Solving a short sea inventory routing problem in the oil industry

We address an optimization problem related to the minimization of the distribution costs associated with product delivery in the oil industry. Particularly, the problem consists of determining a schedule of shipments from production ports to satisfy demand and desired inventory limits at consumptions ports. Products are transported in vessels, which can be viewed as a set of shared resources. The complexity of the problem derives from the problem structure and the number of decisions that need to be made throughout a planning horizon. The context that we studied belongs to the family of short sea inventory routing problems for which the ports are in the same geographical area. We formulate a mixed-integer programming model that captures the most relevant features of the real system. The main decisions include the selection of the vessels that will be used, the paths that each vessel will follow, and the quantities of each product loaded and unloaded at each port visited during the planning horizon. We test the limits of our mathematical programming formulation and develop a heuristic approach for tackling problem sizes that exceed the capabilities of a commercial solver.