We examine the procurement process selection problem of a large industrial buyer who employs reverse auctions for awarding procurement contracts. We contrast two classes of commonly used strategies under multiple sourcing; namely, single-stage reverse auctions, and two-stage processes where price-quantity adjustments between the buyer and the suppliers follow a first-stage reverse auction. Deriving bounds of efficiency for these two classes of procurement processes under convex supplier production costs, we present insights on the conditions under which each class is preferable for the buyer. Considering the effect of contracting and processing costs, a single-stage process is likely to be preferable to a two-stage process when the number of bidding suppliers is high, especially when capacity is rigid. A two-stage process with one information transfer in the second stage may be the preferred procurement mode when production is highly scalable, i.e., when the marginal production cost increase with increased production is small. When the number of suppliers is low, the effect of a decrease in production scalability depends on the current scalability level. For high scalability levels, a decrease in production scalability may decrease the efficiency of both single-stage and simple two-stage processes, whereas for low scalability levels, it tends to increase efficiency for both of these process classes. A decrease in production costs makes employing simple processes more attractive when production is highly scalable or when supplier capacity is rigid. For intermediate production scalability, however, a cost decrease may make employing two-stage processes with multiple information transfers in the second round preferable for the buyer.