Solving interval-valued transportation problem using a new ranking function for octagonal fuzzy numbers

In this paper, we introduce a new method to solve Interval-Valued Transportation Problem (IVTP) to deal with those problems of transportation wherein the information available is imprecise. First, a newly proposed fuzzification method is used to convert the IVTP to octagonal fuzzy transportation problem and then with the help of ranking function proposed in this paper, the fuzzy transportation problem is converted into crisp transportation problem. Lastly, Initial Basic Feasible Solution (IBFS) of this problem is obtained using Vogel’s Approximation Method and the solution is improved using Modified Distribution (MODI) method. A numerical example with interval data is solved using the proposed algorithm to make comparison of the solution with some other methods. Also, a numerical example with parameters in the form of octagonal fuzzy numbers is illustrated to compare the effectiveness of the proposed ranking technique. The proposed fuzzification and ranking technique can be used in the other fields of decision making dealing with the data in the same form as considered in this paper.

Optimization of Fuzzy Species Pythagorean Transportation Problem under Preserved Uncertainties

The transportation of big species is essential to rescue or relocate them and it requires the optimized cost of transportation. The present study brings out an optimized way to handle a special class of transportation problem called the Pythagorean fuzzy species transportation problem. To deal effectively with uncertain parameters, a new method for finding the initial fuzzy basic feasible solution (IFBFS) has been developed and applied. To test the optimality of the solutions obtained, a new approach named the Pythagorean fuzzy modified distribution method is developed. After reviewing the literature, it has been observed that till now the work done on Pythagorean fuzzy transportation problems is solely based on defuzzification techniques and so the optimal solutions obtained are in crisp form only. However, the proposed study is focused to get the optimal solution in its fuzzy form only. Getting results in the fuzzy form will lead to avoid any kind of loss of information during the defuzzification process. A comparative study with other defuzzification-based methods has been done to validate the proposed approach and it confirms the utility of the proposed methodology.

Solving transportation problem using modified ASM method

Transportation problems are related to activities aimed at minimizing the cost of distributing goods from a source to a destination. One of the methods used to solve transportation problems is the ASM Method as a method capable of producing optimal direct solutions without having to determine the initial basic feasible solution first. Determination of the allocation of goods in the ASM Method uses a reduced cost of 0 by calculating the maximum amount in the allocation of goods. Then the ASM method is modified so that the iteration used is simpler in obtaining the optimal direct solution without calculating the maximum number of row and column elements. The method is called Modified ASM Method. This method also provides more optimal results than the ASM method. This research aimed to solve transportation problems using the Modified ASM method to produce optimal solutions directly. The research procedure identifies and forms a model of transportation problems (variable decisions, objective functions and constraint functions), identifies types of transportation problems (balanced or unbalanced), and obtains direct solutions by solving transportation problems using the Modified ASM method. This research shows that the Modified ASM method successfully solves the problem of balanced and unbalanced transportation by producing optimal solutions in a simpler way than the ASM method.

Fundamentals of Transportation Problem

Transportation Problem is a linear programming problem. Like LPP, transportation problem has basic feasible solution (BFS) and then from it we obtain the optimal solution. Among these BFS the optimal solution is developed by constructing dual of the TP. By using complimentary slackness conditions the optimal solutions is obtained by the same iterative principle. The method is known as MODI (Modified Distribution) method. In this paper we have discussed all the aspect of transportation problem.

IMPLEMENTASI KARAGUL-SAHIN APPROXIMATION METHOD UNTUK MEMINIMALISASI BIAYA PENDISTRIBUSIAN AIR PADA MASALAH TRANSPORTASI

Transportation problems such as transportation activities and allocation to reach consumers is one of the factors that determine the level of satisfaction. To find the level of customer satisfaction, it requires an appropriate and efficient transportation model. One of which is in the Air Minum Mata Air Sikumbang business owned by Mr. Zulfikar, located in Rumbio, Kampar. Based on the results of the study the cost of distributing drinking water is still not efficient because it still uses estimation and there is no separate technique used to allocate water distribution. The solution made in this study using the Karagul-Sahin Approximation Method for the initial basic feasible solution and Stepping Stone for the optimal solution value so as to obtain the distribution of water at a minimum cost. Based on research using the method of Karagul-Sahin Approximation and Stepping Stone, a weekly cost savings of Rp.469.515,00 is obtained.

APPLICATION OF TRANSPORTATION MODEL FOR OPTIMAL PRODUCT DISTRIBUTION CHAIN MANAGEMENT

Many business organizations are operating at an unacceptable high distribution chain costs even as industrial competition continues to pose as a major challenge to business success. Linear programming devices can help organizations achieve efficiency. This research aims at establishing the impact of Transportation algorithm in optimal product distribution and scheduling of business organizations. In a field study of NOWAS Oil and Gas, data was significantly secondary sourced, resulting from indepth analysis of existing documented content materials on the subject. Practical application of the least cost method scheduling and North West Corner Rule method of an initial basic feasible solution was imminent. Revising that solution using the stepping stone method translated to an optimal distribution schedule and a minimum cost profit in yearly distribution schedule of Nowas Oil and Gas, Enugu. It is recommended that business organizations carryout careful analysis of their supply and demand constraints in materials and products distribution for cost minimization and overall resource optimization. Keywords: Application, Transportation Model, Basic Feasible Solution, Optimality, Distribution Chain, Management.

A Comprehensive Method for Arriving at Initial Feasible Solution for Optimization Problems in Engineering with Illustrative Examples

Two methods have been used extensively for arriving at initial basic feasible solution (IBF). One of them is Northwest corner rule and the other on is Russell method (Hillier & Lieberman, 2005.) Both methods have drawbacks. The IBF obtained is either far from optimal solution or does not have adequate number of entries to initiate transportation simplex algorithm. The Northwest Corner rule gives an initial feasible solution that is far from optimal while the IBF solution obtained using Russell method doesn’t give enough number of entries to start the transportation simplex algorithm. Hence, there is a need for developing a method for arriving at initial basic feasible solution with adequate number of entries needed to initiate transportation simplex algorithm, which can then be used to get an optimal solution. A computer software has been developed based on the new proposed method for this purpose. The proposed new method has been validated through four simple but illustrative examples.

A Modern Approach For Finding Minimization Cost In Transportation Problem

In this paper, the proposed technique is new and simple for obtaining an initial basic feasible solution (IBFS) of a transportation problem (TP). The objective of this paper is to find how to minimize the transportation cost (TC) by using a new approach. The method is illustrated with some numerical examples using algorithm.