Applied Ocean Research 61 (2016) 1–15 Contents lists available at ScienceDirect Applied Ocean Research journal homepage: www.elsevier.com/locate/apor Simulation based design of a ﬂeet of ships under power and capacity variations Giuliano Vernengo a , Tomaso Gaggero a,∗ , Enrico Rizzuto b a Dept. of Electrical, Electronic and Telecommunication Engineering and Naval Architecture (DITEN), University of Genoa, Italy b Dept. of Industrial Engineering (DII), University of Naples − Frederick II, Italy a r t i c l e i n f o Article history: Received 29 April 2016 Received in revised form 13 September 2016 Accepted 18 September 2016 Keywords: Simulation Based Design (SBD) Ship Synthesis Model (SSM) Compressed Natural Gas (CNG) Fleet design Added resistance in waves Uncertainty quantiﬁcation Multi-criteria decision making a b s t r a c t Achieving the right balance between ﬁxed and operating costs is a key but non-trivial task for optimizing the characteristics of a ﬂeet of ships for a new trade at a very early stage of the design. A wide range of design choices as well as a signiﬁcant number of uncertainties related to the operation of the ﬂeet affects those two expense items. In the proposed analysis, operative uncertainties rising from rough sea conditions are taken into account in a Simulation Based Design (SBD) framework for ﬂeet generation and evaluation. The costs-beneﬁts analysis is aimed at understanding the effects of variations in the installed power and in the ship capacity on the overall ﬂeet performances. These two major characteristics of the ship design (and, accordingly, of the ﬂeet of ships realizing the trade) are introduced in the numerical model considering the sea margin and the nominal capacity as free design parameters instead of ﬁxing them as commonly done in practice. From a design point of view, this corresponds to the introduction of two new variables, enlarging the dimensions of the design space to be explored, better than relaxing the boundaries of a simpler design space. The validity of this approach is demonstrated by a practical application to the design of a ﬂeet of Compressed Natural Gas (CNG) carriers. In this context, the effects of variations in the fuel price and in the voyage length on the optimal ﬂeet characteristics are analyzed and the results are discussed in comparison to those coming from the reference scenario. © 2016 Elsevier Ltd. All rights reserved. 1. Introduction and motivations At a very early stage of the feasibility assessment of a ﬂeet of ships for realizing a marine trade, a number of design decisions are often taken under uncertainties. From a design point of view, taking a decision too early, not supported by enough information, causes the design space boundaries to narrow down, hence excluding pos- sible feasible and competitive solutions. This is the main reason why a recent trend in design methods is to delay as much as possible the decision-making phase, allow- ing for the exploration of wider design spaces than (apparently) necessary [10]. The sources of uncertainties are related to the scenario in which the ship will operate. A relevant example for the case under exam- ination is the price of the fuel, continuously ﬂuctuating in time. Another one is represented by the environmental conditions in which the ﬂeet will operate. Rough sea conditions may imply an intentional variation of the ship course, with a change in the ∗ Corresponding author. E-mail address: tomaso.gaggero@unige.it (T. Gaggero). encounter angle with waves, and/or an involuntary decrease of the ship speed. Both situations induce an increase in costs and in sailing time (delay in cargo delivery). A simpliﬁed way to face the problem of the added resistance in waves of a ship is typically to preset a percent increase in the installed power as compared to the still water power prediction. Such percent increase is usually referred to as Sea Margin, SM. For convenience, the sea margin is assign to a ship during the early design phase, thus eliminating this important quantity from the optimization process. Another variable very often pre-determined in the design pro- cess is the capacity of the ship, generally set on the basis of the nominal speed of the ship and of the total cargo quantity to be transferred. A feature of the present investigation is to let these two quanti- ties (the nominal capacity and the SM), free to change over a certain range in the context of a Simulation Based Design (SBD) framework [22] to investigate a larger design space. The proposed approach, accordingly, considers these quanti- ties as true design variables for the ﬂeet optimization. In order to balance the inﬂuence of adverse sea condition (and the inher- ent reduction in speed and in annual delivery of cargo), in fact, an http://dx.doi.org/10.1016/j.apor.2016.09.003 0141-1187/© 2016 Elsevier Ltd. All rights reserved.