Multi-party multi-period supply chain coordination

We apply combinatorial auction as a coordination mechanism to smooth demands placed on suppliers' limited production capacities, allowing several manufacturers to share common suppliers effectively. Products are bidders bidding for parts from suppliers, consuming their capacities in different time periods. The fourth party logistic (4PL) provider acts as the auctioneer to coordinate bids and perform price iterations. We leverage on the strong links between the Lagrangian relaxation method and combinatorial auction, where the Lagrange multipliers serve as the supply capacity reserve prices, to balance the demand and supply of capacities. To prevent cyclic behaviour and to increase convergence speed, we introduce a non-linear capacity cost component to the sub-problems' objective function. In addition, our formulation permits asynchronous bidding, allowing dynamic changes in production demand and capacity supply, making the model applicable in actual industry setting. Our experimental results suggest the suitability of three different price revision methods for different problem types.