Optimal economic ship speeds, the chain effect, and future profit potential

Abstract

In this research, we study at which speeds an oceangoing ship should ideally travel on each of a series of legs of a journey as to maximise the Net Present Value (NPV) of the ship. A novel class of models for the ship speed optimisation problem, which we refer to as P(n,m,Go), is presented. It is based on incorporating cash-flow functions and is flexible in modelling journey structures of variable composition. By studying properties of optimal leg speeds within this NPV framework, we demonstrate two novel elements of ship speed optimisation: (a) When executing a series of identical journeys, optimal ship speeds from one execution of the journey to the next are shown to change. We refer to this as the chain effect. (b) The ship’s optimal speed is in general highly dependent on the decision maker’s views on the ship’s future profit potential(FPP). We present two efficient algorithms to solve the models. The methodology is applied to case studies based on the literature and the results are compared with classic model formulations. Net Present Value Equivalence Analysis (NPVEA) shows how the proposed framework increases understanding of the applicability and limitations of these classic model formulations. The use of the FPP concept is recommended in speed optimisation and job selection models.