Multi-disruption resilient hub location–allocation network design for less-than-truckload logistics

Less-than-truckload (LTL) logistics presents an interesting and often overlooked practice area of hub location–allocation problems, with its variable discount rates playing a game-changing role. Vulnerability of the roads is another critical factor that has often been neglected when designing hub networks. In this paper, a novel integrated model is designed to solve the LTL hub network design problem, incorporating a practical stepwise discount function. The proposed model is further extended to a reliability-oriented version that can resiliently withstand multiple, simultaneous road disruptions. We use the failure mode and effect analysis (FMEA) technique to encompass the likelihood of experiencing each failure mode, together with the monetary and service-level effects. Coupled with probability theory, it leads to the introduction of a novel closed form for serviceability under multiple concurrent failures. Having such a function enables us to deploy exact optimization methods. Given the natural complexity of the problem, we also present effective linearization approaches. Numerical benchmarks demonstrate the superiority of the novel reliability-oriented approach over the basic version, successfully realizing desired serviceability levels as high as 80%. It also benefits from avoiding unnecessary rerouting, making it even more attractive for policymakers to design efficiently resilient transportation networks, especially if low-range, zero-emission trucks are incorporated.