scholarly journals An Improved Vogel's Approximation Method for the Transportation Problem

2011 ◽  
Vol 16 (2) ◽  
pp. 370-381 ◽  
Author(s):  
Serdar Korukoğlu ◽  
Serkan Ballı
Keyword(s):  
Approximation Method ◽  
Operations Research ◽  
Opportunity Cost ◽  
Transportation Problem ◽  
Large Scale ◽  
Efficient Solutions ◽  
Important Task ◽  
Computational Experiments ◽  
Optimal Solutions ◽  
Transportation Problems

Determining efficient solutions for large scale transportation problems is an important task in operations research. In this study, Vogel’s Approximation Method (VAM) which is one of well-known transportation methods in the literature was investigated to obtain more efficient initial solutions. A variant of VAM was proposed by using total opportunity cost and regarding alternative allocation costs. Computational experiments were carried out to evaluate VAM and improved version of VAM (IVAM). It was seen that IVAM conspicuously obtains more efficient initial solutions for large scale transportation problems. Performance of IVAM over VAM was discussed in terms of iteration numbers and CPU times required to reach the optimal solutions.

EXPERIMENTAL ANALYSIS OF SOME VARIANTS OF VOGEL'S APPROXIMATION METHOD

2004 ◽  
Vol 21 (04) ◽  
pp. 447-462 ◽  
Author(s):  
M. MATHIRAJAN ◽  
B. MEENAKSHI
Keyword(s):  
Approximation Method ◽  
Opportunity Cost ◽  
Optimal Solution ◽  
Efficient Solutions ◽  
Transportation Problems ◽  
Cpu Time ◽  
Problem Instances ◽  
Time Required ◽  
The Military

This paper presents a variant of Vogel's approximation method (VAM) for transportation problems. The importance of determining efficient solutions for large sized transportation problems is borne out by many practical problems in industries, the military, etc. With this motivation, a few variants of VAM incorporating the total opportunity cost (TOC) concept were investigated to obtain fast and efficient solutions. Computational experiments were carried out to evaluate these variants of VAM. The quality of solutions indicates that the basic version of the VAM coupled with total opportunity cost (called the VAM–TOC) yields a very efficient initial solution. In these experiments, on an average, about 20% of the time the VAM–TOC approach yielded the optimal solution and about 80% of the time it yielded a solution very close to optimal (0.5% loss of optimality). The CPU time required for the problem instances tested was very small (on an average, less than 10 s on a 200 MHz Pentium machine with 64 MB RAM).

scholarly journals A New Approach to Solve Mixed Constraint Transportation Problem Under Fuzzy Environment

2017 ◽  
Vol 16 (4) ◽  
pp. 6895-6902
Author(s):  
Nidhi Joshi ◽  
Surjeet Singh Chauhan (Gonder) ◽  
Raghu Raja
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
New Approach ◽  
Transportation Problems ◽  
Mixed Constraints ◽  
Fuzzy Environment ◽  
Mixed Constraint ◽  
Fuzzy Transportation Problem

The present paper attempts to obtain the optimal solution for the fuzzy transportation problem with mixed constraints. In this paper, authors have proposed a new innovative approach for obtaining the optimal solution of mixed constraint fuzzy transportation problem. The method is illustrated using a numerical example and the logical steps are highlighted using a simple flowchart. As maximum transportation problems in real life have mixed constraints and these problems cannot be truly solved using general methods, so the proposed method can be applied for solving such mixed constraint fuzzy transportation problems to obtain the best optimal solutions.

scholarly journals Modified Dynamically-updated Weighted Opportunity Cost Based Algorithm for Unbalanced Transportation Problem

2021 ◽  
Vol 12 (2) ◽  
pp. 119-131
Author(s):  
ARM Jalal Uddin Jamali ◽  
Ringku Rani Mondal
Keyword(s):  
Opportunity Cost ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Transportation Cost ◽  
Engineering Science ◽  
Weight Factor ◽  
Total Cost ◽  
Transportation Problems ◽  
Control Of Flow ◽  
Effectiveness And Efficiency

Recently, Weighted Opportunity Cost (WOC) based algorithms are developed for solving balanced Transportation Problems (TPs). The exceptionality of the WOC based approaches is to introduce supply and demand as weight factor to cost entries for the control of flow of allocations. But in the unbalanced TP, there exist a pitfall whenever balancing the TP with zero dummy transportation cost as done in existing classical approaches, so that the total cost is unaffected due to dummy transportations. A modified dynamically-updated weighted opportunity cost-based algorithm embedded on Least Cost Method (LCM) is proposed which is suitable for both balanced and unbalanced TPs. Numerical instances have been carried out to demonstrate the effectiveness and efficiency of the proposed method. It is observed that, the proposed modified dynamically-updated weighted opportunity cost-based algorithm sometimes outperforms for the LCM as well as the existing weighted opportunity cost-based algorithm in unbalanced TPs. Journal of Engineering Science 12(2), 2021, 119-131

On Solving Bottleneck Bi-Criteria Fuzzy Transportation Problems

2018 ◽  
Vol 7 (4.10) ◽  
pp. 547
Author(s):  
V. E. Sobana ◽  
D. Anuradha ◽  
. .
Keyword(s):  
Transportation Problem ◽  
Efficient Solutions ◽  
Compromise Solution ◽  
Transportation Problems ◽  
Numerical Example

A fuzzy block–dripping method (FBDM) has been proposed to find the best compromise solution and efficient solutions of the bottleneck bi-criteria transportation problem under uncertainty. The procedure of the proposed method is illustrated by numerical example. 

