Designing fee tables for retail delivery services by third-party logistics providers

Manufacturers are increasingly relying on third-party logistics service providers to distribute their products to retail stores. Fee tables, specifying how much to pay for each delivery based on weight and distance, are commonly used as the basis for compensating distributors for their delivery services. This article proposes and solves an optimization model to help a large building products manufacturer design an appropriate fee table for payments to its distributors for delivering products from regional distribution centers to retail stores. Given the distance and the distribution of shipment weights to each store served by every distribution center, the model selects the weight and distance ranges of the fee table and sets the fees for each combination of ranges to minimize total distribution costs while satisfying fee structure requirements and ensuring adequate total compensation for each distributor. Since the problem is difficult to solve using commercial solvers, we develop a tailored approach to obtain near-optimal solutions quickly by adding valid inequalities to strengthen the model formulation and using an optimization-based procedure to generate a heuristic solution. When applied to actual data from the building products manufacturer, our Composite solution method, combining cutting planes and heuristic, was effective (yielding solutions that are within 1% of optimality) and generated substantial savings (of nearly 10%) over the current fee table.