Branch \& Price \& Cut for the Time-Dependent Vehicle Routing Problem with Time Windows (TDVRPTW)

Abstract

In urban contexts, travel times vary strongly with the time of day and traffic conditions. The Time-Dependent Vehicle Routing Problem with Time Windows (TDVRPTW) extends the classical VRPTW by making travel times depend on departure time, with the objective of minimizing the total travel time of at most $k$ vehicle routes serving customers within strict time windows. Exact resolution of this realistic yet understudied problem currently relies on the Branch \& Price approach of Dabia et al. (2013), in which a Column Generation scheme decomposes the problem into a set-partitioning master problem and a resource-constrained shortest-path pricing problem solved by dynamic programming. This work, conducted within the MAMUT project (Machine Learning and Matheuristics for Urban Transport), aims to advance the state of the art for the exact and explainable resolution of the TDVRPTW. We propose to reimplement and revisit the pioneering Branch \& Price algorithm by transferring recent advances made on the single-vehicle variant (TDTSPTW) to the multi-vehicle setting, notably an exact anytime extension of A* and a Large Neighborhood Search guided by dynamic programming for the pricing sub-problem. We further explore the integration of data mining and machine learning to guide column generation by exploiting knowledge from previously computed routes. The goal is a high-performance and interpretable solver that meets the requirements of real-world urban transport while preserving guarantees on solution quality.