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Consolidation carriers transport shipments that are small relative to trailer capacity. To be cost effective, the carrier must consolidate shipments, which requires coordinating their paths in both space and time; i.e., the carrier must solve a service network design problem. Most service network design models rely on discretization of time—i.e., instead of determining the exact time at which a dispatch should occur, the model determines a time interval during which a dispatch should occur. While the use of time discretization is widespread in service network design models, a fundamental question related to its use has never been answered: Is it possible to produce an optimal continuous-time solution without explicitly modeling each point in time? We answer this question in the affirmative. We develop an iterative refinement algorithm using partially time-expanded networks that solves continuous-time service network …