Vogel's Approximation Method Research Articles

Comparative view of the modified Vogel’s approximation methods in transportation problem

Recently, the whole world is experiencing economic hardship and one fast road to ply is to cut out some expenses. Xlife group is equally affected and so the study proposes a means to minimize its transportation cost if effected. A comparative surgery on Vogel’s approximation with its modified versions were conducted on minimizing the cost of transporting manufactured goods from (Xlife group’s) points of supply to certain destinations was undertaken. The Vogel's Approximation Method (VAM) and the Modified Vogel's Approximation Method based on standard deviation, distribution indicators and average cost were applied to determine an initial basic feasible solution and optimal solution for certain transportation problems. All methods yield identical minimum transportation cost except at an instance.

The novel Vogel's approximation method integrated with a random forest algorithm in the vibration analysis of a two-directional functionally graded taper porous beam: Assessment

A functionally graded material is a class of composite materials characterized by gradual variations in composition and microstructure, which further induces the respective changes in the material properties. This study focuses on evaluating the vibration behavior of two directional functionally graded taper porous beams (FGTPB). This approach adopts a rectangular cross-section in order to deal with the challenges related to fluctuating material characteristics and geometric tapering in both thickness and width dimensions. The research employs a novel approach that merges Vogel's approximation technique with the Random Forest algorithm, an approach that has not been used in analyzing structural vibrations, establish boundary conditions and solve equations of motion. Comparative results of the suggested beam theory with the existing literature on FGTPB materials such as alumina and SUS304 at various taper, porosity, gradient and width ratios verified it. The material gradation and porosity developed a uniform pattern in the first three modes of fundamental frequencies. Higher gradient indices increased the rigidity and natural frequencies of the beams whereas the porosity index decreased the rigidity, resulting in lower natural frequencies. By combining Vogel's approximation method with machine learning techniques, the study improved vibration behavior analysis in FGTPB. The disciplines of materials and structural engineering are significantly impacted by this.

A NEW DUAL HEURISTIC ALGORITHM FOR FINDING THE INITIAL BASIC FEASIBLE SOLUTION FOR A TRANSPORTATION PROBLEM

Because determining the best initial basic feasible solution (IBFS) for a transportation problem is so crucial, numerous authors have expended a great deal of energy developing effective algorithms that will result in the lowest possible cost of moving products from a given source to a destination. The goal of this work was to develop an efficient dual algorithm for finding an initial basic feasible solution to a transportation problem (TP). Two distinct algorithms that produce the same IBFS make up our suggested approach. Compared to some popular methods in the literature, Using four numerical examples, the Row Minimum Method (RMM), Column Minimum Method (CMM), Least Cost Method (LCM), Extremum Difference Method (EDM), Northwest Corner Method (NWCM), Vogel's Approximation Method (VAM), etc. In comparison to the other heuristic techniques compared with the optimal dictate solution modified distribution (MODI), the proposed heuristic approach (PS-DESPAN) approximation was shown to provide a better starting solution (a solution that is extremely close to the optimal solution)

OPTIMIZATION OF GEDONG GINCU MANGO DISTRIBUTION COSTS IN MAJALENGKA DISTRICT

Facing free trade, Indonesia is required to increase the performance of mango production in order to compete with mangoes from other countries, but the performance of gedong gincu mango agribusiness still faces a number of obstacles, both on farm and off farm. One of them is to optimize distribution costs by designing a transportation model to determine the amount of goods that must be sent from each source to each destination in such a way that the total transportation cost is minimum. The transportation model used is Vogel's Approximation Method. The purpose of this research was to find out the description of the distribution of gedong gincu mangoes in Majalengka District, the distribution costs incurred from source to destination and find out the optimization of distribution costs. The method used was quantitative with survey research techniques. The results of this research were an overview of the distribution of Gedong Gincu mangoes involving 5 parties, namely farmers, collectors, dealers, retailers and consumers which can be done with 4 marketing channels. The distribution costs incurred were different, on the four channels the lowest distribution costs are Rp 29,000 and the highest fee is Rp 74,000/kg. In channel I, it did not carry out cost optimization calculations because it did not make shipments out of town, for optimization in channel II it is Rp 13,950,000, channel III is Rp 249,100,000 and channel IV is Rp 250,980,000. Thus, it can be concluded that the lowest cost is on ordinary channel II. Further research is recommended to perform optimal testing by means of a stepping stone.

