Optimizing a fully rough interval integer solid transportation problems

2021 ◽  
pp. 1-11
Author(s):  
T. AnithaKumari ◽  
B. Venkateswarlu ◽  
A. Akilbasha
Keyword(s):  
Feasible Solution ◽  
Real Life ◽  
Optimal Solution ◽  
Logistic Models ◽  
Zero Point ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Decision Variables ◽  
Rough Interval ◽  
The Given

An innovative method, namely modified slice-sum method using the principle of zero point method is proposed for finding an optimal solution to fully rough interval integer solid transportation problems (FRIISTP). The proposed method yields an optimal solution to the fully rough interval integer solid transportation problem directly. In this method, there is no necessity to find an initial basic feasible solution to FRIISTP and also need not to use the existing MODI and stepping stone methods for testing the optimality to improve the basic feasible solution to the FRIISTP but directly obtain an optimal solution to the given FRIISTP by using the proposed method. The optimal values of decision variables and the objective function of the fully rough interval integer solid transportation problems provided by the proposed method are rough interval integers. The advantages of the proposed method over existing method are discussed in the context of an application example. The modified slice-sum method has been applied to calculate the optimal compromise solutions of FRIISTP, and then it was solved by using TORA software. The proposed method can be served as an appropriate tool for the decision makers when they are handling logistic models of real life situations involving three items with rough interval integer parameters.

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 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 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 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 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

Methods for Solving Fully Fuzzy Transportation Problems Based on Classical Transportation Methods

2013 ◽  
pp. 328-347 ◽  
Author(s):  
Amit Kumar ◽  
Amarpreet Kaur
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Programming Formulation ◽  
Transportation Problems ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Formulation ◽  
Fuzzy Transportation Problem

There are several methods, in literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as trapezoidal fuzzy numbers. The advantages of the proposed methods over existing methods are also discussed. To illustrate the proposed methods a fuzzy transportation problem (FTP) is solved by using the proposed methods and the obtained results are discussed. The proposed methods are easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

Behavioral Study of Drosophila Fruit Fly and Its Modeling for Soft Computing Application

2016 ◽  
pp. 32-84 ◽  
Author(s):  
Tapan Kumar Singh ◽  
Kedar Nath Das
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Fruit Fly ◽  
Linear Constraints ◽  
Behavioral Study ◽  
Search Optimization ◽  
Life Problems ◽  
Decision Variables ◽  
Wide Range ◽  
Real Life Situation

Most of the problems arise in real-life situation are complex natured. The level of the complexity increases due to the presence of highly non-linear constraints and increased number of decision variables. Finding the global solution for such complex problems is a greater challenge to the researchers. Fortunately, most of the time, bio-inspired techniques at least provide some near optimal solution, where the traditional methods become even completely handicapped. In this chapter, the behavioral study of a fly namely ‘Drosophila' has been presented. It is worth noting that, Drosophila uses it optimized behavior, particularly, when searches its food in the nature. Its behavior is modeled in to optimization and software is designed called Drosophila Food Search Optimization (DFO).The performance, DFO has been used to solve a wide range of both unconstrained and constrained benchmark function along with some of the real life problems. It is observed from the numerical results and analysis that DFO outperform the state of the art evolutionary techniques with faster convergence rate.

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