Integrated Pricing and Routing for Package Express Carriers

We consider an integrated pricing and routing problem on a service network motivated by environments encountered at package express carriers. The decision maker sets the price for each origin-destination market, which determines the demand that needs to be served. The demand can be routed along multiple paths in the service network if desirable. The objective is to maximize the revenues from serving demand minus the transportation costs incurred by serving demand given the capacities in the network. We propose two algorithms for the solution of this problem with theoretical convergence guarantees: (1) a Frank-Wolfe type algorithm, which requires the objective function to be smooth, and (2) a primal-dual algorithm using an online learning technique, which allows non-smooth objective functions. We show that both algorithms have a convergence rate of Õ(1/T ) where T is the number of iterations. Numerical experiments on randomly generated instances show that coordinating pricing and routing decisions can improve profits by more than 10%.