Performance Guarantees for Network Revenue Management with Flexible Products

Problem definition : We consider network revenue management problems with flexible products. We have a network of resources with limited capacities. To each customer arriving into the system, we offer an assortment of products. The customer chooses a product within the offered assortment or decides to leave without a purchase. The products are flexible in the sense that there are multiple possible combinations of resources that we can use to serve a customer with a purchase for a particular product. We refer to each such combination of resources as a route. The service provider chooses the route to serve a customer with a purchase for a particular product. Such flexible products occur, for example, when customers book at-home cleaning services but leave the timing of service to the company that provides the service. Our goal is to find a policy to decide which assortment of products to offer to each customer to maximize the total expected revenue, making sure that there are always feasible route assignments for the customers with purchased products. Methodology/results : We start by considering the case in which we make the route assignments at the end of the selling horizon. The dynamic programming formulation of the problem is significantly different from its analogue without flexible products as the state variable keeps track of the number of purchases for each product rather than the remaining capacity of each resource. Letting L be the maximum number of resources in a route, we give a policy that obtains at least 1 / ( 1 + L ) fraction of the optimal total expected revenue. We extend our policy to the case in which we make the route assignments periodically over the selling horizon. Managerial implications : To our knowledge, the policy that we develop is the first with a performance guarantee under flexible products. Thus, our work constructs policies that can be implemented in practice under flexible products, also providing performance guarantees.