A revenue management model for products with two capacity dimensions

Many perishable products and services have multiple capacity attributes. Shipping capacity of container liners, for example, is measured by both volume and weight. Containers with different size consume various capacities in the two dimensions. Restaurant revenue management aims to maximize the revenue per available seat-hour that captures both the number of dining tables and service manpower. Similar issues arise in the air cargo, trucking and health care industries. We study the revenue management problem with two capacity features and formulate the problem as a continuous-time stochastic control model. Unlike heuristic approaches, we derive the optimal solution in an analytical form. Computation of the optimal solution is fairly efficient. With certain conditions we explore the structural properties of the optimal solution. We show that if the revenue rate is concave in the capacity usage, the expected value of marginal capacity is monotone. As a result, the control policy is featured by a sequence of thresholds which displays a significant difference when the remaining capacity-mix varies. Numerical examples are provided.