Calculating Voyage Operational Cost with Differential Equations
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The purpose of this short paper is for the assignment of mathematics 1 at the department of Marine Engineering ITS. Shortly, it tells you about the applications of mathematical approach, derivatives in this case, for such maritime transportation problems. Hopefully, this will be useful for us and for the sake of the education. Please forgive me as long as there is any mistakes. Thank you.
Calculating Voyage Operational Cost with Differential Equations
- 1. Calculating Voyage Operational Cost with Differential Equations As an engineering student, especially marine engineering, it is important to master mathematical knowledge. Because we are basically using mathematical approach to solve such engineering problems. Even in the maritime transportation things, we also use mathematics equations to calculate the operational costs of a cargo voyage, maximum profits of a shipping company, the best way of lots of options to arrange the most efficient shipping voyage route based on oil consumption and safety, and so on. In the offshore engineering things, we can calculate the affected area of the oil spill from the oil rig or oil tanker ships in the ocean. This can be solved by deriving the oil spill rate speed equation. In addition, differential equations are also used to solve problems in marine engineering as well as in naval architecture. In this case, I would like to elaborate the purpose of applying and studying mathematical things in marine technology engineering, especially in the maritime transportation. The study case is about the efficiency of a voyage of a ship in eastern Indonesia sea. This is all because there is a big gap in the economic sector between the eastern Indonesia and the western side. In 2015, President Joko Widodo has revealed his vision toward maritime development in Indonesia namely Tol Laut which means Sea Highway in English. The aim of Tol Laut is not to construct bridges or land transportation highway all over the sea to connect the islands. Instead, there is big evaluation of the Indonesia ship route network. Big ports or international ports, such as Tanjung Priok, Tanjung Perak, Belawan, and so on, act as hub port or feeder for smaller ports around. For example, a general cargo ship will transport supplies from Tanjung Priok to Sorong. The ship will sail from Tanjung Priok to Tanjung Perak and end at Port of Makassar. There will be smaller ships that continue transporting the needed supplies from Jakarta to Sorong in which the port is so small that it is not possible for bigger ships to sail there as well as the higher operational cost a shipping or logistic company should spend. We need to concern about this issue because after unloading the loads there is so few or even no loads on the ship. Therefore, it will affect the operational cost directly. Now we are heading to the core problem or the study case, namely the mathematical approach related with. Assume there is a general cargo transporting groceries and some home appliances with the speed of 10 knots from Tanjung Perak to Port of Makassar. The company A informs that the operational cost the ship per month during the voyage from Tanjung Perak to Makassar is shown in the equation as follows: (＄) = 3＄2 248＄ + 6050 P defines the operational cost in million IDR, while t defines the time in days.
- 2. a) How long should the ship sail to get the lowest expenditure? b) If the ship sails for a day, how much is the operational cost? Solution: a) (＄) = 3＄2 248＄ + 6050 Firstly, we derive the operational cost equation using the derivative technique and it will be: (＄) = 6＄ 248 Then, we are going to find the minimum operational cost of the ships voyage. That means the derivative of the operational cost equation should be equal to zero. (＄) = 0 0 = 6＄ 248 248 = 6＄ ＄ = 248 6 = 41.33 hours 41 hours Thus, to get the lowest expenditure, the ship should not sail more than 41 hours. b) If t = 24 hours, P = ? (＄) = 3＄2 248＄ + 230 (24) = 3(24)2 248(24) + 6050 (24) = 3(676) 5952 + 6050 (24) = 2028 5952 + 6050 (24) = 2126 The operational cost in a day is IDR 2,126,000,000. So, that is the solution to solve such simple maritime transportation or logistic problems using mathematical approach. By using differential equations, we can approximate or predict the expenditure of a shipping or logistic company for ships on the ships route. Furthermore, there will not be any big loss for companies that operate ships to particular destinations with various conditions and obstacles. However, there is a state that it is not possible to use only mathematical approach to solve maritime problems, especially in maritime transportation. We need a decent combination of it with technology, such as software, etc. with algorithm and mathematics. To sum up, it is important for us to develop the knowledge we already have. Because something new comes from the development of our existing minds towards it. Therefore, I wish that there will be big improvements in the maritime world in Indonesia since Indonesia is an archipelagic country. Thank you, Regards, Dipto Pratomo Nugroho (04211741000014)
- 3. Tags: ITS Institut Teknologi Sepuluh Nopember Fakultas Teknologi Kelautan Sistem Perkapalan Marine Engineering Source: Calculus Concepts and Contexts (Second Edition), James Stewart. Calculus Late Transcendentals (11th edition), Howard Anton https://www.khanacademy.org/math/calculus-home/derivative-applications-calc http://tutorial.math.lamar.edu/Classes/CalcI/DerivAppsIntro.aspx