Optimal auctions for transportation service procurement in an infinite horizon inventory system

This paper presents an auction-based model for transportation service procurement (TSP) in infinite horizon cases where orders are produced in the just-in-time pull mode. 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 state-dependent deliver-down-to allocation policy, which is essentially of state-dependent base-stock type (S(x)-like policy). We also characterize the property of the optimal state-dependent deliver-down-to level. We show that the optimal allocation can be achieved by running a Vickrey-Clarke-Groves (VCG) auction or a first-price auction with closed-form reserve prices. A symmetric equilibrium bidding strategy for each carrier can be easily computed. Finally, we prove that the expected total discounted cost in a first-price auction is less than that in a VCG auction, when carriers are risk-averse.