Dynamic Pricing for Hotel Rooms When Customers Request Multiple-Day Stays

We study the dynamic pricing problem faced by a hotel that maximizes expected revenue from a single type of rooms. Demand for the rooms is stochastic and non-stationary. Our Markov decision process formulation of this problem determines the optimal booking price of rooms (resources) for each individual day, while considering the availability of room capacity throughout the multiple-day stays (products) requested by customers. To offer attractive average daily prices for multiple-day stays, the hotel should not only substantially raise the booking prices for some high-demand days, but also significantly lower the booking prices for the low-demand days that are immediately adjacent to these high-demand days. This policy-structure insight is based on analysis and exact numerical solutions of small problem instances. For larger problem instances, we develop an approximate linear programming based pricing policy and numerically benchmark it against both a fixed-price heuristic and a single-day decomposition approach. Our pricing policy outperforms these benchmarks and generates up to 7% more revenue than the single-day decomposition approach. Enforcing our policy-structure insight, which may simplify the implementation, results in revenue losses of less than 1%. Our findings are potentially relevant beyond the hotel domain for applications involving the dynamic pricing of capacitated resources used by multiple products.