An Integer Programming Formulation of the Bid Evaluation Problem for Coordinated Tasks

We extend the IP models proposed by Nisan and Andersson for winner determination in combinatorial auctions, to the problem of evaluating bids for coordinated task sets. This requires relaxing the free disposal assumption, and encoding temporal constraints in the model. We present a basic model, along with an improved model that dramatically reduces the number of rows by preprocessing the temporal constraints into compatibility constraints. Experimental results show how the models perform and scale, and how they compare with a stochastic solver based on Simulated Annealing. On average, the IP approach finds optimum solutions significantly faster than Simulated Annealing, but with an extreme level of variability that may make it impractical in time-constrained agent negotiation scenarios.