A transportation service procurement problem with combinatorial auction

This paper discusses a practical transportation service procurement problem, which is originated from an external project with the department of transportation purchasing at Royal Philips. A combinatorial auction strategy is developed to help the department to determine the annual transportation service procurement cost. Because of a few preset internal and external policies, to settle an optimal purchasing plan becomes a challenging job for the company. We formulate this problem into a linear integer programming model, and prove it is MV-Hard. We also find that the integer programming model is only solvable for very small cases with only a few lanes, bidders and bids using the state-of-the-art commercial solver ILOG CPLEX 11. We propose an iterative rounding heuristic algorithm that works on the linear-relaxation of the integer programming model. Experiments show that good-quality solutions are achieved for instances of moderate size.