Auction-based transportation procurement in make-to-order systems

This article presents an auction-based model for Transportation Service Procurement (TSP) in make-to-order systems. It is one of the first to integrate auction-based TSP and inventory. The underlying model is applicable in the general context of coordinating TSP and inventory decisions. Using the well-known Revenue Equivalence Principle, we formulate a dynamic programming problem. When no fixed auction costs occur, we establish the optimality of the state-dependent deliver-down-to allocation policy, which is essentially a state-dependent base-stock-type (S(x)-like policy). We characterize the property of the optimal state-dependent deliver-down-to level. When fixed auction costs apply, we establish the optimality of the state-dependent (s(x), S(x))-like policy. We show that the optimal allocation can be achieved by running a Vickrey–Clarke–Groves auction or a first-price auction with closed-form reserve prices. A symmetric equilibrium bidding strategy for each carrier can be easily computed. Our model is also extended to the case where each carrier has multi-unit supply. By mild technical modifications, all of the results derived in the infinite-horizon case can be extended to the finite-horizon case. Some key features of the finite-horizon case are discussed.