Linear Programming-Based Maritime Speed Allocation and Fuel-Cost Efficiency: An Intelligent Decision Support System with an LLM Explanation Layer

Abstract

This applied mathematical study develops a linear-programming model for maritime speed allocation to minimize estimated voyage operating cost under route-distance and sailing-deadline constraints. The decision variables represent the distance assigned to each predefined speed mode, enabling the model to determine a continuous mixed-speed allocation that remains feasible within the permitted sailing time. The model was implemented in a web-based Intelligent Decision Support System (IDSS) using a HiGHS-based linear-programming solver and demonstrated on the Tanjung Priok–Tanjung Perak route using an application-generated distance of 469.84 nautical miles. Under a baseline VLSFO price of USD 755/MT and a 35-hour sailing deadline, the model allocated 390.69 NM to the 13-knot mode and 79.15 NM to the 16-knot mode, producing an estimated minimum operating cost of USD 34,748.16 and total fuel consumption of 38.30 MT. Sensitivity analysis shows that tighter deadlines shift the optimal allocation toward higher-speed modes, increase estimated voyage cost, and eventually produce infeasibility when the required travel time falls below the capability of the fastest available speed mode. At the fixed 35-hour deadline, fuel-price variation changes the objective-function value without altering the selected speed allocation in the tested scenarios. As a supplementary interpretive component, an LLM-based layer transforms structured optimization outputs into a natural-language Voyage Master Plan while preserving the ship master's final authority. The study therefore contributes a traceable mathematical optimization model and a functionally integrated explanation interface. Because the analysis uses model-input parameters rather than empirically calibrated vessel records and does not include user-based evaluation, further validation is required before operational deployment.