Transportation Problem via Median Approximatiom Technique for IBFS and Revised Modi’s Technique

The work sought to improve the modified distribution method (MODI) and propose an approach for estimating the initial basic feasible solution (IBFS) for a transportation problem. The Median Approximation Technique (MAT), an explicit and effective approach for locating an IBFS to a transportation problem, was created and successfully tested on 10 problem sets. The created methodology, MAT, was compared to the five existing approaches for obtaining the IBFS: Vogel Approximation Method{VAM}; North West Corner Method {NWCM}; Least Cost Method{LCM}; Column Minimum Method{CMM}; and Row Minimum Method{RMM} in terms of iterations’ number required to reach the optimum stage. Conclusively, the MAT under development provided a better IBFS across the board, as it produced optimum solutions for around 60% of the solved problem cases, as opposed to the IBFS created by the five existing approaches employed in this study, which gave optimum solutions for roughly 0%, 20%, 20%, 10%, and 10% of the examples, respectively.

Application Of Linear Programming in the Minimization of Transportation Cost in Dangote Cement, Port Harcourt

This study delved into the optimization of transportation expenses for Dangote Cement in Port Harcourt, Rivers State. It aligned the quantities of products required by national distributors with the supply available from their depots, employing linear programming techniques to achieve cost minimization. Three sources (depots) - Onne, Rumuodumaya and Trans Amadi as well as six destinations (national distributors) - Aluu, Bori, Elelewon, Omagwa, Oyibo and Rumuola were examined. The secondary data was obtained from a field survey and it contained the unit cost (in Naira) of transporting the products per bag from their various sources to various destinations as at October, 2023. Also, the data obtained from Dangote Cement National Consumer Promotion 2020 (Redemption Centres Detail) contained the list of eleven national distributors in Port Harcourt; however, only six of the national distributors were used in this research. Initial feasible solutions for the secondary data collected were determined through the application of the North-West Corner Method, the Least Cost Method, and the Vogel Approximation Method resulting in values of ₦452,000, ₦380,750, and ₦370,500, respectively. Upon analyzing the outcomes, it was established that the allocation strategy proposed by the Vogel Approximation Method is the most advantageous for optimizing the company's transportation costs. As such, it is recommended to the company as it offers the potential to reduce transportation expenses to a minimum of ₦370,500.

Optimalisasi Biaya Transportasi Pendistribusian Pasir Menggunakan Model Transportasi Metode Steppingstone (Studi Kasus: Tangkahan Pasir Syawal)

Tangkahan Pasir Syawal is the largest mining or sand excavation business in Gunung Maria Hamlet, Janji Village, West Bilah District, Labuhanbatu Regency. This research aims to determine the optimization of transportation costs in sand distribution. To obtain the objectives of this research, data collection was carried out through direct interviews, while data analysis used the Vogel's Approximation Method (VAM) to determine the initial solution and to determine the optimal solution using the Stepping Stone method. From the research results, an initial solution of Rp. 6.310.000 and the optimal solution is Rp. 6.310.000. Meanwhile, transportation costs from Tangkahan Pasir Syawal before optimization were carried out were Rp. 9.425.000. This shows that Tangkahan Pasir Syawal can optimize transportation costs for sand distribution in November 2023 with cost savings of Rp. 3.115.000 or 4%.

