The Average Sum Method for the Unbalanced Assignment Problems

Sarvesh Kumar Dubey; Avanish Kumar; Virendra Upadhyay

doi:https://doi.org/10.14445/22315373/IJMTT-V55P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 55 | Number 2 | Year 2018 | Article Id. IJMTT-V55P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P512

The Average Sum Method for the Unbalanced Assignment Problems

Sarvesh Kumar Dubey, Avanish Kumar, Virendra Upadhyay

Citation :

Sarvesh Kumar Dubey, Avanish Kumar, Virendra Upadhyay, "The Average Sum Method for the Unbalanced Assignment Problems," International Journal of Mathematics Trends and Technology (IJMTT), vol. 55, no. 2, pp. 89-100, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V55P512

Abstract

Optimally assigning of jobs to the available resources is the fundamental requirement in the assignment problems to achieve the desired results. Several methods of assignment are described in the literature. In this research paper we have also inspiring from the Hungarian assignment method discovered an assignment method which is presented here in simple steps. Although the results are exactly equal to the results from the Hungarian assignment method but the Hungarian method takes more space, time and steps to solve numerical examples, also its step changes for different type of problems while our proposed method is simple, takes less time and does not alters the steps during the applications in the numerical examples. The presented algorithm is implemented on several sets of numerical examples and found that the obtained results are correct. The results achieved from the method are graphically represented here with a comparison.

Keywords

Unbalanced Assignment Problem, Hungarian Method, Optimization, Average Sum Method, Optimal Costs.

References

[1] W. H. Kuhn, The Hungarian Method for the Assignment Problem, Naval Research Logistics, 1, 7-21, 2005. http://dx.doi.org/10.1002/nav.20053
[2] J. Munkres, Algorithms for the Assignment and Transportation Problems, Journal of the Society of Industrial and Applied Mathematics, 5, 32 – 38, 1957. http://dx.doi.org/10.1137/0105003
[3] H. A. Taha, Operations Research: An Introduction, 8th Edition, Pearson Education, Pvt. Ltd, 2007.
[4] B. S. Goel and S. K. Mittal, Operations Research, 5th Edition, 2405-2416, 1982.
[5] H. Basirzadeh, Ones Assignment Method for Solving Assignment Problems, Applied Mathematical Sciences, Vol. 6, No. 47, pp. 2345-2355, 2012.
[6] S. Singh, G. C. Dubey, and R. Shrivastava, A Comparative Analysis of Assignment Problem, IOSR Journal of Engineering. Vol. 2, Issue 8, pp. 01-15, Aug. 2012.
[7] K. P. Ghadle and Y. M. Muley, Revised Ones