Improved bid prices for choice-based network revenue management

In many implemented network revenue management systems, a bid price control is being used. In this form of control bid, prices are attached to resources, and a product is offered if the revenue derived from it exceeds the sum of the bid prices of its consumed resources. This approach is appealing because once bid prices have been determined, it is fairly simple to derive the products that should be offered. Yet it is still unknown how well a bid price control actually performs. Recently, considerable progress has been made with network revenue management by incorporating customer purchase behavior via discrete choice models. However, the majority of authors have presented control policies for the booking process that are expressed in terms of which combination of products to offer at a given point in time and given resource inventories. The recommended combination of products as identified by these policies might not be representable through bid price control. If demand were independent from available product alternatives, an optimal choice of bid prices is to use the marginal value of capacity for each resource in the network. But under dependent demand, this is not necessarily the case. In fact, it seems that these bid prices are typically not restrictive enough and result in buy-down effects. We propose (1) a simple and fast heuristic that iteratively improves on an initial guess for the bid price vector; this first guess could be, for example, dynamic estimates of the marginal value of capacity. Moreover, (2) we demonstrate that using these dynamic marginal capacity values directly as bid prices can lead to significant revenue loss as compared to using our heuristic. Finally, (3) we investigate numerically how much revenue performance is lost due to the confinement of product combinations that can be represented by a bid price. Our heuristic is not restricted to a particular choice model and can be combined with any method that provides estimates of the marginal values of capacity. In our numerical experiments, we test the heuristic on some popular networks examples taken from peer literature. We use a multinomial logit choice model which allows customers from different segments to have products in common that they are considering purchasing. In most instances, our heuristic policy results in significant revenue gains over some currently available alternatives at low computational cost.