A Bi-Level Programming Approach to Optimize Ship Fouling Cleaning

Abstract

Ship fouling has significant adverse effects on vessel performance and environmental sustainability. Therefore, this research study develops a bi-level programming model to simultaneously optimize cleaning equipment deployment by cleaning service providers in the upper level and cleaning decisions by shipping companies in the lower level. To address the interaction within the bi-level problem, the model is transformed into a single-level formulation using the big-M method. This transformation greatly simplifies the complexity of the computation and reduces computation time. Numerical experiments are conducted using real-world data to evaluate the performance of the proposed models. In addition, sensitivity analyses are performed to investigate the influence of key parameters. The results indicate that cleaning service providers primarily purchase equipment in the first year based on the demand distribution. To maximize profit, they may choose to forgo a portion of the demand. The sensitivity analysis reveals that sacrificing part of the demand can lead to an additional USD 27 million in profits compared with satisfying all demand. Moreover, increasing the cleaning price reduces both demand and equipment purchases but increases total profits. Conversely, increasing purchase costs reduces profits and the total amount of equipment purchased. When service providers can no longer generate profits, they are likely to exit the market. These findings offer valuable insights for service providers and shipping companies in the practical deployment of cleaning equipment and foul cleaning decisions, respectively.