Bidding languages and supplier selection for procurement markets with economies of scale and scope

Economies of scale and scope describe key characteristics of production cost functions that influence allocations and prices on procurement markets. Combinatorial auctions have been analyzed intensively, and enable the bidders to express economies of scope, but they typically are designed for single units of each item only and cannot easily be extended to the multi-unit case. Auction designs for markets with economies of scale are much less well understood, they require new bidding languages, and the supplier selection typically becomes a hard computational problem. We suggest a bidding language allowing to describe economies of scope and scale. It enables bidders to specify supply curves, representing economies of scale, and various rebates accounting for economies of scope. In addition, we support a number of side constraints enabling the auctioneer to consider various business rules in the winner determination. We conduct computational experiments based on a branch-and-cut solver to explore the incremental computational burden to determine optimal solutions brought about by the need to express economies of scope for problems of practical size.