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 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.

OPTIMAL FEASIBLE SOLUTIONS TO A ROAD FREIGHT TRANSPORTATION PROBLEM

2020 ◽  
Vol 5 (1) ◽  
pp. 456
Author(s):  
Tolulope Latunde ◽  
Joseph Oluwaseun Richard ◽  
Opeyemi Odunayo Esan ◽  
Damilola Deborah Dare
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Transportation Cost ◽  
North West ◽  
Life Problems ◽  
Basic Feasible Solutions ◽  
Feasible Solutions ◽  
Road Freight Transportation ◽  
The Cost ◽  
Cost Of Transportation

For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are represented in tables and results are compared with the result obtained on Maple 18 software. The study shows various ways in which the initial basic feasible solutions to the problem can be obtained where the best method that saves the highest percentage of transportation cost with for this problem is the NWC. The NWC produces the optimal transportation cost which is 517,040 units.

scholarly journals Stability of Solutions for Parametric Inverse Nonlinear Cost Transportation Problem

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2027
Author(s):  
Abd Allah A. Mousa ◽  
Yousria Abo-Elnaga
Keyword(s):  
Nonlinear Programming ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Solution Stability ◽  
Tuning Parameters ◽  
Input Parameters ◽  
Feasible Alternative ◽  
The Stability ◽  
The Cost

This paper investigates the solution for an inverse of a parametric nonlinear transportation problem, in which, for a certain values of the parameters, the cost of the unit transportation in the basic problem are adapted as little as possible so that the specific feasible alternative become an optimal solution. In addition, a solution stability set of these parameters was investigated to keep the new optimal solution (feasible one) is unchanged. The idea of this study based on using a tuning parameters λ∈Rm in the function of the objective and input parameters υ∈Rl in the set of constraint. The inverse parametric nonlinear cost transportation problem P(λ,υ), where the tuning parameters λ∈Rm in the objective function are tuned (adapted) as less as possible so that the specific feasible solution x∘ has been became the optimal ones for a certain values of υ∈Rl, then, a solution stability set of the parameters was investigated to keep the new optimal solution x∘ unchanged. The proposed method consists of three phases. Firstly, based on the optimality conditions, the parameter λ∈Rm are tuned as less as possible so that the initial feasible solution x∘ has been became new optimal solution. Secondly, using input parameters υ∈Rl resulting problem is reformulated in parametric form P(υ). Finally, based on the stability notions, the availability domain of the input parameters was detected to keep its optimal solution unchanged. Finally, to clarify the effectiveness of the proposed algorithm not only for the inverse transportation problems but also, for the nonlinear programming problems; numerical examples treating the inverse nonlinear programming problem and the inverse transportation problem of minimizing the nonlinear cost functions are presented.

scholarly journals PENYELESAIAN MODEL TRANSPORTASI MENGGUNAKAN METODE ASM

2020 ◽  
Vol 14 (1) ◽  
pp. 40
Author(s):  
Nurul Iftitah ◽  
Pardi Affandi ◽  
Akhmad Yusuf
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Direct Method ◽  
Optimal Solution ◽  
Transportation Model ◽  
Initial Feasible Solution ◽  
The Cost

(demand). the method that could be used for solving the transportation problem is to directly find the optimal solution. The direct method that used in this study id the ASM method for solving the balance transportation problem and revised ASM method for solving the unbalance transportation problem. This study aims to construct a transportation model using those methods and it solution. The method on this study is to identify the transportation model, construct the transportation model matrixes, construct an algorithm table using ASM method and to determine the optimal solution of the transportation problem. The obtained result from this study was the model ASM method could determine the optimum value without using initial feasible solution. On solving the unbalance transportation problem, there is an addition of dummy cell or column step. Then reducing the cost of cell and column and change the dummy cost with the biggest cost of reduced cell or column.

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 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 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 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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