Integrated route planning and cost allocation in truckload shipper collaboration

In truckload shipper collaboration, a group of shippers purchasing the services of carriers come together and try to identify tours which consist of regularly scheduled shipments with minimal empty truck movements with the hope of getting better rates from the carriers in return. Determining the best set of such tours is a challenging optimization problem, the solution of which yields the set of lanes and firms to be included in the collaboration, who will collaborate with whom, and the maximum amount of savings which can be achieved. Allocation of the total calculated cost to the participating firms and individual lanes will determine the final savings for each participating firm. If the allocated costs are not accepted by the participants, the collaboration will face the risk of collapse. In the literature, solving the optimization problem minimizing the total cost and allocating the calculated minimum cost are treated as two successive but distinct phases. In this work, we aim to merge these two phases by formulating an optimization model and develop column generation based algorithms for its solution.