International Journal of Scientific and Technological Research www.iiste.org ISSN 2422-8702 (Online), DOI: 10.7176/JSTR/5-9-02 Vol.5, No.9, 2019 13 | Page www.iiste.org Finding Optimal Number of Ship with the Greatest Integer Function in Maritime Transportation Kadir Mersin (Corresponding author) International Logistics and Transportation, Faculty of Economics, Administrative and Social Sciences, Istanbul Gelisim University 34315 Avcilar, Istanbul, Turkey E-mail: kmersin@gelisim.edu.tr Guler Alkan Barbaros Hayrettin Faculty of Naval Architecture and Maritime, Iskenderun Technical University, Iskenderun, Hatay, Turkey E-mail: güler.alkan@iste.edu.tr Abstract Various parameters are taken into account when calculating fleet in maritime transport. The most important of these is fuel consumption. Since the fuel consumption is proportional to the speed of the ship, high speed brings high fuel consumption. Increasing number of ship means increasing costs. In this study, we use the greatest integer function to find the optimum number of ship with lower cost. In addition, we calculate daily freight for voyage charterer depending on the number of ships by using this function. Keywords: Maritime Transportation, Number of Fleet, Fuel Consumption. DOI: 10.7176/JSTR/5-9-02 1. Introduction Experimental data show that fuel consumption varies geometrically with increasing speed. For example, at some speeds, when you increase your ship's speed by 30%, your consumption is twice as fast as the original speed. While the vessels are anchored in the port, roughly a quarter of the fuel consumption in the sea is produced by fuel fuels [1]. In the case of neglecting the load on it, there is a classical correlation which is proportional to the power to increase the speed and fuel consumption by showing the fuel consumption of a ship with F. That is, F(v) = λ. v Ω λ >0 [2] However, since there are some fixed costs to show with s, a daily cost of a ship is C 1 = s + F(v) . Similarly, the 1-day cost of n homogenous ships is Cn = n(s + F(v)) = n. C1 [3] As can be seen, the number of ships and the cost are increasing in direct proportion, but if the speed is inversely proportional to the strength of the speed, the cost can be further reduced by increasing the number of ships by only 1 and reducing the speed to a very small amount . Example 1.1 For a ship with fixed cost s = $ 1000 and speed v = 20,1 knots, λ = 0,64 means that a 1(one) day cost is C 1 = $ 6197. For two smaller vessels with the same characteristics but with a speed v = 20 knots, the cost would be C 2 = $ 12240. At first glance it may seem more costly to ship 2 slower and smaller vessels, but the increase in the number of vessels will cause the cost to decrease. For example, for n = 10 vessels, C 10 = $ 61970, C 11 = $ 67320. For the convenience of calculation, Ω = 3 is taken for convenience, and the fixed cost is considered unaffected by a very small reduction of 0.1 knots. In Table 1, ship number relationships are given for s = $ 1000 and λ = 0.64. [4]