Robust convoy movement problem under travel time uncertainty

A convoy represents a collection of vehicles traveling with a spacing of 50-100 m between them for tactical purposes. The convoy movement problem is a variant of the vehicle routing problem, an NP-hard problem aimed at determining the paths and schedules of convoys. Given the uncertainties in travel times during wartime, attributable to various factors such as road conditions and enemy threats, it is essential to consider uncertain travel times when determining convoy paths and schedules. Therefore, this study introduces a robust convoy movement problem under travel time uncertainty. A polyhedral set for uncertain travel times is used to derive a robust counterpart for the problem. To solve the proposed problem, we establish an exact algorithm that determines optimal solutions by iteratively generating and integrating multiple paths of convoys. This algorithm involves four steps: generation of k-th robust shortest paths, construction of path combinations, adjustment of departure times, and conduction of optimality check. These steps are iterated sequentially until the optimal solution is obtained. In computational experiments, the exact algorithm demonstrates superior performance and reduced computation time compared with the commercial solver CPLEX on both real instances and randomly generated instances. In addition, we conduct a sensitivity analysis for several parameters related to the problem, providing valuable managerial insights for decision-makers.