A Comparative Study on the Higher-Dimensional Transportation Problems: FSTP and MODI

An optimal allocation aids a company to get its desired outcome. Their aims are distributed into two core sections; they want to maximize the profit and also try to minimize the related cost. Transportation cost is one of the unwanted costs for the companies. They want to abate it as well. To cut it down, there are a lot of solving methods developed recently. From the recent developments we choose the two effective methods Faster Strongly Polynomial method (FSTP) and the Modified Distribution method worked on Vogel's Approximation Method (VAM-MODI) to find the best one. On our selected higher-dimensional problems, the findings show us that FSTP is best if we compare the number of steps, but concerning the short execution time, VAM-MODI performs well. GANIT J. Bangladesh Math. Soc. 43.1 (2023) 37- 48

Penerapan Metode Transportasi untuk Mengoptimalkan Waktu Pengiriman Produk pada PT. Sera Banyu Urip

This study aims to find out and analyze the optimal delivery time, to find out and analyze the initial solution for transportation costs using the North West Corner, Least Cost, and Vogel's Approximation Method (VAM) methods for the initial solution, to find out and analyze the optimization of shipping costs goods using Stepping Stone and Modified Distribution at PT. Sera Banyu Urip Ciputat, South Tangerang. To achieve this research, researchers used qualitative methods by conducting documentation, observation, interviews and triangulation using a research instrument in the form of the PDCA method. For the study population at PT. Sera Banyu Urip, South Tangerang. The results showed that after using the transportation method there was a very significant increase in the delivery of each vehicle which experienced an increase in delivery, and costs became more efficient.

IMPROVING THE OPTIMIZATION OF DATE DISTRIBUTION THROUGH COST EFFICIENCY USING THE TRANSPORTATION METHOD APPROACH: CASE STUDY AT PT. XYZ

PT. XYZ faces several challenges in optimizing the distribution of dates, especially in terms of costs and delivery allocation. In the efficiency of the cost of distribution of dates, companies need to reduce operational costs associated with distribution activities. The research objective to be achieved is to analyze the minimum cost of distributing dates at PT. XYZ with the approach of transportation methods. The transportation methods used in this study are Vogel's Approximation Method, Least Cost, North-West Corner, and Stepping Stones. Vogel's Approximation Method, Least Cost, and North-West Corner are used to find the initial solution. While the Stepping Stones method is used to find the final solution. Data processing is carried out using Cbom-Atozmath and POM-QM to obtain fast, detailed, and accurate results. Data processing using the VAM (Vogel's Approximation Method) method results in a total date distribution cost of IDR 171,983,5100.00. Data processing using the NWC (North-West Corner) method resulted in a total date distribution cost of IDR 171,983,5100.00. Data processing using the LC (Least Cost) method resulted in a total date distribution cost of IDR 1,719,835,100.00. The results of calculations using the Cbom-Atozmath and POM-QM software also show the same results. The use of transportation methods to streamline the cost of distributing dates to the Company resulted in savings of Rp. 69,224,000.00. The total cost of distribution of dates by PT. XYZ before efficiency using the transportation method was Rp. 1,789,059,100. The total cost of distribution of dates by PT. XYZ after efficiency using the transportation method was Rp. 1,719,835,100.00

Optimasi Biaya Distribusi Semen Menggunakan Uji Optimal Metode Stepping Stone Dan Metode Medified Distribution (MODI)

TB. Medang Indah is a building materials store located in Medang, Tangerang Regency, Banten which has been established since 2008. This study aims to obtain optimal transportation costs with an effective route in distributing cement to TB. Medang Indah. To achieve the objectives of this research, several steps were carried out, namely, by creating a transportation model from the data obtained, determining the initial solution using the Vogel's Approximation (VAM) method, and determining the optimal solution using two methods, namely the Stepping Stone method and the Modified Distribution (MODI) method. From determining the initial solution of Rp. 52,460,000.00 and the optimal solution from both methods has the same cost and route, which is Rp. 52,350,000.00. This indicates that the route to be used by TB. Medang Indah in optimizing costs with efficient routes, namely Rp. 52,350,000.00.

