Vogel's Approximation Method Research Articles

Optimasi OPTIMASI BIAYA TRANSPORTASI PADA UKM DI KOTA BATAM

This research was conducted at UKM Jovelyn in Batam city. Jovelyn's UKM produces various kinds of cakes and is marketed in markets in Batam City. The UKM opened 4 branches and marketed its products to 7 markets in the city of Batam. Product distribution is still random and not properly regulated. This resulted in a very large transportation cost, up to 1/3 of the total production cost. This shows that product transportation is still not carried out effectively and efficiently. The transportation problem is converted into a mathematical form so that the problem can be solved by the transportation method. The transportation method aims to minimize the objective function which is a function of transportation costs. The transportation method is basically the same as the linear program where at each iteration a selection is made to enter the basic variabel and leave the basic variabel. There are several iteration methods, namely the northwest corner method, minimum cost method, genetic algorithm, Vogel's approximation method, minimum row method, Russell's approximation method and column minimum method. Previous research has shown that the Vogel's approximation method, and Russell's approximation method are more efficient and accurate. This study uses both methods and a sensitivity analysis is performed to optimize the calculation results. The sensitivity analysis aims to determine the extent to which the objective function constants and the constraint function constants can change
 Keywords: Transportation, Sensitivity, SME

Minimizing Cost of Transportation By Vogel’s Approximation Method: A Case Study of Maisango Cement Nigeria Plc

This piece of research was conducted to optimize the procedures of transporting and distributing of Cement products from MAISANGO Cement Plc to the require destinations which resultant to the reduction of operating cost of transportation problems that usually occurs due to the nature of bad roads to some selected locations in Lagos state- Nigeria. To minimize the cost, a mathematical optimization model (Vogel Approximation method) has been utilized to ease the processes of transporting the product to the various locations.

Minimizing the cost using an inventive proposal in transportation problems

In linear programming problem, transportation problem is a particular approach to achieve the cost. An innovative hypothesis is discussed for getting optimal cost in transportation problem in this paper and Vogel’s Approximation Method (VAM) and MODI method are compared with the projected method. This work is verified by various transportation problems.

A new heuristic method of finding the initial basic feasible solution to solve the transportation problem

Many real applications use the transportation problems for finding the optimal solution for product shipment from supply to demand. The transportation problem (TP) is related to delivering some products from the supply to the demand. The initial basic feasible solution (IBFS) is a significant step to achieve the minimal total cost (optimal solution) of the transportation problem. However, the existing methods of IBFS do not always provide a good feasible solution which can reduce the number of iterations to find the optimal solution. Therefore, it is still challenging to develop a better method of IBFS. In this paper, a new method to obtain the IBFS of transportation problem called Bilqis Chastine Erma method (BCE) was proposed. The thirty-five numerical examples were used to evaluate the performance of the proposed method. It was compared to other IBFS methods, namely: Vogel’s Approximation Method (VAM), Total Differences Method 1 (TDM1), Total opportunity cost matrix – Minimal total (TOCM-MT), and Juman & Hoque Method (JHM). The experiment results indicate that BCE obtained lower total minimal cost than VAM, TDM1, TOCM-MT, and JHM and reached the fastest solving time. It reached its optimal solution for thirty-one of thirty-five numerical examples (88.57%).

A Modification to Vogel’s Approximation Method to Solve Transportation Problems

Transportation Problem (TP) is singular of the paradigms in the Linear Programming Problems (LPP). The TP in Operations Research represent vastly applied optimization. (TP) has some goals, like reducing transportation costs or reducing transportation time, etc. Whereas meeting both supply level and request level requirements. Transportation problem plays a major role in industry, trade, logistics, etc. To get the most possible profit, organizations are always looking for better ways to reduce cost and improve revenue. To solve the transportation problems, it is always required to find an initial basic feasible solution (IBFS) for get the optimal solution. The Vogel’s Approximation Method (VAM) is the important known traditional methods for obtaining an IBFS of TP. In this work, we introduce a new modification to the VAM for finding an IBFS for the transportation problems almost nearer to the optimal solve. Proposed modification is illustrated with solved numerical examples. A comparison study was also conducted with the results of classic methods. This modified approach most of times give better solution and very nearer to the optimal solve, furthermore, occasionally gives the optimal solve. This method is clear, easy to comprehend.

