Optimal Procurement Auctions Under Multistage Supplier Qualification

We consider a firm that solicits bids from a fixed-sized pool of yet-to-be-qualified suppliers for an indivisible contract. The contract can only be awarded to a supplier who passes a multistage qualification process. For each stage of the qualification process, the buyer incurs a fixed testing cost for each supplier she chooses to test. The buyer seeks an optimal mechanism—that is, one that minimizes her total expected cost. Motivated by the buyer’s urgency (or the lack of it) of time for completing the qualification process, we obtain optimal mechanisms for two testing environments: (1) simultaneous testing, where in each stage, the buyer selects a subset of those suppliers who have passed all the previous stages and tests them simultaneously; and (2) nonsimultaneous testing, where the simultaneous-testing requirement is not imposed. Under simultaneous testing, the admission policy for selecting suppliers at each stage is based on nonuniform reserve-price thresholds. Under nonsimultaneous testing, too, the admission policy is threshold based, but the selection process is sequential in nature. The relative increase in cost due to the simultaneous-testing requirement is (under a mild condition) monotonically increasing in the number of suppliers, the expected multistage testing cost, and the overall passing probability. We also study the optimal sequencing of the qualification stages and show that the buyer should schedule the stages in increasing order of the ratio of their testing cost to their failing probability. Finally, for the simpler setting of a single-stage qualification process and a single supplier, we study a two-dimensional mechanism design problem where, in addition to cost, the passing probability is also private to the supplier. Here, too, threshold-based admission remains optimal, and the buyer offers either a pooling or a separating contract.