An exact method for the combinatorial bids generation problem with uncertainty on clearing prices, bids success, and contracts materialization

Abstract

We address a new variant of the Bid Construction Problem (BCP) with stochastic clearing prices in combinatorial auctions for the procurement of truckload transportation service that tackles uncertainty on bids success and auctioned contracts materialization. We propose the first exact method to generate multiple non-overlapping bids while ensuring a non-negative profit for the carrier regardless of the auction outcomes and auctioned contracts materialization. Our exact method iteratively solves a relaxed then a restricted version of the BCP with stochastic clearing prices while checking all routes generated in each optimal solution and dynamically adds cuts to forbid what we define as risky routes. Risky routes are the ones that could yield a negative profit if some bids are lost or some auctioned contracts do not materialize later. Our experimental study highlights the good performance of our exact approach and points out the potential gains in profits yielded by our new variant compared to a standard BCP.