Nonlinear programming for fleet deployment, voyage planning and speed optimization in sustainable liner shipping

Abstract

Limiting carbon dioxide emissions is one of the main concerns of green shipping. As an important carbon intensity indicator, the Energy Efficiency Operational Index (EEOI) represents the energy efficiency level of each ship and can be used to guide the operations of ship fleets for liner companies. Few studies have investigated an integrated optimization problem of fleet deployment, voyage planning and speed optimization with consideration of the influences of sailing speed, displacement and voyage option on fuel consumption. To fill this research gap, this study formulates a nonlinear mixed-integer programming model capturing all these elements and subsequently proposes a tailored exact algorithm for this problem. Extensive numerical experiments are conducted to show the efficiency of the proposed algorithm. The largest numerical experiment, with 7 ship routes and 32 legs, can be solved to optimality in four minutes. Moreover, managerial insights are obtained according to sensitivity analyses with crucial parameters, including the weighting factor, unit price of fuel, Suez Canal toll fee per ship, weekly fixed operating cost and cargo load in each leg.