Greening of maritime transportation: a multi-objective optimization approach

This article is motivated by growing concerns related to shipping CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CO}_{2}$$\end{document} and SOx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SO}_{\mathrm{x}}$$\end{document} emissions in the hope that ship operators further consider the environmental impacts of their activities when attempting to maximize profit. The article proposes a liner shipping multi-objective optimization (MOO) model based on profit maximization, CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CO}_{2}$$\end{document} emissions minimization, and SOx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SO}_{\mathrm{x}}$$\end{document} emissions minimization for which all objective functions are a function of vessel sailing speed. Two demand configurations are considered: elastic and inelastic. The MOO model is solved using three different methods and is applied to two liner services deployed on the trans-Pacific and Europe–Far East markets. A single-objective optimization approach is also proposed in which the monetary value of the emissions is considered in an objective function. The main conclusion of the article is that the sensitivity of demand to transit time is based on the gap between economic and environmental optimal solutions and that policies considering imposing a tax on CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CO}_{2}$$\end{document} or SOx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SO}_{\mathrm{x}}$$\end{document} to reduce the negative externalities from international shipping should account for this element.