[Paper Review] Simultaneous Planning of Liner Ship Speed Optimization, Fleet Deployment, Scheduling and Cargo Allocation with Container Transshipment

Jasashwi Mandal, Adrijit Goswami+2 more|arXiv (Cornell University)|Jul 21, 2023

Maritime Transport Emissions and Efficiency4 citations

TL;DR

This paper proposes a bi-objective mixed-integer non-linear programming (MINLP) model that simultaneously optimizes liner ship speed, fleet deployment, scheduling, and cargo allocation with transshipment, considering payload-dependent fuel consumption and CO₂ emissions. The model balances total cost and shipping time, solved via NSGA-II and OCEA, yielding Pareto-optimal solutions for real-world liner shipping complexity and sustainability.

ABSTRACT

Due to a substantial growth in the world waterborne trade volumes and drastic changes in the global climate accounted for CO2 emissions, the shipping companies need to escalate their operational and energy efficiency. Therefore, a multi-objective mixed-integer non-linear programming (MINLP) model is proposed in this study to simultaneously determine the optimal service schedule, number of vessels in a fleet serving each route, vessel speed between two ports of call, and flow of cargo considering transshipment operations for each pair of origin-destination. This MINLP model presents a trade-off between economic and environmental aspects considering total shipping time and overall shipping cost as the two conflicting objectives. The shipping cost comprises of CO2 emission, fuel consumption and several operational costs where fuel consumption is determined using speed and load. Two efficient evolutionary algorithms: Nondominated Sorting Genetic Algorithm II (NSGA-II) and Online Clustering-based Evolutionary Algorithm (OCEA) are applied to attain the near-optimal solution of the proposed problem. Furthermore, six problem instances of different sizes are solved using these algorithms to validate the proposed model.

Motivation & Objective

• To address the growing need for operational and energy efficiency in maritime shipping due to rising global trade and CO₂ emissions.
• To simultaneously optimize four interconnected decisions: vessel speed, fleet deployment, service scheduling, and container cargo allocation with transshipment.
• To integrate realistic operational factors such as payload-dependent fuel consumption and transshipment handling/holding costs into a single optimization framework.
• To balance conflicting objectives: minimizing total shipping cost (including CO₂ emissions) and minimizing total shipping time.
• To provide decision-makers with a holistic, sustainable planning tool for liner shipping networks with multiple routes and transshipment hubs.

Proposed method

• Formulates a bi-objective mixed-integer non-linear programming (MINLP) model that captures the trade-off between total cost (including CO₂ emissions, fuel, and operational costs) and total shipping time.
• Incorporates a payload-speed-dependent fuel consumption function, reflecting real-world bunker usage that increases non-linearly with speed and load.
• Models transshipment operations by including inventory holding and handling costs at transshipment ports for containers transferred between vessels.
• Applies two multi-objective evolutionary algorithms—NSGA-II and Online Clustering-based Evolutionary Algorithm (OCEA)—to generate near-optimal Pareto fronts.
• Validates the model on six problem instances of varying size (e.g., 18–27 ports, 3–5 routes), demonstrating scalability and solution quality.
• Uses a weighted sum approach to evaluate solution quality and convergence, with performance assessed via hypervolume and spacing metrics.

Experimental results

Research questions

• RQ1 How can liner shipping operations be simultaneously optimized across speed, fleet deployment, scheduling, and cargo allocation while accounting for transshipment and environmental costs?
• RQ2 What is the trade-off between minimizing total shipping cost (including CO₂ emissions) and minimizing total shipping time in a multi-route liner shipping network?
• RQ3 How does incorporating payload-dependent fuel consumption improve the realism and accuracy of the optimization model compared to speed-only fuel models?
• RQ4 To what extent do NSGA-II and OCEA effectively solve the complex, non-linear, and mixed-integer nature of the proposed multi-objective maritime planning problem?
• RQ5 How do transshipment costs and holding times affect the overall cost and scheduling decisions in a multi-port, multi-route liner shipping system?

Key findings

• The proposed MINLP model successfully integrates four critical liner shipping decisions—vessel speed, fleet deployment, scheduling, and cargo allocation—into a single holistic framework with transshipment.
• The model captures the non-linear relationship between vessel speed and fuel consumption, which is dependent on both speed and payload, enhancing realism compared to simpler models.
• OCEA and NSGA-II generated well-distributed Pareto fronts across all six test instances, with OCEA showing superior convergence and diversity in larger instances (e.g., 24–27 ports).
• For instance (18,3,4), the best solution achieved a total cost of approximately $4.402 × 10⁶ and a total shipping time of 969 hours, with CO₂ emissions and fuel costs forming a major share of the total cost.
• The results demonstrate that reducing vessel speed to cut emissions increases shipping time, while increasing speed reduces time but raises fuel and emission costs, confirming the inherent trade-off.
• Managerial insights show that integrating CO₂ emission costs and transshipment handling into the optimization model leads to more sustainable and economically viable operational decisions.