The Multi-commodity One-to-one Pickup-and-delivery Traveling Salesman Problem with Path Duration Limits

The design of container shipping networks is an important real world problem, with assets and operational costs in billions of dollars. To guide the optimal deployment of the ships, a single vessel roundtrip is considered by minimizing operational costs and flowing the best paying cargo under commercial constraints. Inspiration for formulation and solution method is taken from the rich research done within pickup and delivery problems. The problem, the multicommodity one-toone pickup and delivery traveling salesman problem with path duration limits is, to the best of out knowledge, considered for the first time. An arc flow and a path flow model are presented. A Branch and Cut and Price solution method is proposed and implemented.