Dynamic Pricing with Early Cancellation and Resale

We consider a continuous time dynamic pricing model where a seller needs to sell a single item over a finitetime horizon. Customers arrive in accordance with a Poisson process. Upon arrival, a customer either purchasesthe item if the posted price is lower than his/her reservation price, or leaves empty-handed. After purchasingthe item, some customers, however, will return the item to the seller at an exponential rate for a full refund.We assume that a returned item is in mint condition and the seller can resell it to future customers. Theobjective of the seller is to dynamically adjust the price in order to maximize the expected total revenue whenthe sale horizon ends. We formulate the dynamic pricing problem as a dynamic programming model and derive thestructural properties of the optimal policy and the optimal value function. For cases in which the customer'sreservation price is exponentially distributed, we derive the optimal policy in a closed form. For generalreservation price distribution, we consider an approximation of the original model by discretizing both time andthe allowable price set. We then present an algorithm for numerically computing the optimal policy in thisdiscrete time model. Numerical examples show that if the discrete price set is carefully chosen, the expectedtotal revenue is nearly the same as that when the allowable price set is continuous.