Supply chain resilience analysis aims to identify the critical elements in the supply chain, measure its reliability, and analyze solutions for improving vulnerabilities. While extensive methods like stochastic approaches have been dominant, robust optimization-widely applied in robust planning under uncertainties without specific probability distributions-remains relatively underexplored for this research problem. This paper employs robust optimization with budget-of-uncertainty as a tool to analyze the resilience of multi-modal logistics service networks under time uncertainty. We examine the interactive effects of three critical factors: network size, disruption scale, disruption degree. The computational experiments offer valuable managerial insights for practitioners and researchers.