Combined ship routing and inventory management in the salmon farming industry

We consider a maritime inventory routing problem for Norway's largest salmon farmer both producing the feed at a production factory and being responsible for fish farms located along the Norwegian coast. The company has bought two new ships to transport the feed from the factory to the fish farms and is responsible for the routing and scheduling of the ships. In addition, the company has to ensure that the feed at the production factory as well as at the fish farms is within the inventory limits. A mathematical model of the problem is presented, and this model is reformulated to improve the efficiency of the branch-and-bound algorithm and tightened with valid inequalities. To derive good solutions quickly, several practical aspects of the problem are utilized and two matheuristics developed. Computational results are reported for instances based on the real problem of the salmon farmer.