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 Alternate Solutions Analysis For Transportation Problems

2011 ◽  
Vol 7 (11) ◽  
Author(s):  
Veena Adlakha ◽  
Krzysztof Kowalski
Keyword(s):  
Load Distribution ◽  
Transportation Problem ◽  
Shadow Price ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Price Theory ◽  
Font Size ◽  
Systematic Analysis ◽  
Transportation Problems ◽  
Constraint Structure

<p class="MsoNormal" style="text-align: justify; margin: 0in 0.5in 0pt; mso-pagination: none;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The constraint structure of the transportation problem is so important that the literature is filled with efforts to provide efficient algorithms for solving it.<span style="mso-spacerun: yes;">&nbsp; </span>The intent of this work is to present various rules governing load distribution for <span style="mso-bidi-font-weight: bold;">alternate optimal solutions in transportation problems, a subject that has not attracted much attention in the current literature, with the result that the load assignment for an alternate optimal solution is left mostly at the discretion of the practitioner.<span style="mso-spacerun: yes;">&nbsp; </span>Using the Shadow Price theory we illustrate the structure of alternate solutions in a transportation problem and provide a systematic analysis for allocating loads to obtain an alternate optimal solution.<span style="mso-spacerun: yes;">&nbsp; </span>Numerical examples are presented to explain the proposed </span>process.</span></span></p>

scholarly journals Genetic algorithm for solving transportation problems on networks with one source and multiple sinks

2020 ◽  
Vol 34 ◽  
pp. 02006
Author(s):  
Tatiana Paşa
Keyword(s):  
Genetic Algorithm ◽  
Transportation Problem ◽  
Large Scale ◽  
Cost Functions ◽  
Local Optimum ◽  
Transportation Problems ◽  
Multiple Sinks ◽  
Large Scale Problems ◽  
Optimum Solution

In this paper we propose a genetic algorithm for solving the nonlinear transportation problem on a network with multiple sinks and concave piecewise cost functions. We prove that the complexity of one iteration of the algorithm is O(n2) and the algorithm converges to a local optimum solution. We show that the algorithm can be used to solve large-scale problems and present the implementation and several testing examples of the algorithm using Wolfram Language.

scholarly journals Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems

2021 ◽  
Vol 13 (3) ◽  
pp. 1372
Author(s):  
Abd Elazeem M. Abd Elazeem ◽  
Abd Allah A. Mousa ◽  
Mohammed A. El-Shorbagy ◽  
Sayed K. Elagan ◽  
Yousria Abo-Elnaga
Keyword(s):  
Transportation Problem ◽  
Efficient Solution ◽  
Efficient Solutions ◽  
Nondominated Solutions ◽  
Multi Index ◽  
Transportation Problems ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Nondominated Set ◽  
The Stability

Multi-dimensional transportation problems denoted as multi-index are considered as the extension of classical transportation problems and are appropriate practical modeling for solving real–world problems with multiple supply, multiple demand, as well as different modes of transportation demands or delivering different kinds of commodities. This paper presents a method for detecting the complete nondominated set (efficient solutions) of multi-objective four-index transportation problems. The proposed approach implements weighted sum method to convert multi-objective four-index transportation problem into a single objective four-index transportation problem, that can then be decomposed into a set of two-index transportation sub-problems. For each two-index sub-problem, parametric analysis was investigated to determine the range of the weights values that keep the efficient solution unchanged, which enable the decision maker to detect the set of all nondominated solutions for the original multi-objective multi-index transportation problem, and also to find the stability set of the first kind for each efficient solution. Finally, an illustrative example is presented to illustrate the efficiency and robustness of the proposed approach. The results demonstrate the effectiveness and robustness for the proposed approach to detect the set of all nondominated solutions.

scholarly journals METHODOLOGY RECOMMENDATION FOR ONE‐CRITERION TRANSPORTATION PROBLEMS: CAKMAK METHOD

Transport ◽  
2007 ◽  
Vol 22 (3) ◽  
pp. 221-224 ◽  
Author(s):  
Tanyel Çakmak ◽  
Filiz Ersöz
Keyword(s):  
Approximation Method ◽  
Operations Research ◽  
Feasible Solution ◽  
New Method ◽  
Basic Solution ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Solution Methods ◽  
Optimum Solution

Transportation problems (TP) are one of the most prominent fields of application of the mathematical disciplines to optimization and operations research. In general, there are three starting basic feasible solution methods: Northwest Corner, Least Cost Method, VAM – Vogel's Approximation Method. The three methods differ in the quality of the starting basic solution. In this study, we actually show a new method for starting basic feasible solution to one‐criterion‐transportation problems: Çakmak Method. This method can be used for balanced or unbalanced one-criterion transportation problems, and gives the basic feasible optimum solution accordingly.

scholarly journals Temporal concatenation for Markov decision processes

2021 ◽  
pp. 1-28
Author(s):  
Ruiyang Song ◽  
Kuang Xu
Keyword(s):  
Markov Decision Processes ◽  
Large Scale ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Black Box ◽  
Decision Processes ◽  
Optimal Solutions ◽  
Wide Range ◽  
Markov Decision ◽  
Speed Up

We propose and analyze a temporal concatenation heuristic for solving large-scale finite-horizon Markov decision processes (MDP), which divides the MDP into smaller sub-problems along the time horizon and generates an overall solution by simply concatenating the optimal solutions from these sub-problems. As a “black box” architecture, temporal concatenation works with a wide range of existing MDP algorithms. Our main results characterize the regret of temporal concatenation compared to the optimal solution. We provide upper bounds for general MDP instances, as well as a family of MDP instances in which the upper bounds are shown to be tight. Together, our results demonstrate temporal concatenation's potential of substantial speed-up at the expense of some performance degradation.

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