A heuristic policy for dynamic pricing and demand learning with limited price changes and censored demand

In this work we study a dynamic pricing problem with demand censoring and limited price changes. In our problem there is a seller of a single product that aims to maximize revenue over a finite sales horizon. The seller does not know the form of the mean demand function but does have some limited knowledge. We assume that the seller has a hypothesis set of mean demand functions and that the true mean demand function is an element of this set. Furthermore, the seller faces a business constraint on the number of price changes that is allowed during the sales horizon. More specifically, the number of price changes that the seller is allowed to make is bounded above by a finite integer. We furthermore assume that the seller can only observe the sales (minimum between realized demand and available inventory) and thus that demand is censored. In each period the seller can replenish his inventory to a particular level. The objective of the seller is to set the best price and inventory level in each period of the sales horizon in order to maximize his profit. The profit is determined by the revenue of the sales minus holding costs and costs for lost sales (unsatisfied demand). In determining the best price and inventory level the seller faces and exploration-exploitation trade-off. The seller has to experiment with different prices and inventory levels in order to learn from historical sales data which contains information about market responses to offered prices. On the other hand, the seller also needs to exploit what it has learned and set prices and inventory levels that are optimal given the information collected so far. We propose a heuristic policy for this problem and study its performance using numerical experiments. The results are promising and indicate that the growth rate of regret of the policy is sub-linear with respect to the sales horizon.