Solving a maritime inventory routing problem under uncertainty using optimization and simulation

The problem studied in this paper is inspired by one of the world’s largest producers of aluminium. The company produces alumina in South America that needs to be transported to aluminium production plants along the west coast of Norway. The problem is to determine the optimal shipping plan that satisfies the production plants’ alumina demand at minimum cost while satisfying requirements on inventory levels. Both departure time from the loading ports and sailing times are subject to uncertainty. We present a combined optimization and simulation framework for solving this maritime inventory routing problem under uncertainty. We solve the problem heuristically with an iterative solution approach that combines optimization with simulation: In phase 1 of our approach we solve a deterministic optimization model to generate a candidate solution. The performance of this solution is then evaluated in phase 2 by a simulation over a set of realizations of the uncertain parameters, resulting in an expected cost of uncertainty for this solution. The expected cost of uncertainty is then included in the phase 1 model and associated with the simulated solution, before the model is solved again. This process is repeated until no new solution is found. We apply this approach to a case based on real-world data. The results show that our approach finds solutions that perform considerably better under uncertainty than solutions resulting from a purely deterministic planning approach.