Multi Process Three Dimensional Job Assignment Model

P.Guravaraju; C. Suresh Babu; R. Vijaya Lakshmi; M. Sundara Murthy

doi:https://doi.org/10.14445/22315373/IJMTT-V22P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 22 | Number 1 | Year 2015 | Article Id. IJMTT-V22P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V22P510

Multi Process Three Dimensional Job Assignment Model

P.Guravaraju, C. Suresh Babu, R. Vijaya Lakshmi, M. Sundara Murthy

Abstract

So many researchers introduced variant problems for assignment model. In this Problem there is a set of n jobs, m machines and r periods. This is three dimensional problem. Number of jobs to be completed is n0 . The total number of assigned jobs should be 2 n0 . D(i,j,k) be the cost array of assignment of ith Job on jth machine at kth period. Each job requires two processes among A,B and C Processes and there are given. Any machine can do process A in 1st or 3rd period, process B in 2nd or 4th period and process C in any one of the four periods. For our convenience we consider processes A, B and C .as 1,2 and 3. One machine can do a job process in one period .i.e different jobs processes can be done on a machine in different periods. Each n0 job has to be assigned twice to machines for the two processes, hence the total number of assignment is 2 n0 . The objective of the problem is to assign each n0 job twice to the machines such that the total processing cost is minimum subject to conditions.

Keywords

assignment, jobs ,machines , periods, process and n0

References

[1] Balakrishna.U(2009)-GTSP,GTDSP & ASP Models,Ph.D Thesis,S.V.University, Tirupati
[2] Barr, R.S., Glover, F. & Klingman, D, the alternating basis algorithm for assignment Problem, Math. Prog., 13. 1-13, 1977.
[3] Bertsekas, D.P., A New Algorithm for the Assignment problem, Math. Prog.21,152-171, 1981.
[4] Garfinkel,R.S(1971):”An improved algorithm for bottleneck assignment problem”,Operations Research 18,pp-(1717-1751)
[5] Geetha, S. & Nair, K.P.,A variation of the Assignment problem, Euro.J. Of Ors, 68, 422-426, 1993.
[6] Hung, M.S.& Rom,W.O., Solving the Assignment problem by relaxation. Ops.Res., 18, 969-982, 1980.
[7] Kuhn, H.W, the Hungarian Method for the Assignment Problem, Navl Rec. Log.Qtly.2, 83-97, 1955
[8] Purusotham, S et.al. International Journal of Engineering Science and Technology (IJEST Vol. 3 No. 8, 2011
[9] Ross G.T. and Soland, R.M1975):”A Branch and Bound algorithm for Generalized Assignment Problemmathematical program-ming”, pp:91-103.
[10] Sobhan Babu. K et.al. International Journal on Computer Science and Engineering, (IJCSE), Vol. 02, No. 05, 2010, 1633-1640.
[11] Subramanyam,Y.V.(1979):”Some special cases of assignment problem”, Op search, vol:16(1),pp:45-47.
[12] Sundara Murthy, M - (1979). Combinatorial Programming - A Pattern Recognition Approach. PhD, Thesis REC, Warangal, India.
[13] Suresh Babu C, Purusotham, S. and Sundara Murthy, M (2008), Pattern Recognition based Lexi-Search Approach to the Variant Multi-Dimensional Assignment Problem” in the International Journal of Engineering Science and Technology. Vol. 3(8), 2011.
[14] Vidhyullatha, A Thesis( Pattern Recognition Lexi-Search Exact Algorithms For Variant ASP and Bulk TP models), Department of Mathematics, Sri Venkateswara University, Tirupati, 2011.

Citation :

P.Guravaraju, C. Suresh Babu, R. Vijaya Lakshmi, M. Sundara Murthy, "Multi Process Three Dimensional Job Assignment Model," International Journal of Mathematics Trends and Technology (IJMTT), vol. 22, no. 1, pp. 55-67, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V22P510