Convex Optimisation Model for Ship Speed Profile: Optimisation under Fixed Schedule

Abstract

We present a novel convex optimisation model for ship speed profile optimisation under varying environmental conditions, with a fixed schedule for the journey. To demonstrate the efficacy of the proposed method, a combined speed profile optimisation model was developed that employed an existing dynamic programming approach, along the novel convex optimisation model. The proposed model was tested with 5 different ships for 20 journeys from Houston, Texas to London Gateway, with differing environmental conditions, which were retrieved from actual weather forecasts. As a result, it was shown that the combined model with both dynamic programming and convex optimisation was approximately 22% more effective in developing a fuel saving speed profile compared to dynamic programming alone. Overall, average fuel savings for the studied voyages with speed profile optimisation was approximately 1.1% compared to operation with a fixed speed and 3.5% for voyages where significant variance in environmental conditions was present. Speed profile optimisation was found to be especially beneficial in cases where detrimental environmental conditions could be avoided with minor speed adjustments. Relaxation of the fixed schedule constraint likely leads to larger savings but makes comparison virtually impossible as a lower speed leads to lower propulsion energy needed.

Hybrid dynamic modeling and receding horizon speed optimization for liner shipping operations from schedule reliability and energy efficiency perspectives

“…Therefore, the sailing speed can be adjusted to consider varying environmental factors and remain optimal throughout the whole voyage. Huotari et al (2021) presented a novel convex optimization model for ship speed profile optimization under varying environmental conditions and timetable constraints. Tzortzis and Sakalis (2021) proposed a dynamic speed optimization problem, transforming the optimization problem into several sub-problems for improved weather forecasting by segmenting the full time horizon into smaller time regions.…”