2) Heuristic Algorithm
Both carrier and shipper problems are formulated using Variational Inequalities (VI). The individual
carrier and shipper models are solved employing the projection algorithm which resolves VI into a
sequence of sub-problems by the general iterative scheme and the three-level model is solved by a
heuristic algorithm. The heuristic to solve the bi-level model is as follows: Carriers make pricing and
routing decisions. Shippers determine production, shipment and consumption pattern, considering
carriers' pricing and routing. Carriers examine the reactions of shippers for every feasible scenario. From
all these reactions, carriers choose the one that gives them the maximum profit.