Mixed-Integer Optimization for Ship Retrofitting in Green Logistics

Abstract

Maritime transportation plays a pivotal role in global trade and international supply chains. However, the sector is also a significant source of emissions. One of the most promising technologies for reducing these emissions is air lubrication, which involves installing bubbles along the hull of a ship. Despite its potential, the design of cost-effective bubble-installation plans for ship fleets over the planning horizon remains unexplored in the literature. This paper addresses this gap by proposing a mathematical programming model designed to optimize the installation of bubble-based systems. We present several propositions concerning the model’s properties, supported by rigorous proofs. To validate the model’s effectiveness, we conduct a series of computational experiments. The findings demonstrate that our optimization model enables shipping companies to devise bubble-installation plans that are cost-effective. This contribution not only extends the current understanding of emission reduction technologies in maritime transportation, but also offers practical insights for their implementation.

Keywords

• maritime logistics
• bubble installation
• mixed-integer programming
• sensitivity analysis