Dynamic programming for optimal ship refueling decision

This study investigates an optimal control policy for a liner ship to decide at which ports and how much fuel the liner ship should be refueled under stochastic fuel consumption in each leg and stochastic fuel price at each port. Based on some properties proved in this study, a dynamic programming algorithm is then designed to obtain some important threshold values, which are used in the optimal control policy for ship refueling decision. Extensive experiments show that the proposed method can obtain the optimal decision within a reasonable time (about 170 s) for various scales of problem instances (up to 30 ports) as well as various settings of probability distributions. In addition, some comparative experiments also show that the proposed optimal decision policy can save at least 8% fuel consumption cost by comparing with some relatively simple rules and save about 1% cost on average by comparing with some brilliantly-designed rules.