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 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.

scholarly journals Mathematical models and a constructive heuristic for finding minimum fundamental cycle bases

2005 ◽  
Vol 15 (1) ◽  
pp. 15-24 ◽  
Author(s):  
Leo Liberti ◽  
Edoardo Amaldi ◽  
Francesco Maffioli ◽  
Nelson Maculan
Keyword(s):  
Linear Programming ◽  
Total Cost ◽  
Fundamental Cycle ◽  
Cycle Basis ◽  
Cpu Time ◽  
Constructive Heuristic ◽  
Cycle Bases ◽  
Time Required ◽  
Application Fields

The problem of finding a fundamental cycle basis with minimum total cost in a graph arises in many application fields. In this paper we present some integer linear programming formulations and we compare their performances, in terms of instance size, CPU time required for the solution, and quality of the associated lower bound derived by solving the corresponding continuous relaxations. Since only very small instances can be solved to optimality with these formulations and very large instances occur in a number of applications, we present a new constructive heuristic and compare it with alternative heuristics.

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 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.

Aggregating Functional and Non-Functional Properties to Identify Service Compositions

2011 ◽  
pp. 145-174 ◽  
Author(s):  
Eduardo Blanco ◽  
Yudith Cardinale ◽  
María-Esther Vidal
Keyword(s):  
Experimental Study ◽  
Dynamic Programming ◽  
Quality Of Service ◽  
Functional Properties ◽  
Petri Net ◽  
Optimal Solution ◽  
Initial State ◽  
Programming Technique ◽  
Time Required

This chapter presents an aggregated metric to estimate the quality of service compositions, and two algorithms to select the best compositions based on this metric. Both algorithms follow different strategies to prune the space of possibilities while minimizing the evaluation cost. The first algorithm, DP-BF, combines a best first strategy with a dynamic-programming technique. The second one, PT-SAM, adapts a Petri-net unfolding algorithm and tries to find a desired marking from an initial state. An experimental study was conducted in order to evaluate the behavior of DP-BF and PT-SAM compared to SAM and to the exhaustive solution. The experiments show that the quality of the compositions identified by the presented algorithms is close to the optimal solution produced by the exhaustive algorithm, while the optimization time is close to the time required by SAM to identify a solution.

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 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.

Heat Transfer Enhancement in Separation Process of Ethanol from Ethanol Water Mixture by Using Surfactants

2020 ◽  
pp. 9-14 ◽  
Author(s):  
Acharya Anil Ramchandra ◽  
R. Kadam ◽  
A. T. Pise
Keyword(s):  
Heat Transfer ◽  
Ammonium Chloride ◽  
Sodium Dodecyl ◽  
Water Mixture ◽  
Transfer Enhancement ◽  
Surface Tension Reduction ◽  
Surface Active Agents ◽  
Surface Active ◽  
Time Required

Here the investigations are done while distillation of ethanol-water mixture for separating ethanol from fermentation process. Focus is to study reduction in time required and hence saving in energy for the distillation process of ethanol-water mixture under the influence of surface-active agents (Surfactants). This novelty is from observation of these surfactants to enhance heat transfer rate because of surface tension reduction in aqueous solutions. SDS (Sodium Dodecyl Sulphate), NH4Cl (Ammonium Chloride) and SLBS (Sodium lauryl benzene sulphonate) surfactants in different concentration are experimented. The concentration of these surfactant is varied from 1700 ppm to 2800 ppm. This range is decided by observing critical micelle concentration of used surfactants. Results showed that time is reduced and hence energy consumption is also reduced. Results shown by NH4Cl are found to be more useful as it is ecofriendly surfactant which is not affecting ethanol-water mixture. Use of ammonium chloride as surfactant in distillation is actually useful to reduce energy without hampering the quality of process is the novelty of this work.

scholarly journals Least-looping stepping-stone-based ASM approach for transportation and triangular intuitionistic fuzzy transportation problems

2021 ◽  
Author(s):  
Kedar Nath Das ◽  
Rajeev Das ◽  
Debi Prasanna Acharjya
Keyword(s):  
Optimal Solution ◽  
Transportation Engineering ◽  
Key Factors ◽  
Solution Quality ◽  
Transportation Problems ◽  
Stepping Stone ◽  
Intuitionistic Fuzzy ◽  
Real World Problem ◽  
Statistical Results ◽  
Made In

AbstractTransportation problem (TP) is a popular branch of Linear Programming Problem in the field of Transportation engineering. Over the years, attempts have been made in finding improved approaches to solve the TPs. Recently, in Quddoos et al. (Int J Comput Sci Eng (IJCSE) 4(7): 1271–1274, 2012), an efficient approach, namely ASM, is proposed for solving crisp TPs. However, it is found that ASM fails to provide better optimal solution in some cases. Therefore, a new and efficient ASM appoach is proposed in this paper to enhance the inherent mechanism of the existing ASM method to solve both crisp TPs and Triangular Intuitionistic Fuzzy Transportation Problems (TIFTPs). A least-looping stepping-stone method has been employed as one of the key factors to improve the solution quality, which is an improved version of the existing stepping-stone method (Roy and Hossain in, Operation research Titus Publication, 2015). Unlike stepping stone method, least-looping stepping-stone method only deals with few selected non-basic cells under some prescribed conditions and hence minimizes the computational burden. Therefore, the framework of the proposed method (namely LS-ASM) is a combination of ASM (Quddoos et al. 2012) and least-looping stepping-stone approach. To validate the performance of LS-ASM, a set of six case studies and a real-world problem (those include both crisp TPs and TIFTPs) have been solved. The statistical results obtained by LS-ASM have been well compared with the existing popular modified distribution (MODI) method and the original ASM method, as well. The statistical results confirm the superiority of the LS-ASM over other compared algorithms with a less computationl effort.

scholarly journals Allocating Students to Industry Placements Using Integer Programming and Ant Colony Optimisation

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 219
Author(s):  
Dhananjay Thiruvady ◽  
Kerri Morgan ◽  
Susan Bedingfield ◽  
Asef Nazari
Keyword(s):  
Integer Programming ◽  
Gender Equity ◽  
Programming Model ◽  
Original Data ◽  
Ant Colony ◽  
Ant Colony Optimisation ◽  
Integer Programming Model ◽  
Problem Instances ◽  
Work Integrated Learning ◽  
Time Required

The increasing demand for work-ready students has heightened the need for universities to provide work integrated learning programs to enhance and reinforce students’ learning experiences. Students benefit most when placements meet their academic requirements and graduate aspirations. Businesses and community partners are more engaged when they are allocated students that meet their industry requirements. In this paper, both an integer programming model and an ant colony optimisation heuristic are proposed, with the aim of automating the allocation of students to industry placements. The emphasis is on maximising student engagement and industry partner satisfaction. As part of the objectives, these methods incorporate diversity in industry sectors for students undertaking multiple placements, gender equity across placement providers, and the provision for partners to rank student selections. The experimental analysis is in two parts: (a) we investigate how the integer programming model performs against manual allocations and (b) the scalability of the IP model is examined. The results show that the IP model easily outperforms the previous manual allocations. Additionally, an artificial dataset is generated which has similar properties to the original data but also includes greater numbers of students and placements to test the scalability of the algorithms. The results show that integer programming is the best option for problem instances consisting of less than 3000 students. When the problem becomes larger, significantly increasing the time required for an IP solution, ant colony optimisation provides a useful alternative as it is always able to find good feasible solutions within short time-frames.

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