Internatonal Journal of Mathematcs and Statstcs Inventon (IJMSI) E-ISSN: 3 4767 P-ISSN: 3-4759 Volume Issue 8 August. 04 PP-57-6 Manpower Plannng Process wth Two Groups Usng Statstcal Technques Dr. P. Mohanumar, V.Amrthalngam and A.Ramesh 3. Professor of Mathematcs, Aaarupadaveedu Insttute of Techonology, Vnayaa Msson Unversty, Kanchpuram, Tamlnadu, Inda Ph.D Scholar, Vnayaa Msson Unversty, Salem, Tamlnadu, Inda 3 Senor Lecturer n Mathematcs, Dstrct Insttute of Educaton and Tranng, Uthamacholapuram, Salem-636 00, Tamlnadu Inda ABSTRACT: Accordng to Bartholomew and Forbes (979 In any organzaton the requred staff strength s mantaned through new recrutments. In ths paper, we consder the Recrutment model Manpower plannng wth two groups A and B. Group A conssts of manpower other than top management level executves. Group B conssts of top management level executves. The shortages of group A occur n accordance wth Modfed Erlang process and group B has shortage process wth varyng shortage rates. Recrutment s done to fll all the shortages of the two groups and fnd the expected tme to recrut and recrutment tme. Numercal llustratons are presented. Mathematcs Subject Classfcaton: 90B05 KEYWORDS: Manpower plannng, Recrutment, Modfed Erlang, Settng the cloc bac to zero I. INTRODUCTION Employees are the most mportant asset for a busness. They serve to create or promote an organzaton's culture, and they sgnfcantly affect the success of a busness. In challengng economc tmes, the cost of hrng neffcent personnel may prove to be detrmental to the proftablty of an organzaton. An effectve and thorough manpower-recrutng process requres an employer to carefully choose the most talented employees who wll postvely beneft the organzaton or busness. II. NEED FOR THE STUDY A needs analyss ntates the manpower recrutng process. Ths phase entals dentfyng a vacant poston or creatng one to meet new needs that have arsen n the organzaton. ths may be an entry md- or upper-level management poston. The employer then develops a job descrpton descrbng the dutes nvolved wth ths poston. Crtera such as slls and competences, experence, age, and educaton that best serve the poston are also dentfed. Usng ths nformaton, the employer prepares a standard applcaton form to collate nformaton provded by the applcants, n addton to ther own resumes. The vacancy s then advertsed. III. REVIEW OF THE LITERATURE The Manpower Plannng Process (MPP) of an organzaton due to resgnaton, dsmssal and death s called shortage. Ths shortage, due to the manpower loss, should be compensated by recrutment. But recrutment nvolves huge cost and hence cannot be made frequently to match the attrtons. Hence the MPP s allowed to undergo Cumulatve Shortage Process (CSP). The accumulated random amount of shortages due to successve attrtons leads to the breadown of the MPP when the total shortage crosses a random threshold level. The breadown pont or threshold s that pont at whch mmedate recrutment becomes necessary. The shortage of MPP due to manpower loss depends on many factors. Such models have been dscussed by Grnold and Marshall [5], Bartholomew and Forbes [7] and Vajda [6]. Statstcal approach n manpower plannng has been dscussed by Bartholomew []. Marovan models are desgned for shortage and promoton n MPP by Vasslou [4]. Subramanan. V. [9] has made an attempt to provde optmal polcy for recrutment, tranng, promoton and shortages n manpower plannng models. Lesson [8] has gven methods to compute shortages and promoton ntenstes whch produce the proportons correspondng to some desred plannng proposals. Esary et al. [3] have dscussed that any component or devce, when exposed to shocs whch cause damage to the devce, s lely to fal when the total accumulated damage exceeds a level called threshold. Gaver. D.P. [] has dscussed pont process problems n Relablty Stochastc pont processes.s. Mythl and R. Ramanarayanan have done probablstc analyss of tme to recrut and recrutment tme n manpower plannng [3]. They have also analysed the same n MPS wth two groups [4]. 57 P a g e
