A smart market for industrial procurement with capacity constraints

We address the problem of designing multi-item procurement auctions for a monopsonistic buyer in capacity-constrained environments. Using insights from classical auction theory, we construct an optimization-based auction mechanism (‘smart market’) relying on the dynamic resolution of a linear program minimizing the buyer's cost under the suppliers' capacity constraints. Suppliers can modify their offers in response to the optimal allocation corresponding to each set of bids, giving rise to a dynamic competitive bidding process. To assist suppliers, we also develop a bidding-suggestion device based on a myopic best-response (MBR) calculation that solves an associated optimization problem. Assuming linear costs for the suppliers, we study within a game-theoretic framework the sequence of bids arising in this smart market. Under a weak behavioral assumption and some symmetry requirements, an explicit upper bound for the winning bids is established. We-then formulate a complete behavioral model and solution methodology based on the MBR rationale and show that the bounds derived earlier continue to hold. We analytically derive some structural and convergence properties of the MBR dynamics in the simplest nontrivial market environment, which suggests further possible design improvements, and investigate bidding dynamics and incentive compatibility issues via numerical simulations.