scholarly journals METHODOLOGY RECOMMENDATION FOR ONE‐CRITERION TRANSPORTATION PROBLEMS: CAKMAK METHOD

Transport ◽  
2007 ◽  
Vol 22 (3) ◽  
pp. 221-224 ◽  
Author(s):  
Tanyel Çakmak ◽  
Filiz Ersöz
Keyword(s):  
Approximation Method ◽  
Operations Research ◽  
Feasible Solution ◽  
New Method ◽  
Basic Solution ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Solution Methods ◽  
Optimum Solution

Transportation problems (TP) are one of the most prominent fields of application of the mathematical disciplines to optimization and operations research. In general, there are three starting basic feasible solution methods: Northwest Corner, Least Cost Method, VAM – Vogel's Approximation Method. The three methods differ in the quality of the starting basic solution. In this study, we actually show a new method for starting basic feasible solution to one‐criterion‐transportation problems: Çakmak Method. This method can be used for balanced or unbalanced one-criterion transportation problems, and gives the basic feasible optimum solution accordingly.

scholarly journals Sorting Out Fuzzy Transportation Problems via ECCT and Standard Deviation

2021 ◽  
Vol 12 (2) ◽  
pp. 1-14
Author(s):  
Krishna Prabha Sikkannan ◽  
Vimala Shanmugavel
Keyword(s):  
Standard Deviation ◽  
Approximation Method ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
New Method ◽  
Transportation Problems ◽  
North West ◽  
Numerical Example ◽  
Optimum Solution ◽  
Better Than

A well-organized arithmetical procedure entitled standard deviation is employed to find the optimum solution in this paper. This technique has been divided into two parts. The first methodology deals with constructing the entire contingency cost table, and the second deals with optimum allocation. In this work, the method of magnitude is used for converting fuzzy numbers into crisp numbers as this method is better than the existing methods. This technique gives a better optimal solution than other methods. A numerical example for the new method is explained, and the authors compared their method with existing methods such as north west corner method, least cost method, and Vogel's approximation method.

scholarly journals Overview of Optimality of New Direct Optimal Methods for the Transportation Problems

2019 ◽  
pp. 1-10
Author(s):  
Sanaullah Jamali ◽  
Muhammad Mujtaba Shaikh ◽  
Abdul Sattar Soomro
Keyword(s):  
Feasible Solution ◽  
Optimal Solution ◽  
New Method ◽  
Large Set ◽  
Basic Feasible Solution ◽  
Optimal Method ◽  
Transportation Problems ◽  
Optimal Methods ◽  
Transportation Models ◽  
Dea Method

In this paper, we investigate the claimed optimality of a new method – Revised Distribution (RDI) Method – for finding optimal solution of balanced and unbalanced transportation models directly and compare the RDI method with other such methods. A large set of problems have been tested by RDI and other methods, and the results were compared with the Modified distribution (MODI) method – an optimal method. We found that the mostly the results of RDI are not optimal. For reference to prove our observations, we have added three example transportation problems here in this work and compared their results with MODI method to show that the RDI method like the direct exponential approach (DEA) method is not optimal method; but it is just an initial basic feasible solution (IBFS) for transportation problems.

scholarly journals New Procedure of Finding an Initial Basic Feasible Solution of the Time Minimizing Transportation Problems

2015 ◽  
Vol 05 (10) ◽  
pp. 634-640 ◽  
Author(s):  
Mollah Mesbahuddin Ahmed ◽  
Md. Amirul Islam ◽  
Momotaz Katun ◽  
Sabiha Yesmin ◽  
Md. Sharif Uddin
Keyword(s):  
Feasible Solution ◽  
Basic Feasible Solution ◽  
Transportation Problems

scholarly journals Statistical Methods for Solving Transportation Problems

2019 ◽  
Vol 25 (2) ◽  
pp. 10-13
Author(s):  
Alina Baboş
Keyword(s):  
Linear Programming ◽  
Statistical Methods ◽  
Approximation Method ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Basic Feasible Solution ◽  
Statistical Tools ◽  
Numerical Examples ◽  
North West ◽  
Shipping Cost

Abstract Transportation problem is one of the models of Linear Programming problem. It deals with the situation in which a commodity from several sources is shipped to different destinations with the main objective to minimize the total shipping cost. There are three well-known methods namely, North West Corner Method Least Cost Method, Vogel’s Approximation Method to find the initial basic feasible solution of a transportation problem. In this paper, we present some statistical methods for finding the initial basic feasible solution. We use three statistical tools: arithmetic and harmonic mean and median. We present numerical examples, and we compare these results with other classical methods.

EXPERIMENTAL ANALYSIS OF SOME VARIANTS OF VOGEL'S APPROXIMATION METHOD

2004 ◽  
Vol 21 (04) ◽  
pp. 447-462 ◽  
Author(s):  
M. MATHIRAJAN ◽  
B. MEENAKSHI
Keyword(s):  
Approximation Method ◽  
Opportunity Cost ◽  
Optimal Solution ◽  
Efficient Solutions ◽  
Transportation Problems ◽  
Cpu Time ◽  
Problem Instances ◽  
Time Required ◽  
The Military

This paper presents a variant of Vogel's approximation method (VAM) for transportation problems. The importance of determining efficient solutions for large sized transportation problems is borne out by many practical problems in industries, the military, etc. With this motivation, a few variants of VAM incorporating the total opportunity cost (TOC) concept were investigated to obtain fast and efficient solutions. Computational experiments were carried out to evaluate these variants of VAM. The quality of solutions indicates that the basic version of the VAM coupled with total opportunity cost (called the VAM–TOC) yields a very efficient initial solution. In these experiments, on an average, about 20% of the time the VAM–TOC approach yielded the optimal solution and about 80% of the time it yielded a solution very close to optimal (0.5% loss of optimality). The CPU time required for the problem instances tested was very small (on an average, less than 10 s on a 200 MHz Pentium machine with 64 MB RAM).

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