Clique Inequalities Applied to the Vehicle Routing Problem with Time Windows

This work presents an exact branch-cut-and-price (BCP) algorithm for the vehicle routing problem with time windows (VRPTW) where the well-known clique inequalities are used as cutting planes defined on the set partitioning master problem variables. It is shown how these cutting planes affect the dominance criterion applied in the pricing algorithm, which is a labeling algorithm for solving the elementary shortest path problem with resource constraints (ESPPRC). To our knowledge, this is a first attempt at incorporating, for the VRPTW, a set of valid inequalities specialized for the set partitioning polytope. Computational results show that the use of clique inequalities improves the lower bound at the root node and reduces the number of nodes in the search tree.