International Journal of Science and Research (IJSR) ISSN: 2319-7064 ResearchGate Impact Factor (2018): 0.28 | SJIF (2018): 7.426 Volume 8 Issue 12, December 2019 www.ijsr.net Licensed Under Creative Commons Attribution CC BY Minimising the Transportation Cost of an Oil Mill Company Otoo Henry 1 , Sampson Takyi-Appiah 2 , Apodei Michael 3 1 University of Mines and Technology, P. O. Box 237, Tarkwa, Ghana hotoo[at]umat.edu.gh 3 University of Energy and Natural Resources, Sunyani, Ghana stappiah[at]umat.edu.gh 3 University of Mines and Technology, P. O. Box 237, Tarkwa, Ghana mapodei100[at]gmail.com Abstract: It is very common in Ghana to transport products from sources to destinations by road, which can be seen in multiple business entities whose daily activities include manufacturing. The manufacturing sites, storage and final destinations are sometimes linked by road. Finding methods to reduce the transportation costs has always been an issue and it continues to affect the decision- making process of several establishments. In this study, the cost of transporting raw materials of an Oil Mill Company from its various farm gates (sources) to its various warehouses (destinations) is minimised using the transportation problem. The initial feasible solution is generated using the Least Cost and the Vogel Approximation Method, after which the Modified Distribution Method is then applied to determine optimality. From the optimal solution, the cost of transporting the raw materials from the various farm gates to the factory warehouses was obtained to be GH₵ 30351.45. Keywords: Transportation problem, optimal solution, Initial feasible solution, degeneracy 1. Introduction The transportation problem is a particular form of a linear programming problem, which minimizes the cost of distributing goods from specific sources (warehouses) to distinct locations while meeting both supply and demand limitations [1]. Transportation model can be applied in areas such as personnel assignment, inventory control, financial planning, farm planning, work scheduling and transporting goods [2]. The Oil Mill Company under study, is a palm oil producing company concerned with refined oil trade with some companies and individuals nationwide. The company spends about GH₵53247.74 on transporting raw materials from the farm gates to their various warehouses. This high cost contributes to low profit achieved at the end of their financial year. It is the desire of the management of the company to minimise the cost of transporting raw materials in order to improve their financial records. According to [3], the French mathematician Monge formally established the transportation problem in 1781. The Soviet / Russian mathematician and economist Leonid Kantorovich made major advances in the field during the Second World War. Kantorovich [4] conducted a study on the ongoing version of the problem and later extended it to the problem of capacitated transport system [4]. This is widely studied in the literature of mathematical programming and engineering, most often referred to as the facility location and assignment problem. The issue of transport optimization can be described as a linear programming problem with a large-scale blended integer. [5] researched on a two-dimensional dynamic network routing model. The model uses heuristic techniques to fix issues of instability. The heuristics routing techniques are likened to the simulation of discrete events in the dynamic routing scheme. [6] utilized a linear programming module and management scientist transportation to help minimise Guinness Ghana limited transportation costs when their products were distributed to retailers from different warehouses. From the research, the same findings were achieved for both the linear programming module and the transportation module for management scientists in terms of the optimal solution. [7] also minimized the complete transportation cost of a beverage industry using the Regret Method and the U-V method. Quantitative manager for windows (QMW) was used for the analysis. It was realized that there is a great distinction between the lean and festive seasons in the monthly transportation cost. [8] also minimised the total transportation cost of Asuo Bomosadu Timber Sawmill Limited (A.B.T.S) using the Least cost method and the stepping stone method. This study, therefore, intends to employ the Least Cost Method, Vogel Approximation Method and the Modified Distribution Method to determine the optimal allocation of raw materials that will minimise the transportation cost of the Oil Mill Company. 2. Methods Used 2.1 Transportation Problem The most significant and effective applications of linear programming problem are the physical allocation of goods, frequently known as transportation problem. The aim is to minimize the cost of transporting goods from one location to another so that each location's requirements are met and each supply place operates within its capability. However, the transportation problem can be formulated in the form of linear programming which has a lot of applications other than physical commodity allocation. Consider a commodity generated in different centres known as sources and demand in different locations. Each source's manufacturing capability (availability) and each destination's demand are known and fixed. The transportation problem considers the cost of transporting a unit of goods from each source to each location. The goods are to be transported from multiple shipping costs. This optimal distribution of the product to Paper ID: ART20203019 DOI: 10.21275/ART20203019 1417