Analysis of Vehicle Operating Cost Efficiency in IECO Trans Company Using Transportation Methods

This research arose because of problems with travel costs, which the company judged were not optimal, and the profits obtained by the company were also not optimal. This research was taken from a case study at the IECO Trans company. This study aims to achieve the efficiency of the IECO Trans Company using the Transportation method. The method used from the transportation method is the northwest corner, the least cost combination, and the Vogel Approximation Method (VAM). This study uses qualitative research methods. Two data are used in this study: primary, taken from interviews and company data, and secondary, taken from previous research journals, websites, government data, and books. The results of this study will show the composition of route destinations and types of vehicles at the IECO Trans company, which results in cost efficiency. As an implementation of transportation methods and cost efficiency, the IECO Trans company will get options from the composition of route destinations and vehicle types based on analyzing transportation methods with a more efficient cost.

Applying Particle Swarm Optimization Variations to Solve the Transportation Problem Effectively

The Transportation Problem (TP) is a special type of linear programming problem, where the objective is to minimize the cost of distributing a product from a number of sources to a number of destinations. Many methods for solving the TP have been studied over time. However, exact methods do not always succeed in finding the optimal solution or a solution that effectively approximates the optimal one. This paper introduces two new variations of the well-established Particle Swarm Optimization (PSO) algorithm named the Trigonometric Acceleration Coefficients-PSO (TrigAc-PSO) and the Four Sectors Varying Acceleration Coefficients PSO (FSVAC-PSO) and applies them to solve the TP. The performances of the proposed variations are examined and validated by carrying out extensive experimental tests. In order to demonstrate the efficiency of the proposed PSO variations, thirty two problems with different sizes have been solved to evaluate and demonstrate their performance. Moreover, the proposed PSO variations were compared with exact methods such as Vogel’s Approximation Method (VAM), the Total Differences Method 1 (TDM1), the Total Opportunity Cost Matrix-Minimal Total (TOCM-MT), the Juman and Hoque Method (JHM) and the Bilqis Chastine Erma method (BCE). Last but not least, the proposed variations were also compared with other PSO variations that are well known for their completeness and efficiency, such as Decreasing Weight Particle Swarm Optimization (DWPSO) and Time Varying Acceleration Coefficients (TVAC). Experimental results show that the proposed variations achieve very satisfactory results in terms of their efficiency and effectiveness compared to existing either exact or heuristic methods.

Optimization of Aqua Gallon Water Distribution Cost at Mega Mas Water Depot by VAM and MODI

This study aims to obtain optimal distribution costs for selling gallons of water at the Air Mega Mas Depot, Sekaran. The data analysis method used is the transportation method, using the VAM (Vogel's Approximation Method) method for the initial solution and the optimal test using the MODI (Modified Distribution) method. Air Mega Mas Depot is faced with the problem of increasing marketing costs due to the lack of regular distribution patterns from the source to the marketing destination, so the company tries to optimize the transportation costs incurred. The distribution of gallon water products at the Air Mega Mas Depot using the transportation method gets optimal results. The costs incurred by the Air Mega Mas Depot for the distribution of gallons of water for a 2-month period (March-April) are Rp. 2.520.000 while for the optimal calculation results for the distribution of gallons of water, a cost of IDR 2.435.000 is obtained. Based on this analysis, Air Mega Mas Depot can optimize distribution costs for the March-April period of IDR 85.000.

Comparison of completion of VAM, TCOM-SUM Transportation problems with Stepping Stone to Determine optimal solutions

This research discusses to optimize the path and find out the distribution of minimum transportation costs using the VAM (Vogel’s Approximation Method) method, TOCM-SUM is then optimized through the stepping stone test. The VAM method is one of the methods of preparing a initial feasible solution by Determining the distribution table allocation to the cell that has the least cost. TOCM-SUM method to find a suitable initial solution of the transportation problem. The optimal stepping stone test aims to test the initial solution table by calculating the cost of empty cells that are passed by the stepping stone path.