In ths paper, we consder MPP wth two groups A and B. Group A conssts of manpower other than top management level executves, group B conssts of top management level executves. Group A s exposed to shortage process whch s Modfed Erlang. The shortage process of group B has varyng short age rates. In ths model, we apply a new concept that s slghtly modfed upon the concept ntroduced as Settng the Cloc Bac to Zero by Raja Rao [0] and studed by S. Murthy and R. Ramanarayanan []. Sathyamoorth. R. and Parthasarathy. S. [] has found the expected tme to recrut when threshold dstrbuton has Settng the Cloc Bac to Zero property. The shortage rate changes after an exponental tme from one rate to another. The tme to recrut T s gven by T = mn{t, T } where T and T are the tmes to breadown of groups A and B respectvely. Assumng that the recrutment tme R of a shortage s ndependent of the shortage magntude, we fnd the jont Laplace-Steltjes transform of tme to recrut and recrutment tme. IV. OBJECTIVE OF THIS PAPER. To analyss recrutment model of Recrutment model Manpower plannng wth two groups A and B V. METHODOLOGY In ths paper we used followng methodology. Exponental dstrbuton, Laplance-Steltjes tansformaton and Settng the cloc bac to zero VI. RESULT AND DISCUSSION 6. Assumptons Group A s gven at the most observaton tmes each wth exponental dstrbuton wth parameter before recrutment. On completon of the frst exponental observaton tme, recrutment s done wth probablty, or, the second observaton starts wth probablty, where. The process s repeated upto observatons for. On completon of the th observaton, recrutment s done wth probablty =. If T s the tme to recrut due to group A and X ;X,.. are the shortages caused by manpower loss n group A, then, T X j j T X wth probablty j j for or, wth probablty Group B has shortage process wth varyng shortage rates. At tme 0, the shortage rate of the group s. Let T be the tme at whch breadown of group B occurs necesstatng mmedate recrutment. Recrutment for MPP starts f ether of the groups A or B has a breadown. All the shortages due to manpower loss are compensated by recrutment. When recrutment s done due to breadown of group A, recrutment tme correspondng to the th observaton s R, When the breadown occurs due to group B, recrutment s done for shortages n group B and also for shortages n group A for the number of observatons completed. All the recrutment tmes are ndependent and dentcally and dstrbuted random varables wth dstrbuton functon R(y) such that ydr( y) y. o 6. Analyss Based on the assumptons, recrutment starts at tme T = mn{t,t }. Identfyng the exponental phase tme of the modfed Erlangan, the pdf of tme T s gven by x x x x f ( x) e e ()!! 0 58 P a g e
x ( x) x e r ( y) e r ( y)! ( x) x 3 e r ( y)...! PT x, Rt y H ( x) xy ( x) x ( ) e r ( y) ( )! ( x) x e r ( y) ( )! ( x) h( x) e r! 0 x ( ) ( y) () The frst term corresponds to breadown due to group A and the second terms corresponds to breadown due to group B Usng () and (), we get, x x x x ( ) P T x, Rt y e e e r ( y) x y 0 x x x x e e e r y x x x x ( ) 0!! ( )! ( ) e e e r ( y) (3) (3) can be smplfed by tang Double Laplace transform. T Rt e E e r ( ) r ( ) r ( ) r ( ) r ( ) r ( ) r ( ) r ( ) (4) for 0 and 0, we obtan from (6) r ( ) r ( ). t Ee ( ). (5) 59 P a g e
Rt r ( ) r ( ) r ( ) Ee r ( ) r ( ) r ( ) r ( ) r ( ) r ( ) r ( ) From (5) and (6), by dfferentatng, ET ( ). (7) (6) E( Rt) E( R) (8) 6.3 Numercal Illustraton By gvng dfferent values to the parameters n E(T) and E(Rt) and by varyng λ from to 0, we present the graphs of E(T) and E(Rt). 0.07, 0.05, 0.4, 0.6,, E( R) 3 Table : 3 4 5 6 7 8 9 0 ET 3.479.93.30.003 0.809 0.678 0.583 0.5 0.456 0.4 E(RT).7 3.3 3.45 3.35 3.9 3.5 3. 3.9 3.7 3.6 Table : 0.07, 0.05, 0.6, 0.4,, E( R) 3 3 4 5 6 7 8 9 0 ET.876.566.069 0.80 0.65 0.546 0.469 0.4 0.366 0.330 E(RT).640.500.43.385.350.3.98.78.60.45 60 P a g e
VII. CONCLUSION From tables and, we observe the behavor of E(T) and E(Rt).e., mean tme to recrut and mean Recrutment tme for fxed values of,,,, and E(R). When the parameter λ ncreases, the value of E(T) ncreases and E(Rt) decreases. When α ncreases, both E(T) and E(Rt) decrease. REFERENCES [] D.J. Bartholomew, The Statstcal Approach to Manpower Plannng, Statstcan, 0(97), 3-6. [] D.P. Gaver, Pont process problems n Relablty Stochastc pont processes, (Ed.P.A.W.LEWIS) Wley- nterscence, New Yor (97), 774-800. [3] J.D.Esary, A.W.Marshall and F.Proschan, Shoc models and wear processes, Ann.Probablty, (4) (973), 67-649. [4] P.G.G. Vasslou, A hgher order Marovan model for predcton of wastage n manpower system, Operat. Res. Quart., 7 (976), 59-76. [5] R.C. Grnold and K.J. Marshall, Manpower Plannng models, New Yor (977) [6] Vajda, Mathematcs and Manpower Plannng, John Wley, Chchester, (978) [7] D.J. Bartholomew and A.F. Forbes, Statstcal Technques for Manpower Plannng, john Wley and Sons, (979) [8] G.W. Lesson, Wastage and promoton n desred manpower structures, J.Opl. Res Soc., 33 (98), 433-44. [9] V.Subramanan, Optmum promoton reate n manpower models, Internatonal Journal of Management and Systems, () (996), 79-84. [0] B. Raja Rao, Lfe expectancy for settng the cloc bac to zero property, Mathematcal Bo Scences, (998), 5-7. 6 P a g e