New heuristic to generate an initial basic feasible solution for the balanced transportation problem

In this research, a new and efficient approach of finding an initial basic feasible solution to transportation problems is proposed. The proposed approach is named “Inverse Coefficient of Variation Method (ICVM)”, and the method is illustrated with seven numerical examples. Six existing methods; North West Corner Method (NWCM), Column Minimum Method (CMM), Least Cost Method (LCM), Row Minimum Method (RMM),Vogel’s Approximation Method (VAM), and Allocation Table Method (ATM) were compared with the proposed approach. It can be said conclusively that the proposed Inverse Coefficient of Variation Method (ICVM) provides an improved Initial Basic Feasible Solution to all the transportation problems used in the experiment. Further, the new method leads to the optimal solution to many of the problems considered.

A Supply Selection Method for better Feasible Solution of balanced transportation problem

One of the popular operation research problems is transportation problem. Its solution is basically divided into two parts. Initially Initial Basic Feasible Solution (IBFS) is obtained then the result is used to calculate the optimal solution. The popular methods to find IBFS of transportation problem are North West Corner Method (NWCM), Least Cost Method (LCM), and Vogel's Approximation Method (VAM). In this paper, a novel approximation method is proposed to find out the IBFS of the transportation problem. There are five different examples used for which the IBFS are calculated using NWCR, LCM, VAM, and our proposed method. The results show that our proposed method provides the best result among them.

Ant Colony Optimisation (ACO) is a meta-heuristic method that has drawn much interest in solving challenging optimisation issues. This paper examines the use of ACO to reduce the time spent on moving goods and people in Covenant University's transportation system. Covenant University is a private Christian university in Ota, Ogun State, Nigeria. Covenant University started on 21st October 2002, and since its opening, it has grown to be one of the world-class universities that have been ranked and recognised all around the globe. The data was collected from an article that computed the time per unit distance between origins and destinations within the university using Google Maps. The three traditional transportation techniques (Northwest corner method, least cost method, and Vogel's approximation method) alongside Ant colony meta-heuristics were used to get the initial basic feasible solution, which gave (361.3, 361.7, 359.8, 361.7) minutes, respectively. Then, the MODI approach was used to find the optimal solution (346.6 minutes). Also, the R programming language was used to run the Codes for the three traditional methods and the ACO method, which gave the result of solving manually. The optimal solution showed that if the time spent is reduced, the movement of people and goods would be enhanced, resulting in more time to handle important matters.

TRANSPORTATION MANAGEMENT ANALYSIS USING VOGEL'S APPROXIMA-TION (VAM) AND METHOD OF DISTRIBUTION MODIFIED (MODI). This study aimed to analyze the problems of transportation, especially the problem transportation costs by using Vogel's Approximation (VAM) and modified distribution method (MODI). In this study VAM methods used to find the initial solution and then proceed with the search for the optimal solution by using MODI. The data obtained is data derived from PT.Pilar Inkasari Karya - East Jakarta on shipment per month for 3 years ie 2011 to 2013. The analysis showed that the optimization of the burden of transportation costs Rp 2.225.288.000 annually is obtained by using initial solution Vogel's Approximation method (VAM) and final solution to the Modified method Distribution (MODI). From these results it can be concluded that the method of Vogel's Approximation (VAM) and modified distribution method (MODI) can be used to solve the problem of transportation. Keywords : Vogel’s Approximation Method. Modified Distribution Method

Transportation problem (TP) in operations research is a widely used optimization technique to study the problems concerned with transporting goods from production places to sale points. The TP may have one or more objectives such as minimization of transportation cost, minimization of distance with respect to time, and so on. There is a systematic method to solve such problems. For this, we find the Initial Basic Feasible Solution (IBFS) to the given problem. North West corner method, least cost method, Vogel’s approximation method are the standard methods one uses to find the IBFS. In recent years, there are several other methods are proposed to solve such problems. In this paper, we propose a new technique named as Direct Sum Method (DSM) and its effectiveness is compared with the standard methods. The result shows that it is easy to compute and near to the optimum solution of the problem.

