Joint design of fleet size, hub locations, and hub capacities for third-party logistics networks with road congestion constraints

This paper describes third-party logistics (3PL) systems with consolidation hubs as a hub-and-spoke network. We propose a multiple assignment (MA) model for the joint design of the fleet size and the number, locations and capacities of hubs. The objective is to minimize the total costs, including congestion costs. We explicitly model the road congestion by formulating the route travel time as an increasing function of the number of trucks on the route. We consider two types of trucks to model economies of scale. Similar to a truck booking system, we control the node and road congestions by delaying some of the overfull demand at the origin nodes. We derive the asymptotic behavior as design variables increase and demonstrate how the 3PL system throughput is bounded by the bottleneck routes. When the existing road congestion on the bottleneck routes is heavy, excessively large fleets and hub capacities will worsen the traffic conditions and downgrade the system throughput. We develop a math-heuristic algorithm to solve our problem, which is decomposed into two subproblems. We prove that the two subproblems can be linearized. The numerical experiments reveal some interesting findings: (1) heavier congestion on an existing road network (without 3PL trucks) generates a design with higher requirements (a larger number of hubs, a larger hub capacity and a larger fleet size) and larger economies of scale; (2) neglecting the road congestion constraints optimistically estimates the system performance and generate a design with fewer hubs and a larger number of large trucks; and (3) decreasing the fixed costs of establishing hubs or the large truck-related costs can significantly increase the economies of scale and reduce the total number of trucks.