scholarly journals An Approach for Solving the Fixed Charge Transportation Problems

2021 ◽  
Vol 23 (07) ◽  
pp. 583-590
Author(s):  
Hanan Hussein Farag ◽  
Keyword(s):  
Approximate Solution ◽  
Lower Limit ◽  
Approximation Method ◽  
Transportation Problem ◽  
Optimal Solution ◽  
Fixed Charge ◽  
Transportation Problems ◽  
Numerical Example ◽  
Fixed Charge Transportation Problem ◽  
Better Than

This paper presents modified Vogel’s method that solves the fixed charge transportation problems, the relaxed transportation problem proposed by Balinski in 1961 to find an approximate solution for the fixed charge transportation problem (FCTP). This approximate solution is considered as a lower limit for the optimal solution of FCTP. This paper developed the modified Vogel’s method to find an approximate solution used as a lower limit for the FCTP. This is better than Balinski’s method in 1961. My approach relies on applying Vogel’s approximation method to the relaxed transportation problem. In addition, an illustrative numerical example is used to prove my hypothesis.

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 A review on fuzzy and stochastic extensions of the multi index transportation problem

2017 ◽  
Vol 27 (1) ◽  
pp. 3-29 ◽  
Author(s):  
Sungeeta Singh ◽  
Renu Tuli ◽  
Deepali Sarode
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Review Article ◽  
Fixed Charge ◽  
Fixed Cost ◽  
Multi Index ◽  
Transportation Problems ◽  
Single Criterion ◽  
Fixed Charge Transportation Problem

The classical transportation problem (having source and destination as indices) deals with the objective of minimizing a single criterion, i.e. cost of transporting a commodity. Additional indices such as commodities and modes of transport led to the Multi Index transportation problem. An additional fixed cost, independent of the units transported, led to the Multi Index Fixed Charge transportation problem. Criteria other than cost (such as time, profit etc.) led to the Multi Index Bi-criteria transportation problem. The application of fuzzy and stochastic concept in the above transportation problems would enable researchers to not only introduce real life uncertainties but also obtain solutions of these transportation problems. The review article presents an organized study of the Multi Index transportation problem and its fuzzy and stochastic extensions till today, and aims to help researchers working with complex transportation problems.

scholarly journals Near Optimal Solution for the Step Fixed Charge Transportation Problem

2013 ◽  
Vol 7 (2L) ◽  
pp. 661-669 ◽  
Author(s):  
Khalid M. Altassan ◽  
Mahmoud M. El-Sherbiny ◽  
Bokkasam Sasidhar
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Fixed Charge ◽  
Fixed Charge Transportation Problem

Multi-Objective Fixed-Charge Transportation Problem with Random Rough Variables

2018 ◽  
Vol 26 (06) ◽  
pp. 971-996 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Sudipta Midya ◽  
Vincent F. Yu
Keyword(s):  
Transportation Problem ◽  
Deterministic Model ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Programming ◽  
Fixed Charge ◽  
Optimal Solutions ◽  
Multi Objective ◽  
Proposed Model ◽  
Fixed Charge Transportation Problem

This paper considers a multi-objective fixed-charge transportation problem (MOFCTP) in which the parameters of the objective functions are random rough variables, while the supply and the demand parameters are rough variables. In real-life situations, the parameters of a multi-objective fixed-charge transportation problem may not be defined precisely, because of globalization of the market, uncontrollable factors, etc. As such, the multi-objective fixed-charge transportation problem is proposed under rough and random rough environments. To tackle uncertain (rough and random rough) parameters, the proposed model employs an expected value operator. Furthermore, a procedure is developed for converting the uncertain multi-objective fixed-charge transportation problem into a deterministic form and then solving the deterministic model. Three different methods, namely, the fuzzy programming, global criterion, and ϵ-constrained methods, are used to derive the optimal compromise solutions of the suggested model. To provide the preferable optimal solution of the formulated problem, a comparison is drawn among the optimal solutions that are extracted from different methods. Herein, the ϵ-constrained method derives a set of optimal solutions and generates an exact Paretofront. Finally, in order to show the applicability and feasibility of the proposed model, the paper includes a real-life example of a multi-objective fixed-charge transportation problem. The main contribution of the paper is that it deals with MOFCTP using two types of uncertainties, thus making the decision making process more flexible.

scholarly journals Three dimensional fixed charge bi-criterion indefinite quadratic transportation problem

2004 ◽  
Vol 14 (1) ◽  
pp. 83-97 ◽  
Author(s):  
S.R. Arora ◽  
Archana Khurana
Keyword(s):  
Transportation Problem ◽  
Three Dimensional ◽  
Fixed Charge ◽  
Fixed Cost ◽  
Trade Off ◽  
Numerical Example ◽  
Fixed Charge Transportation Problem ◽  
Indefinite Quadratic

The three-dimensional fixed charge transportation problem is an extension of the classical three-dimensional transportation problem in which a fixed cost is incurred for every origin. In the present paper three-dimensional fixed charge bi-criterion indefinite quadratic transportation problem, giving the same priority to cost as well as time, is studied. An algorithm to find the efficient cost-time trade off pairs in a three dimensional fixed charge bi-criterion indefinite quadratic transportation problem is developed. The algorithm is illustrated with the help of a numerical example.

scholarly journals Solving unbalanced intuitionistic fuzzy transportation problem

10.26524/cm61 ◽  
2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Soundararajan S ◽  
Suresh Kumar M
Keyword(s):  
Approximation Method ◽  
Fuzzy Number ◽  
Transportation Problem ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number ◽  
Fuzzy Transportation Problem ◽  
Number Of Iterations

In this paper, we find the optimal solution for an unbalanced intuitionistic fuzzy transportation problem by using monalisha’s approximation method. The main aim of this method is to avoid large number of iterations. To illustrate this method a numerical example Triangular intuitionistic fuzzy number, unbalanced intuitionistic fuzzy transportation problem, accuracy function.is given.

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