A New Revised Efficient of VAM to Find the Initial Solution for the Transportation Problem

Transportation Problem (TP) is a very important problem which has been vastly studied in Operations Research domain. There are some classical methods to find the initial basic feasible solution (IBFS) which minimize the total shipping cost of (TP) such as north-west corner method (NWCM), minimum cost method (MCM) and Vogel’s approximation method (VAM) which the best one of them. In this paper, we suggest a new amendment to (VAM) to find (IBFS) of (TP), which is an iterative method and the results will be near the optimal solution and in some cases equal to the optimal solution. In the numerical experiences we compare the results of the new approach with other classical methods to verify the efficiency of the new method. The proposed method is very effective and well-suited for use in solving these problems of various sizes.

STUDY OF TRANSPORTATION PROBLEM OF IRON AND STEEL INDUSTRY IN TURKEY BASED ON LINEAR PROGRAMMING, VAM AND MODI METHODS

The subject of this study is the investigation of the minimization of the total transportation costs for finished product produced by Alter Iron and Steel Industry Company in its own production facilities in Karabuk. Firstly, the current situation in the Iron and Steel Industry in the world and Turkey are briefly discussed. In the second stage, the distribution to the demand point from the factory operating in the Iron and Steel Sector is considered as the basic problem. The demand points were determined as geographical regions. We have two targets: the total cost to be minimized and the total amount of goods to be sent from supply center to the demand centers to be equal to the total demand or supply amount. The optimum solution of the transportation model were solved both the traditional transportation model methods such as Vogels Approximation Method (VAM), Modified Distribution (MODI) method and the linear programming method. The optimal solution for last model was found using the R /SIMPLEX package program. Obtained results by different approachs are discussed. Critical aspect of this problem is to use the single source transportation model, where all demand amounts are met from a single production center.

ANALISIS BIAYA TRANSPORTASI DISTRIBUSI PUPUK MENGGUNAKAN SOFTWARE LINGO

The distribution of fertilizers in Central Sulawesi Province has not been efficient due to the large transportation costs in March 2016, the distribution of fertilizers could not go directly to retailers because the distance between regencies was far enough so that fertilizer was sent to distributors before to retailers to minimize costs to be incurred. company. Transhipment problems are in the form of indirect distribution problems because the products sent must go through several stages before reaching the consumer. This study will compare the Vogel Approximation method in previous studies with the completion of linear programming with Lingo software tools. Transportation costs using the Vogel Approximation method in previous studies compared with transportation costs using the Lingo software tool have the same cost of IDR 508,289,000, but there are several different fertilizer distributions. Lingo software simplifies data processing so that the results obtained are more accurate than the Vogel Approximation method. Companies can use lingo software to minimize costs by working effectively and efficiently.

OPTIMAL FEASIBLE SOLUTIONS TO A ROAD FREIGHT TRANSPORTATION PROBLEM

For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are represented in tables and results are compared with the result obtained on Maple 18 software. The study shows various ways in which the initial basic feasible solutions to the problem can be obtained where the best method that saves the highest percentage of transportation cost with for this problem is the NWC. The NWC produces the optimal transportation cost which is 517,040 units.

Efficient Cost Optimization using Transportation Mechanisms for Cloud Computing Environment

Efficient computations are increasing now a day, so their need is very high in the world. Infrastructure and computation techniques are not as much as efficient in conventionally or in present scenario, therefore the cloud computing is new to deal this type of problems. Sequencing of hardware and software technologies, for giving scalable and low cost computational understandings in cloud computing. The major focus of this research is to diminish the transportation cost of resource allocation along with various virtual machines in cloud computing environment. In this research paper, implementation of Vogel's Approximation Method (VAM) to obtain an Initial Basic Feasible Solution (IBFS) and an algorithm to optimize the cost of resource transportations for cloud service provider (CSP) as well as present an example also to understand the proposed method for total supply values and total demand values. Although the calculation of cost reduction until the iteration still has a non-negative values, and the calculation is done again until the last iteration. A comparison has been shown the cost of the proposed mechanism is much less from other technique.

