scholarly journals A Note on Feasibility and Optimality of Transportation Problem

2014 ◽  
Vol 10 (1) ◽  
pp. 59-68 ◽  
Author(s):  
Purnima Adhikari ◽  
Gyan Bahadur Thapa
Keyword(s):  
Decision Making ◽  
Operations Research ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Business Management ◽  
Optimal Solution ◽  
Basic Feasible Solution ◽  
Primal Dual ◽  
Dual Case ◽  
Decision Making Tool

 Transportation problem is one of the predominant areas of operations research, widely used as a decision making tool in engineering, business management and many other fields. In this paper, we present a brief literature review of transportation problem with its mathematical models in balanced and unbalanced cases. We report the basic feasible solution and hence the methods to attain optimal solution of the balanced transportation problem. Finally, we describe the primal-dual case of the problem with counter examples. DOI: http://dx.doi.org/10.3126/jie.v10i1.10879Journal of the Institute of Engineering, Vol. 10, No. 1, 2014, pp. 59–68

scholarly journals Fundamentals of Transportation Problem

2021 ◽  
Vol 10 (5) ◽  
pp. 90-103
Author(s):  
Bhabani Mallia ◽  
Manjula Das ◽  
C. Das
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method

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.

scholarly journals Optimization of Fuzzy Species Pythagorean Transportation Problem under Preserved Uncertainties

2021 ◽  
Vol 6 (6) ◽  
pp. 1629-1645
Author(s):  
Priyanka Nagar ◽  
Pankaj Kumar Srivastava ◽  
Amit Srivastava
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Uncertain Parameters ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method ◽  
New Approach ◽  
Work Done ◽  
Cost Of Transportation

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.

scholarly journals An algorithm for solving a capacitated indefinite quadratic transportation problem with enhanced flow

2014 ◽  
Vol 24 (2) ◽  
pp. 217-236 ◽  
Author(s):  
Kavita Gupta ◽  
S.R. Arora
Keyword(s):  
Special Class ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Flow Problem ◽  
Optimal Solution ◽  
Total Flow ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Indefinite Quadratic

The present paper discusses enhanced flow in a capacitated indefinite quadratic transportation problem. Sometimes, situations arise where either reserve stocks have to be kept at the supply points say, for emergencies, or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied, where the total transportation flow is enhanced to a known specified level. A related indefinite quadratic transportation problem is formulated, and it is shown that to each basic feasible solution called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this enhanced flow problem. The optimal solution to enhanced flow problem may be obtained from the optimal solution to the related transportation problem. An algorithm is presented to solve a capacitated indefinite quadratic transportation problem with enhanced flow. Numerical illustrations are also included in support of the theory. Computational software GAMS is also used.

scholarly journals A Simple and Efficient Algorithm for Solving Type-1 Intuitionistic Fuzzy Solid Transportation Problems

2018 ◽  
Vol 9 (3) ◽  
pp. 90-122 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Real Life ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number

This article describes how in solving real-life solid transportation problems (STPs) we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation, many authors have suggested the intuitionistic fuzzy (IF) representation for the data. In this article, the author tried to categorise the STP under uncertain environment. He formulates the intuitionistic fuzzy solid transportation problem (IFSTP) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The STP has uncertainty and hesitation in supply, demand, capacity of different modes of transport celled conveyance and when it has crisp cost it is known as IFSTP of type-1. From this concept, the generalized mathematical model for type-1 IFSTP is explained. To find out the optimal solution to type-1 IFSTPs, a single stage method called intuitionistic fuzzy min-zero min-cost method is presented. A real-life numerical example is presented to clarify the idea of the proposed method. Moreover, results and discussions, advantages of the proposed method, and future works are presented. The main advantage of the proposed method is that the optimal solution of type-1 IFSTP is obtained without using the basic feasible solution and the method of testing optimality.

scholarly journals A New Method to Obtain an Initial Basic Feasible Solution of Transportation Problem with the Average Opportunity Cost Method

2019 ◽  
Vol 9 (2) ◽  
pp. 206-209
Keyword(s):  
Opportunity Cost ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
The Other ◽  
New Method ◽  
Basic Feasible Solution ◽  
Distribution Method

In this preset article, we have explained all new method to get Initial Basic Feasible solution (IBFS) of Transportation Problem (TP) with the Average Opportunity Cost Method (AOCM). It is very simple arithmetical and logical calculation.After finding the IBFS we use Modified Distribution Method (MODI) method to optimize the IBFS. Results obtained by using this method we found that IBFS of most of the transportation problem closer to optimal solution than using the other existing methods. We illustrate the same by suitable examples.

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.

Sign in / Sign up

Export Citation Format

Share Document