The crude oil tanker routing and scheduling problem with split pickup and split delivery is a maritime transportation task where an industrial operator needs to ship different types of crude oil from production sites to oil refineries. The different crude oils are supplied and demanded in many ports in certain time windows. Pickup and delivery quantities are known in advance but no pairing of pickup and delivery needs to be predefined and can be decided together with shipment quantities during optimization. Pickup and delivery quantities may be split arbitrarily among the ships in the fleet. We compare two alternative path flow model approaches to investigate their degree of applicability in a column generation setup. For this purpose we apply route pregeneration prior to optimization. The first approach uses continuous decision variables for pickup and delivery to decide on shipment quantities. In the considerably shorter second formulation cargo quantities are discretized and included into the paths. The second approach is capable to solve larger instances and is more efficient in terms of computational performance, however solution quality may decrease due to the discretization. 
Alternative approaches to the crude oil tanker routing and scheduling problem with split pickup and split delivery