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ExxonMobil annually transports significant volumes of vacuum gas oil (VGO) from supply points in Europe to refineries in the United States. Optimizing these transportation costs by using modern mathematical programming technology can provide significant cost savings. We developed a mixed-integer programming formulation for VGO routing and inventory management, and we integrated it into a decision support tool to enable experienced traders and schedulers to further improve the performance of ExxonMobil's downstream supply chain.

The maritime oil tanker routing and scheduling problem is known to the literature since before 1950. In the presented problem, oil tankers transport crude oil from supply points to demand locations around the globe. The objective is to find ship routes, load sizes, as well as port arrival and departure times, in a way that minimizes transportation costs. We introduce a path flow model where paths are ship routes. Continuous variables distribute the cargo between the different routes. Multiple products are transported by a heterogeneous fleet of tankers. Pickup and delivery requirements are not paired to cargos beforehand and arbitrary split of amounts is allowed. Small realistic test instances can be solved with route pregeneration for this model. The results indicate possible simplifications and stimulate further research.

A branch-price-and-cut algorithm is developed for a complex maritime inventory-routing problem with varying storage capacities and production/consumption rates at facilities. The resulting mixed-integer pricing problem is solved exactly and efficiently using a dynamic program that exploits certain “extremal” characteristics of the pricing problem. The formulation is tightened by using the problem's boundary conditions in preprocessing and to restrict the set of columns that are produced by the pricing problem. Branching schemes and cuts are introduced that can be implemented efficiently and that preserve the structure of the pricing problem. Some of the cuts are inspired by the capacity cuts known for the vehicle-routing problem, whereas others specifically target fractional solutions brought about by individual vessels “competing” for limited inventory at load ports and limited storage capacity at discharge ports. The branch-price-and-cut approach solves practically sized problems motivated by the operations of an oil company to optimality, and it provides reasonable bounds for larger instances.