Transportation Model
Mathematical Theory and Modeling
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.4, No.1, 2014
www.iiste.org
A comparative study of initial basic feasible solution methods for transportation problems
Abdul Sattar Soomro1 Gurudeo Anand Tularam2 Ghulam Murtaa Bhayo3 dr_sattarsoomro@yahoo.co.in, a.tularam@griffith.edu.au, gmsindhi@yahoo.com
1
Professor of Mathematics, Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Sindh, Pakistan
2
Senior Lecturer, Mathematics and Statistics, Science Environment Engineering and
Technology [ENV], Griffith University, Brisbane Australia
3
Lecturer, Govt. Degree College, Pano Akil, Sukkur, Sindh, Pakistan
Abstract
In this research three methods have been used to find an initial basic feasible solution for the balanced transportation model. We have used a new method of Minimum Transportation Cost Method (MTCM) to find the initial basic feasible solution for the solved problem by Hakim [2]. Hakim used Proposed Approximation
Method (PAM) to find initial basic feasible solution for balanced transportation model and then compared the results with Vogel’s Approximation Method (VAM) [2]. The results of both methods were noted to be the same but here we have taken the same transportation model and used MTCM to find its initial basic feasible solution and compared the result with PAM and VAM. It is noted that the MTCM process provides not only the minimum transportation cost but also an optimal solution.
Keywords: Transportation problem, Vogel’s Approximation Method (VAM), Maximum
Penalty of largest numbers of each Row
1.
Introduction
The transportation problem is a special linear programming problem which arises in many practical applications in other areas of operation, including, among others, inventory control, employment scheduling, and personnel assignment [1].
In this problem we determine optimal shipping patterns between origins or sources and
destinations. The transportation problem deals with the
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.4, No.1, 2014
www.iiste.org
A comparative study of initial basic feasible solution methods for transportation problems
Abdul Sattar Soomro1 Gurudeo Anand Tularam2 Ghulam Murtaa Bhayo3 dr_sattarsoomro@yahoo.co.in, a.tularam@griffith.edu.au, gmsindhi@yahoo.com
1
Professor of Mathematics, Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Sindh, Pakistan
2
Senior Lecturer, Mathematics and Statistics, Science Environment Engineering and
Technology [ENV], Griffith University, Brisbane Australia
3
Lecturer, Govt. Degree College, Pano Akil, Sukkur, Sindh, Pakistan
Abstract
In this research three methods have been used to find an initial basic feasible solution for the balanced transportation model. We have used a new method of Minimum Transportation Cost Method (MTCM) to find the initial basic feasible solution for the solved problem by Hakim [2]. Hakim used Proposed Approximation
Method (PAM) to find initial basic feasible solution for balanced transportation model and then compared the results with Vogel’s Approximation Method (VAM) [2]. The results of both methods were noted to be the same but here we have taken the same transportation model and used MTCM to find its initial basic feasible solution and compared the result with PAM and VAM. It is noted that the MTCM process provides not only the minimum transportation cost but also an optimal solution.
Keywords: Transportation problem, Vogel’s Approximation Method (VAM), Maximum
Penalty of largest numbers of each Row
1.
Introduction
The transportation problem is a special linear programming problem which arises in many practical applications in other areas of operation, including, among others, inventory control, employment scheduling, and personnel assignment [1].
In this problem we determine optimal shipping patterns between origins or sources and
destinations. The transportation problem deals with the
References: Problem, Annals of Pure and Applied Mathematics, Vol. 1, No. 2, 2012, 203-209. [3] S. K Goyal, Improving VAM for unbalanced transportation problems, Journal of Operational Research Society, 35(12) (1984) 1113-1114. [4] P. K. Gupta and Man Mohan. (1993). Linear Programming and Theory of Games, 7th edition, Sultan Chand & Sons, New Delhi (1988) 285-318. [6] Goyal (1984) improving VAM for the Unbalanced Transportation Problem, Ramakrishnan (1988) discussed some improvement to Goyal’s Modified Vogel’s Approximation method for Unbalanced Transportation Problem. [7] Veena Adlakha, Krzysztof Kowalski (2009), Alternate Solutions Analysis For Transportation problems, Journal of Business & Economics Research – November,Vol 7. [8] Sudhakar VJ, Arunnsankar N, Karpagam T (2012). A new approach for find an Optimal Solution for Trasportation Problems, European Journal of Scientific Research 68 254-257.