New valid inequalities for the symmetric vehicle routing problem with simultaneous pickup and deliveries

The symmetric vehicle routing problem with simultaneous pickup and deliveries is considered. The current state‐of‐the‐art method to solve this problem employs the idea of a no‐good cut. This article achieves an order of magnitude improvement in the computational time needed to solve difficult problem instances by generalizing the no‐good cuts and developing a way to generate improved no‐good cuts much earlier in a branch‐and‐bound tree. Results are reported on benchmark instances in literature and new difficult instances generated by the authors. Some polyhedral results are presented about the strength of the generalized no‐good cuts for a special case of the problem.