The increase in annual turnover in a drug distribution company reflects positive growth but is often accompanied by a significant increase in operating costs that can reduce profit margins if not managed efficiently. This study aims to optimize distribution costs using a transportation method approach by comparing three initial solution methods, namely Vogel's Approximation Method (VAM), Russell Approximation Method (RAM), and Northwest Corner Method (NWC). The study was conducted at a drug distribution company with three central warehouses serving four distribution branches, based on distribution data for December 2024, which was arranged in the form of a transportation table. From the calculation results, the VAM method produced the lowest total distribution cost of IDR23,426,407. Evaluation of this solution was carried out using the Steppingstone method and the Modified Distribution Method (MODI) to determine whether the solution was optimal. The evaluation results show that all opportunity cost values ​​are positive, which means that no additional iterations or re-allocations are required so that the solution from the VAM method can be stated as an optimal solution. The novelty of this study lies in the integration of three initial solution methods with two optimal solution methods in one drug distribution case study, which has not been widely discussed in an integrated manner in previous studies. These findings provide strategic contributions to more precise and efficient logistics decision-making and support the sustainable operational growth of pharmaceutical distribution companies.

This study discusses the development of optimization models in transportation costs and routes and resource distribution based on Linear programming using various methods. This study aims to improve logistics efficiency, maximize the utilization of transportation equipment, infrastructure, operations management, and minimize transportation costs. The methods used include data collection, data processing, and the application of mathematical models to determine the optimal route with iteration methods such as the Simplex Method or Simplex Algorithm (SIMPLEKS), Modified Distribution Method (MODI), Vogel's Approximation Method (VAM), North-West Corner Method, Least Cost Method, and Initial Cost Minimum Method (ICMM). This study successfully shows that this method is able to reduce the cost of reducing carbon emissions, significantly reduce shipping costs and increase the efficiency of goods distribution that can be applied to complex distribution systems, support efficiency, and sustainability of transportation management. Using Linear programming and transportation methods to reduce SME costs and produce more efficient costs and fast solutions. In general,optimizationThis supports economic development, efficiency and sustainability of transportation management.

In this paper Vogel's Approximation Method and Least Cost Method for Transportation Problem were investigated to obtain the solution at a faster rate using Key-Value Pair approach. Computation experiments were carried out to investigate the effectiveness of Key-Value pair over 1900 problem instances for Vogel's Approximation Method and Least Cost Method each. It was seen that Key-Value pair greatly enhanced the rate of solving for both methods over traditional coding approach. Time comparison is shown for square balanced transportation problems.

The distribution of ice cubes and ice blocks is a crucial aspect of business operations, particularly in tropical climates like Indonesia. Efficient distribution is directly linked to profitability. PT Prima Maesa Putra, a producer and distributor of these products, is focused on optimizing distribution costs. Transportation methods provide a valuable tool for minimizing delivery expenses from factories to their destinations. This can be achieved by, for instance, analyzing using the North-West Corner (NWC) method and Vogel's Approximation Method (VAM) to establish initial solutions. These solutions are then evaluated using the Modified Distribution Method (MODI), yielding a total Rp 14.130.000,

In this paper to solve the initial basic solution for transportation problem and Minimizing transportation time and getting optimal solutions are always considered as important factors while solving transportation problem. This paper shows a new approach for finding initial basic solution for transportation problem which reduces cost of transportation more than any transportation method such as Northwest Corner Method(NCM), Least Cost Method(LCM), northwest, Vogel’s approximation, Total Opportunity Cost Matrix-Minimal Total (TOCM-MT) and so on. This method has been illustrated by taking an Numerical example.

Indonesia has several potential plantation commodities, one of them is tea plant, because tea is one of the most consumed beverages in the world. West Java Province accounts for 70% of national tea production. The X Indah Tea Factory is one of the managers of tea from the results of the people's tea plantations located in Tasikmalaya, which supplies processed dried tea to various cities. The tendency of high distribution costs requires a combination of the right product allocation so that it can make distribution costs to be optimal (minimum cost). The transportation method is a method used to find the cheapest way to distribute products from several sources (distribution centers: factories, warehouses) to several destinations so that total transportation costs are minimized. The transportation method used is North West Corner, Least Cost and Vogel's Approximation Method (VAM) to find the initial problem resolution followed by the Stepping Stone method and Modified Distribution (MODI) to determine the optimum solution. Before using the Transportation Method, X Indah Tea Factory spent a distribution cost was IDR. 69,900,000,- in March 2019, after using the transportation method, the distribution cost was IDR. 64,400,000,- so the company saves distribution costs of IDR. 5,500,000 every month. This method is recommended that factories located in Bojonggambir should distribute dry tea only to Singaparna, Bandung, Sumedang and Purwakarta. Whereas the factory located in Bantarkalong should distribute the tea to Subang, Sukabumi and fulfill some of the requests from Purwakarta in order to achieve optimum distribution costs.

