An Algorithm for the Multiattribute, Multicommodity Flow Problem with Freight Consolidation and Inventory Costs

To remain competitive, manufacturers must seek transportation strategies that both reduce costs and maintain high levels of service. One approach is to consolidate inbound freight at transshipment points. This provides economies of scale and promotes capacity efficient mixes of high and low density items. When service level considerations are included via inventory holding costs, the approach yields a nonlinear network model with multiattribute multicommodity flows. The model is difficult to solve for global optimality in that the objective function is neither convex nor concave; therefore, a composite algorithm is proposed. The algorithm alternates between a linearization technique to find local optima and a heuristic search based on “adjacent concave flows” to provide local improvements. Computational results demonstrate the ability of the multiattribute approach to identify savings in overall transportation and inventory costs when compared to a single attribute approach.