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 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 Sequentially Updated Weighted Cost Opportunity Based Algorithm in Transportation Problem

2019 ◽  
Vol 38 ◽  
pp. 47-55
Author(s):  
ARM Jalal Uddin Jamali ◽  
Pushpa Akhtar
Keyword(s):  
Opportunity Cost ◽  
Feasible Solution ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Basic Feasible Solution ◽  
New Approach ◽  
Cost Matrix ◽  
Transportation Problems ◽  
The Cost ◽  
First Time

Transportation models are of multidisciplinary fields of interest. In classical transportation approaches, the flow of allocation is controlled by the cost entries and/or manipulation of cost entries – so called Distribution Indicator (DI) or Total Opportunity Cost (TOC). But these DI or TOC tables are formulated by the manipulation of cost entries only. None of them considers demand and/or supply entry to formulate the DI/ TOC table. Recently authors have developed weighted opportunity cost (WOC) matrix where this weighted opportunity cost matrix is formulated by the manipulation of supply and demand entries along with cost entries as well. In this WOC matrix, the supply and demand entries act as weight factors. Moreover by incorporating this WOC matrix in Least Cost Matrix, authors have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems. But in that approach, WOC matrix was invariant in every step of allocation procedures. That is, after the first time formulation of the weighted opportunity cost matrix, the WOC matrix was invariant throughout all allocation procedures. On the other hand in VAM method, the flow of allocation is controlled by the DI table and this table is updated after each allocation step. Motivated by this idea, we have reformed the WOC matrix as Sequentially Updated Weighted Opportunity Cost (SUWOC) matrix. The significance difference of these two matrices is that, WOC matrix is invariant through all over the allocation procedures whereas SUWOC   matrix is updated in each step of allocation procedures. Note that here update (/invariant) means changed (/unchanged) the weighted opportunity cost of the cells. Finally by incorporating this SUWOC matrix in Least Cost Matrix, we have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems.  Some experiments have been carried out to justify the validity and the effectiveness of the proposed SUWOC-LCM approach. Experimental results reveal that the SUWOC-LCM approach outperforms to find out IBFS. Moreover sometime this approach is able to find out optimal solution too. GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 47-55

scholarly journals Impaired flow multi-index transportation problem with axial constraints

1988 ◽  
Vol 29 (3) ◽  
pp. 296-309 ◽  
Author(s):  
Lakshmisree Bandopadhyaya ◽  
M. C. Puri
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Flow Problem ◽  
Optimal Solution ◽  
Multi Index ◽  
Standard Problem ◽  
Feasible Solutions

AbstractThis paper studies the impairing of flows in multi-index transportation problem with axial constraints. For any curtailed flow, the problem is shown to be equivalent to a standard axial sum problem, whose solution can be obtained by known methods. The equivalence is established only for specially defined solutions (referred to as M-feasible solutions) of the standard problem. It is also proved that an optimal solution of the impaired flow problem corresponds to such an M-feasible solution.

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 Solving Fuzzy Transportation Problem Using ASM Method and Zero Suffix Method

2021 ◽  
Vol 1 (01) ◽  
pp. 28-35
Author(s):  
Aurora Nur Aini ◽  
Ali Shodiqin ◽  
Dewi Wulandari
Keyword(s):  
Linear Programming ◽  
Fuzzy Number ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Demand And Supply ◽  
Transportation Problems ◽  
Initial Feasible Solution ◽  
Fuzzy Transportation Problem ◽  
Special Case

The transportation problem is a special case for linear programming. Sometimes, the amount of demand and supply in transportation problems can change from time to time, and thus it is justified to classify the transportation problem as a fuzzy problem. This article seeks to solve the Fuzzy transportation problem by converting the fuzzy number into crisp number by ranking the fuzzy number. There are many applicable methods to solve linear transportation problems. This article discusses the method to solve transportation problems without requiring an initial feasible solution using the ASM method and the Zero Suffix method. The best solution for Fuzzy transportation problems with triangular sets using the ASM method was IDR 21,356,787.50, while the optimal solution using the Zero Suffix method was IDR 21,501,225.00. Received February 5, 2021Revised April 16, 2021Accepted April 22, 2021

scholarly journals A New Technique for Solving Transportation Problems by Using Decomposition-Based Pricing and its Implementation in Real Life

2016 ◽  
Vol 64 (1) ◽  
pp. 45-50
Author(s):  
Sajal Chakroborty ◽  
M Babul Hasan
Keyword(s):  
Feasible Solution ◽  
Real Life ◽  
Optimal Solution ◽  
Computer Code ◽  
The Other ◽  
New Technique ◽  
Business Organization ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
A New Technique

In this paper, we develop a new technique for solving transportation problems (TP) and develop a computer code by using mathematical programming language AMPL. There are many existing techniques for solving TP problems in use. By these techniques one has to determine initial basic feasible solution at first then improve this solution to determine optimal solution by another method. But this process is very lengthy and time consuming. By our technique we can determine optimal solution directly without determining initial basic feasible solution and optimal solution separately and we hope that this technique will provide an easier way than that of the other methods. We use the idea of decomposition based pricing (DBP) method to develop our technique. To our knowledge, there is no other paper which used DBP to solve TP. We demonstrate our technique by solving real life models developed by collecting data from a business organization of Bangladesh.Dhaka Univ. J. Sci. 64(1): 45-50, 2016 (January)

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 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.

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