Problem description: We study the problem of designing large-scale resilient relay logistics hub networks. We propose a model of Capacitated Relay Network Design under Stochastic Demand and Consolidation-Based Routing (CRND-SDCR), which aims to improve a network’s efficiency and resilience against commodity demand variability through integrating tactical decisions.
Methodology: We formulate CRND-SDCR as a two-stage stochastic optimization program where we locate relay logistics hubs and decide their capacities in the first stage and design a minimum-cost consolidation plan in the second stage. As an exact solution approach, we design a branch-and-cut algorithm with a nested Benders decomposition and integer L-shaped method. We decompose CRND-SDCR twice: (i) across the stochastic demand scenarios, and (ii) across each origin-destination pair within the scenario-dependent subproblems; and utilize Benders decomposition at each of these decomposition stages to add the associated Benders feedback cuts. We guarantee the exactness of our solution approach by adding integer L-shaped cuts, obtained by solving the second-stage subproblem exactly through Benders decomposition as well.
Results: We apply our methodology to design large-scale resilient relay networks to be used for finished vehicle deliveries for a US-based car manufacturer partner. Our computational experiments demonstrate that our developed approach can obtain near-optimal solutions for practically relevant instances using sample average approximation. The resulting logistics networks showcase a significant improvement in capabilities to sustain commodity demand variability, in comparison with relay networks designed to fulfill average commodity demand. In particular, our networks lead to a $\sim7\%$ decrease in average delivery costs as compared to networks designed under a deterministic demand setting. Moreover, we depict the importance of considering consolidation-based routing at the network design stage through benchmarking against literature-proposed relay networks that continuously approximate the routing operations.
Implications: Our analysis provides decision-makers with recommendations regarding inducing network flexibility to hedge against commodity demand uncertainty.