Optimalisasi Biaya Transportasi Produk UMKM Naturies Indonesia Dengan Metode Northwest Corner Dan Vogel’s Approximation

Naturies Indonesia is one of the UMKM for spice drinks in Macanan, Klaten, Central Java which is developing. As one of the growing UMKM, Naturies Indonesia is experiencing problems related to the distribution of its products. Naturies Indonesia has incurred transportation costs of Rp.442,100.00 per week in distributing its products to 5 distributors (Kudus, Jakarta, Shopee, Bandung, and offline). Due to human resource constraints, Naturies Indonesia does not yet have a thorough plan to reduce shipping costs in allocating products from production sites to customers or distributors. Through this applied research, this research aims to find the optimization of product delivery costs. Data were collected through interviews and documentation, then analyzed using the Northwest Corner and Vogel's Approximation methods. Analysis using the Northwest Corner method found a shipping cost of IDR 431,600.00, while the Vogel's Approximation method found a shipping cost of IDR 427,900.00. The shipping costs found were actually lower than the financing that had been issued so far. Keyword: northwest cor, spice drinks, optimization of transportation, UMKM Naturies Indonesia, vogel’s approximation

Application of Linear Programming to Minimize Transportation Cost in Nigeria Breweries Plc, Ibadan, Oyo State, Nigeria

This research paper work analyzed the transportation cost of Nigeria Breweries Plc, Ibadan in Oyo State in relation to the units of its products demanded at the various deports and the capacity of the factories. Five origins which are Ibadan, Osogbo, Ikeja, Oyo and Ondo as well as twelve destinations (warehouses): Gbagi, Dugbe, Oje, Ikorodu, Mowe, Ife, Ilesa, Iseyin, Ogbomosho, Owode, Akure and Ore were examined. The data also include the requirements at each destination and capacity at each source. The costs represent the average transportation cost from June to December 2019. Initial feasible solution was obtained for the secondary data collected by using North-West corner Method, and Vogel Approximation Method. The result of the analysis showed that the allocations of Vogel Approximation Method will give the optimal transportation cost of the company and is recommended to the company for reduction in transportation with a minimum transportation cost of ₦1,168,431.

A Comparison Study between the Recently Developed Methods of Transportation Problem:A Study on the Lower-Dimensional Problems

Resource allocation is one of the crucial challenges to the decision-makers. It has a significant impact on the profitability of any company. Freight transport is one type of resource allocation; here the decision-maker has to choose the quantity of products for delivering at a minimum cost from the several plants/factories/sources to the several destinations/ warehouses. We have conducted a comparative study based on secondary data to figure out the best technique for solving the freight transportation problems. Here we have selected 40 balanced and unbalanced problems randomly with dimensions 3×3 to 7×7. We have selected 23 existing methods, some of them are popular and some are recently developed. We compare these 23 methods regarding firstly the optimal solution criterion, and secondly which one can give us the solution in the least step or short time. We have checked the solution at first manually, then by GNU Octave to figure out if there is any inconsistency. Here, the GNU octave is chosen for its easy acceptance and easy input procedure. On our selected problems, the findings show us that the Faster STrongly Polynomial method (FSTP) is best if we consider the least step but concerning the short time MOdifiedDIstribution method worked on Vogel's Approximation Method, well known as VAM-MODI is performing the best. GANIT J. Bangladesh Math. Soc. 42.1 (2022) 035- 049

New Vogel’s Approximation Method (NVAM) to Determine Better Feasible Solution of Transportation Problem

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.

COMPARISON OF METHODS OF SOLVING TRANSPORTATION PROBLEMS (TP) AND RESOLVING THE ASSOCIATED VARIATIONS

Purpose: Transportation Problem is a Linear Programming application to physical distribution of goods and services from various origins to several destinations at a minimum cost.
 Methodology: In this study, five different methods were employed to solve transportation problems arising from unequal demand and supply of goods and variations. The methods considered were in terms of North West Corner Rule, Least Cost Method, Vogel’s Approximation Method, Row Minima Method and Column Minima Method were compared. Unbalanced transportation problems were resolved using Vogel’s Approximation Method (VAM) and Modified Distribution (MODI) methods.
 Findings: The methods compared produced different results with VAM generating the least transportation cost and better solution. With the MODI method, economic values were generated for the dual variables, uis and vjs associated with the source and demand points respectively.