A Lagrangean decomposition approach for a novel two-echelon node-based location-routing problem in an offshore oil and gas supply chain

In this paper, a new node-based mixed-integer non-linear programming (MINLP) model in an offshore oil and gas industry is proposed. The model, which is a supply vessel planning (SVP) one, is developed to a two-echelon fleet composition mix periodic location-routing problem with time windows (2E-FCMPLRPTW). In the first echelon, the number and type of vehicles, routes, schedules and the best allocation of suppliers are determined. In the second echelon, the number and type of supply vessels, related voyages and schedules are calculated. A Lagrangean decomposition method, which is a particular case of Lagrangean relaxation, is presented to solve the problem.