Solving non-quadratic Matrices in Assignment Problems with an improved Version of Vogel's Approximation Method

The efficient allocation of tasks to vehicles in a fleet of self-driving vehicles (SDV) becomes challenging for largescale systems (e.g. more than hundred vehicles). Operations research provides different methods that can be applied to solve such assignment problems. Integer Linear Programming (ILP), the Hungarian Method (HM) or Vogel’s Approximation Method (VAM) are frequently used in related literature (Paul 2018; Dinagar and Keerthivasan 2018; Nahar et al. 2018; Ahmed et al. 2016; Korukoglu and Balli 2011; Balakrishnan 1990). The underlying paper proposes an adapted version of VAM which reaches better solutions for non-quadratic matrices, namely Vogel’s Approximation Method for non-quadratic Matrices (VAM-nq). Subsequently, VAM-nq is compared with ILP, HM and VAM by solving matrices of different sizes in computational experiments in order to determine the proximity to the optimal solution and the computation time. The experimental results demonstrated that both VAM and VAM-nq are five to ten times faster in computing results than HM and ILP across all tested matrix sizes. However, we proved that VAM is not able to generate optimal solutions in large quadratic matrices constantly (starting at approx. 15×15) or small non-quadratic matrices (starting at approx. 5×6). In fact, we show that VAM produces insufficient results especially for non-quadratic matrices. The result deviate further from the optimum if the matrix size increases. Our proposed VAM-nq is able to provide similar results as the original VAM for quadratic matrices, but delivers much better results in non-quadratic instances often reaching an optimum solution. This is especially important for practical use cases since quadratic matrices are rather rare.

A heuristic for obtaining better initial feasible solution to the transportation problem

Vogel’s Approximation Method (VAM) is known as the best algorithm for generating an efficient initial feasible solution to the transportation problem. We demonstrate that VAM has some limitations and computational blunders. To overcome these limitations we develop an Improved Vogel’s Approximation Method (IVAM) by correcting these blunders. It is compared with VAM on obtained initial feasible solutions to a numerical example problem. Reduction in the total transportation cost over VAM by IVAM is found to be 2.27%. Besides, we have compared IVAM with each of twelve previously developed methods including VAM on solutions to numerical problems. IVAM leads to the minimal total cost solutions to seven, better solutions to four and the same better solution to the remaining one. Finally, a statistical analysis has been performed over the results of 1500 randomly generated transportation problems with fifteen distinct dimensions, where each of them has 100 problems instances. This analysis has demonstrated better performance of IVAM over VAM by reducing the total transportation cost in 71.8% of solved problems, especially for large size problems. Thus IVAM outperforms VAM by providing better initial feasible to the transportation problem.

Heuristics-based design and optimization of offshore wind farms collection systems

A parallel-based algorithmic framework for automated design of Offshore Wind Farms (OWF) collection systems is proposed in this paper. The framework consists basically on five algorithms executed simultaneously and independently, followed by a combined analysis aiming to generate the best results in terms of different objective functions. The main inputs of the framework are the location coordinates of the Wind Turbines (WT) and the Offshore Substation (OSS), wind power production time series, and the set cables considered for the collection system design. Four heuristics and one metaheuristic algorithm are considered. The heuristics are based on modified versions of well-known graph-theory algorithms: Kruskal (KR), Prim (PR), Esau-Williams (EW), and Vogel’s Approximation Method (VAM); all of them coded in a unified framework with quartic time complexity. The metaheuristic is built upon a Genetic Algorithm (GA) designed using a hierarchical-restricted penalization system. Comparisons between all of these methods are performed from different perspectives, taking into consideration the particular constraints treated for OWF practical applications. In general, primals from heuristics lead to faster and better results when only a single cable is available, and provide collection systems with lower electrical power losses for multiple cables choice, whilst the GA shows better results when the initial investment is prioritized and several cable types are considered.

Problem of Modelling Road Transport

Abstract The article addressed road transport based on the proprietary numerical example. It is a typical optimization issue consisting in reducing the transportation costs between different drop-off locations. To determine the optimum transport plan, the following methods were used: North West Corner Method, Matrix Minima Method and Vogel’s Approximation Method (VAM).

