two dynamic programming models for both full refund and partial refund respectively. Our main objective is to study the structural properties of optimal pricing and return polices for both models, which would shed managerial insight and facilitate efficient algorithms for computing the optimal policies. Numerical examples are conducted and used for comparison purposes between full refund and partial refund policies. As a result of the numerical studies, it is concluded that under certain circumstances, a store can take advantage of the cancellation with resale as an opportunity to improve the total revenue by issuing a partial refund policy.