Transportation procurement with seasonally varying shipper demand and volume guarantees

Transportation companies that operate in seasonal markets where differences in demand occur in peak and nonpeak periods often negotiate for some form of demand smoothing with the customer - i.e., the shipper. In this paper, we study a shipper's transportation procurement model, in which the shipper gives assurances, through volume guarantees negotiated with the transportation companies, that shipments made in nonpeak periods will be commensurate with shipments in peak periods. The shipper uses the model in an auction process, in which the transportation companies bid for routes giving prices and capacity limits, to procure freight services from the companies, which minimizes its total transportation costs. The model is formulated as an integer programming problem that is shown to be strongly NP-hard even for a single-route network. We develop a solution approach that builds on the solution of the subproblem when only one transportation company is available to construct heuristic algorithms, including a linear programming relaxation-based method. Worst-case analysis is given, and the effectiveness of the algorithms is tested in numerical experimentation. By examining parameter sensitivity, insight is provided on how the algorithms can be used by the shipper for making procurement decisions. The practical usefulness of the model and the solution approaches is substantiated by its deployment with a multinational shipper.