We consider sealed- and open-bid total-cost procurement auctions where two attributes are used for contract award decisions: price, which is bid by the supplier, and a fixed cost adjustment, which is included by the buyer to capture nonprice factors such as logistics costs. Suppliers know only their own true production cost and their own cost adjustment, and the buyer does not know the suppliers' true production costs but does know all suppliers' cost adjustments, which she herself sets in order to make an informed total-cost decision. The buyer, who seeks to minimize her total (price and cost adjustment) procurement cost, can choose to run a first-price sealed-bid auction, where suppliers' bids are affected by their beliefs about each other's total costs, or a descending open-bid auction, where only the actual realizations of suppliers' total costs drive the auction outcome. We characterize the buyer's choice between the two formats as a threshold decision over suppliers' cost adjustments and analyze the effect of supplier beliefs on her decision. We also study the impact of additional suppliers on the buyer's decision, the effect of correlation between suppliers' production costs and their cost adjustments, and additive as well as multiplicative total-cost functions. The results suggest that procurement managers can use their evaluations of suppliers' cost adjustments to make better auction format decisions.