Optimizing Municipal Solid Waste Transportation Routes for Pune City using MATLAB

The environment is heading towards a potential risk due to unsustainable waste disposal. It is a sensitive issue which concerns about serious environmental problems in today’s world. The present situation of direct dumping of the waste without proper inspection and separation leaves a serious impact of environmental pollution causing a tremendous growth in health related problems. “Domestic, industrial and other wastes, whether they are of low or medium level wastes, they are causing environmental pollution and have become perennial problems for mankind. If this situation is not handled in a proper manner within time then it would lead to worse consequences on a global level. There has been development of new technologies for improving the waste management systems. In this paper we attempt to show a detailed analysis of three crucial parameters: distance, time and cost affecting the solid waste management system by a direct comparison of existing routes and through the routes obtained by application of Arc GIS. Method adopted for analysis is VAM (Vogel’s Approximation Method) a part of Transportation model, and results of the same are validated using MATLAB Software programmed exclusively for VAM.

Total opportunity cost matrix – Minimal total: A new approach to determine initial basic feasible solution of a transportation problem

Transportation Problem (TP) deals with cost planning for delivering the product from the source to the destination and Initial Basic Feasible Solution (IBFS) is presented to find the way out in obtaining an optimal solution. IBFS is an important element to reach an optimal result. The previous methods related to it did not always provide the satisfied result all the time. Therefore a new method called Total Opportunity Cost Matrix – Minimal Total (TOCM-MT) to determine IBFS as a basic solution to solve TP was proposed. The objective is to achieve a total cost with similar or closer values to the optimal solution. TOCM for the initial matrix and a better mechanism are highly considered to obtain IBFS. Thirty-one numerical examples, in which twenty-five were selected from some journals and six were generated randomly, were used to evaluate the performance of it. The proposed method has been compared to Vogel’s Approximation Method (VAM), Juman and Hoque Method (JHM), and Total Differences Method 1 (TDM1). TOCM-MT was proven to have twenty-four numerical examples with similar values and seven numerical examples with closer values to the optimal solution. The experiment results indicated that TOCM-MT obtained better minimal cost than that of VAM, JHM, and TDM1.

Time-cost trade-off in a multi index bi-criteria fixed charge transportation problem

This paper is motivated by the necessity of finding efficient time-cost trade-off pairs for multi index bi-criteria fixed charge transportation problem wherein time criteria assumes greater significance than cost criteria and is therefore minimised first. So far no study on finding optimal time-cost pairs of the problem has been undertaken, a gap which the newly developed algorithm aims to fulfil. Results of a numerical illustration are obtained by the proposed algorithm by applying extended Vogel's approximation method and extended modified distribution method; it has been observed that the proposed algorithm is a far better alternative in problems in which time minimisation holds priority over cost minimisation.

An effective algorithm to solve cost minimizing transportation problem

The developed algorithm in this article provides an initial basic feasible solution (IBFS) of the transportation problem (TP) of the linear programming problem. The proposed method, which involves fewer calculations and fewer steps or iterations, is able to provide a better approximate solution to the TP than classical methods, especially Vogel's approximation method (VAM). This method is also easier and more effective than some recent methods to solve TPs, which were introduced by various researches. This article illustrates the simplicity and effectiveness of the developed algorithm by providing a good number of examples.

Solution of Transportation Problem with South-East Corner Method, North-East Corner Method and Comparison with Existing Method

Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems. In this paper, two methods are proposed to find an initial basic feasible solution for the transportation problems. The South-East Corner Method (SECM) and the North-East Corner Method (NECM) are adopted to compute the Initial Basic Feasible Solution (IBFS) of the transportation problem. A comparative study is carried out with existing methods like Vogel’s approximation method (VAM) which is to find an initial basic feasible solution and Modified Distribution (MODI) Method which is to find the optimal solution and the methods are also illustrated with numerical examples.

An effective algorithm to solve cost minimising transportation problem

The developed algorithm in this article provides an initial basic feasible solution (IBFS) of the transportation problem (TP) of the linear programming problem. The proposed method, which involves fewer calculations and fewer steps or iterations, is able to provide a better approximate solution to the TP than classical methods, especially Vogel's approximation method (VAM). This method is also easier and more effective than some recent methods to solve TPs, which were introduced by various researches. This article illustrates the simplicity and effectiveness of the developed algorithm by providing a good number of examples.