Fermat minimizes environmental risk in multi-anisotropic sea passages

Reducing the possibility of ship accidents is highly important to all economic, environmental and cultural sectors. Oil spill cleanups can cost over 1 billion Euros, whereas accidents involving water soluble cargos would result in irrecoverable changes to the ecosystem. Shipping companies would directly benefit from a system that can reduce the possibility of a serious accident involving their own ship in order to reduce their own financial risk as well as to assure their reputation. Supposing that the risk level has been defined in predefined areas we are looking to plan a vessel minimizing the total risk. Usually a hazardous area consists of several layers with different risk level and this fact increases the problem complexity whenever a vessel should cross this area. An optimization module whereas parameters are time dependent variables reducing the risk is required. There are several heuristic algorithms providing with critical delay solutions not necessarily the optimum. In this paper we present an optimization model and we prove that this is the optimum.