Nowadays, getting substantial results for problems in operations research is crucial. The transportation problem can be solved very effectively with Vogel's Approximation Method (VAM) and discover a workable solution that is closer to the ideal solution. The basic principle of VAM is to allocate as many resources as possible to the cell with the smallest cost in the column or row with the greatest penalty. This cell will receive the maximum number of resources. A problem arises when the magnitudes of the least cost and the next-least cost are identical. Then, we devised a new method called the "New Vogel's Approximation Method (NVAM)" to provide a workable solution to the transportation problem that may then be used to determine the optimal solution. Transporting capacity to the required location is done by three distinct companies. The supply chain's participants seek to move their goods from warehouse to distribution centre, from plant to warehouse, and from distribution centre to retail store. In this study, the VAM method and the NVAM approach are used to determine the optimal transportation cost. These techniques are examined to provide potential supply chain management techniques.

In the present scenario, transportation model plays a crucial role in supply chain management that reduce the cost and improve the services as per user requirement. There are several methods to find the optimal solution like Vogel’s Approximation Method (VAM), Row minima, Column minima, North-West Corner method etc. In this paper, the proposed method gives the optimal solution and takes less number of iterations for a fuzzy transportation problem as compare to VAM. The Proposed method is illustrated for the secure data transfer from source to the destination node which is considered as Laptop/ Desktop/ Mobile Devices/ Hand-held Devices. Keywords: Fuzzy Transportation; North-West corner method; Optimal Solution; Supply Chain Management.

This study describes the final comparison of the minimum cost of pertalite product distribution and knowing the optimal results of pertalite product distribution costs using the Stepping Stone method and POM-QM software comparison. The type of research used is quantitative research with data processing used is the Northwest Corner Method, the Least Cost Method, and the Vogel Method as the method used as the initial feasible solution. The final solution used to find the optimal solution is the Stepping Stone Method and the use of POM-QM software as a comparison. The distribution cost results obtained using the Northwest Corner Method are Rp. 276,892,208, the Least Cost Method obtained Rp. 186,058,754, and the Vogel Method Rp. 77. 415.457. The Stepping Stone Method as the final result obtained Rp.77,415,457. The method that is closest to the optimal value is the Vogel Approximation Method because it can provide minimum costs and provide greater benefits when compared to other methods. Keywords: Northwest Corner Method, Least Cost Method, Vogel’s Approximation Method. ABSTRAK Penelitian ini menjelaskan tentang perbandingan akhir biaya minimum distribusi produk pertalite dan mengetahui hasil optimal biaya distribusi produk pertalite dengan menggunakan Metode Stepping Stone dan perbandingan software POM-QM. Jenis penelitian yang digunakan adalah penelitian kuantitatif dengan pengolahan data yang digunakan adalah Metode Barat Laut, Metode Biaya Terendah, dan Metode Vogel sebagai metode yang digunakan sebagai solusi awal yang layak. Solusi akhir yang digunakan untuk mencari solusi optimal adalah Metode Stepping Stone dan penggunaan software POM-QM sebagai pembanding. Hasil biaya distribusi yang diperoleh dengan menggunakan Metode Barat Laut sebesar Rp. 276.892.208, Metode Biaya Terendah diperoleh Rp. 186.058.754, dan Metode Vogel sebesar Rp. 77.415.457. Metode Stepping Stone sebagai hasil akhir diperoleh Rp. 77.415.457. Metode yang paling mendekati nilai optimal adalah Metode Vogel karena dapat memberikan biaya yang minimum dan memberikan keuntungan yang lebih besar jika dibandingkan dengan metode lainnya. Kata kunci: Metode Barat Laut, Metode Biaya Terendah, Metode Vogel.