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

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

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.