Although supply disruption is ubiquitous because of natural or man-made disasters, many firms still use the price-only reverse auction (only the cost is considered) to make purchase decisions. We first study the suppliers’ equilibrium bidding strategies and the buyer’s expected revenue under the first- and second-price price-only reverse auctions when the suppliers are unreliable and have private information on their costs and disruption probabilities. We show that the two auctions are equivalent and not efficient. Then we propose two easily implementable reverse auctions, namely the first-price and second-price format announced penalty reverse auction (APRA), and show that the “revenue equivalence principle” holds, i.e., the two auctions generate the same ex ante expected profit to the buyer. We further show that the two reverse auctions are efficient and “truth telling” is the suppliers’ dominant strategy in the second-price format APRA. We conduct numerical studies to assess the impacts of some parameters on the bidding strategies, the buyer’s profit and social profit.
