Fleet Composition Optimization with Truckload and Less-Than-Truckload Shipping Options

Abstract: This study considers a vehicle fleet composition problem with stochastic delivery demands that must be fulfilled via a combination of internal truckload (TL) capacity and external less-than-truckload (LTL) shipments. Internal capacity costs include a fixed vehicle ownership cost and a fixed dispatch cost per truck, while LTL costs are incurred per unit shipped. We characterize the expected total transportation cost per period as a function of the internal fleet size for both homogeneous and heterogeneous fleets. We propose a solution approach that provides optimal shipping policies with analytical solutions for homogeneous fleets and certain types of heterogeneous fleets. For fleets with a broad range of available truck types, we create a two-stage stochastic programming model that minimizes the expected transportation cost per period as a function of the number of trucks of each type acquired. We further develop a decomposition-based algorithm that can effectively solve the proposed model, which provides solutions that are nearly as good as the solutions obtained using a commercial solver in substantially reduced computational time. Our numerical results reveal that the optimal fleet composition strategy is significantly affected by the LTL freight rate, the number of truck types, and the properties of the probability distribution of demand.