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arXiv · 2608.26360

The Time-Dependent Traveling Salesman Problem with Loose Time Windows

Francisco J. Soulignac
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Abstract

The time-dependent traveling salesman problem with time windows (TDTSPTW) generalizes the well-known traveling salesman problem with time windows by accounting the effects of congestion on travel times. In this paper, we develop an exact framework for the TDTSPTW with a makespan objective that extends the range of instances solvable to optimality under loose time windows while remaining effective across all levels of time-window tightness. Our framework relies on a dynamic-programming labeling algorithm and combines column generation, ng-memory augmentation, and exact search, using completion bounds for state-space sparsification, variable fixing, and exact search pruning. Embedded within a branch-and-price method, the framework solves all instances with up to 45 customers in a benchmark comprising more than 10,000 instances, including all instances without time windows with up to 50 customers.

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Francisco J. Soulignac. 2026-08-26. The Time-Dependent Traveling Salesman Problem with Loose Time Windows. https://arxiv.org/abs/2608.26360

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