•We introduce the time-dependent location-routing problem.•We propose a mathematical formulation and valid inequalities for this problem.•We generate a large set of instances based on real traffic data.•We propose several heuristics… Click to show full abstract
•We introduce the time-dependent location-routing problem.•We propose a mathematical formulation and valid inequalities for this problem.•We generate a large set of instances based on real traffic data.•We propose several heuristics to provide good quality initial solutions.•We propose a matheuristic that solves a set partitioning problem to improve solutions.
               
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