Dynamic ship assignment problem with uncertain demands

Product tanker shipping companies in the spot market face severe volatility in demand and in price. We explore shipping companies' two problems: evaluating supply and demand of the market and assigning cargoes in order to maximize profitability. By approximating the market as a queueing system, we obtain utilization ratios, which effectively model supply and demand of the market. This approach directly evaluates the impact of ton-mile on utilization ratios, even a small growth of which may result in a significant supply shortage. Queueing approximation also allows formulation of dynamic ship assignment as a semi-Markov average cost problem, attaining stationary policies. When profit margins are low, a stationary policy frequently rejects cargoes. Despite rejections, it yields the highest profit per cargo, compared to other methods. Such optimal controls remain valid even when demand fluctuates.