Dynamic Pricing for Truckload Transportation Marketplaces

Abstract

We consider a truckload transportation marketplace in which a market maker sells transportation services to shippers and buys transportation services from carriers. Shippers enter into contracts with the market maker that specify the prices that the shippers have to pay the market maker for transportation. These contracts cover multiple loads over a relatively long specified period of time. When a shipper wants a load to be transported, the shipper enters the load data, including the origin, destination, load type, and requested pickup time, into the marketplace. The market maker chooses the prices offered to carriers for transporting the loads. The market maker can adjust these prices over time based on the dynamics of supply and demand. Carriers check the offers in the marketplace and choose among the available loads. We formulate the market maker's load pricing problem as a Markov decision process (MDP). The MDP captures randomness in the load and carrier arrival processes, as well as carriers' random choice behavior. As it is computationally inefficient to solve this MDP as the market size increases, we study a discrete-time fluid approximation of the problem. This approximation results in a simple pricing policy whose price for each load depends on the time remaining until the load has to be picked up, but does not depend on the other loads in the marketplace. We show that this policy is asymptotically optimal with a loss ratio of order $O(1/\theta)$, where $\theta$ represents the scale of shipper demand and carrier supply. We also present a continuous-time fluid model and discuss the managerial insights provided by its solution.