A Bid Generation Problem in Truckload Transportation Service Procurement Considering Multiple Periods and Uncertainty: Model and Benders Decomposition Approach

Transportation service procurement is often realized by an auction. With the rolling horizon planning concept adopted in logistics, carriers usually plan their transportation operations of several periods (days) in advance. This implies that carriers must consider multiple periods when participating in combinatorial auctions organized by shippers. Since transportation requests in future cannot be foreseen, carriers must consider request uncertainty in such auctions. In this paper, we consider a carrier's bid generation problem appeared in a multi-round combinatorial auction for truckload transportation service procurement with the consideration of multiple periods and request uncertainty. The problem is to maximize the total expected net profit of the carrier in a planning horizon of multiple periods by optimally determining the transportation requests to bid, the period to serve each request, and the routes to serve all requests including the carrier's reserved requests. This problem is hard to solve because of its stochastic nature. By adopting the scenario approach of stochastic optimization, a mixed integer linear programming model is formulated for the problem. A Benders decomposition approach is then proposed to solve the model, with Pareto-optimal cuts to accelerate its solution process. The performance of the approach is evaluated by numerical experiments on randomly generated instances. The computational results demonstrate that the Bender decomposition approach is much more efficient than CPLEX solver in solving large instances of the problem. In addition, the value of considering uncertain requests and multi-period in the bid generation is evaluated.