Route selection on freight networks with weight and volume constraints

This paper investigates the properties of freight networks where flow is measured with two attributes (weight and volume) and where costs are linear. Two dual variables are associated with each arc, one representing the marginal cost of increasing the weight flow on the arc and the other representing the marginal cost of increasing the volume flow. Optimal routes are determined in two steps: (1) set weight and volume prices and solve shortest path problems, and (2) adjust weight and volume prices in a way that causes the dual objective to increase. Each iteration provides a feasible solution and a bound on the maximum improvement in the objective function. The algorithm is applied to various test problems, to identify the conditions where it is most important to account for multiattribute freight flows.