Knowledge-Graded Manpower Planning Model for the Manufacturing. Industry

Transcription

1 Iteratoal Joural of Egeerg Iovato ad Maagemet (0) Kowledge-Graded Mapower Plag Model for the Maufacturg Idustry B. Kareem, Federal Uversty of Techology, Akure, Ngera, S.O. Akade, Kog State Polytechcs, Lokoja Campus, Ngera, Abstract: I developg the model, kowledge levels of workers whch were categorzed as usklled, sem- sklled ad sklled wth ther respectve producto capabltes were frst detfed. A lear programmg (LP) model was formulated based o the aforemetoed kowledge levels wth the cluso of varables such as productvty of workers, product demad, cost of hrg of mapower, trag cost of mapower, ad the umber of avalable workers at dfferet stages of kowledge developmet kowledge tesve operatos. The model was also exteded to the maagemet of kowledge mx of workers dfferet kowledge levels whch was used determg quatty of workers at each level that sustaed expected producto target(s). The movemet of mapower from oe kowledge grade to aother was acheved through trag, ad /or kowledge acqusto. The model was appled to agrcultural equpmet maufacturg compay based Lokoja, Ngera. The outcomes of the ew scheme were compared wth the covetoal approach formerly used the Compay. The results obtaed from the developed scheme showed substatal savgs both cost ad umber of usklled, sem sklled ad sklled mapower the compay. The model formulated s very approprate for meetg mapower eeds of developg ecoomy such as Ngera. Key-ords: Huma Resource Plag; Kowledge Itesve Operato; Maufacturg; Cotrol.. Itroducto Plag for people becomes mportat whe job requremets specfy scarce sklls ad capabltes []. Qualfed ad sklled people have become scarce, ad huma resource plag has become a ecessty for log term survval dustral ecoomy []. Huma resource eeds plag to meet busess objectves ad ga advatage over compettors []. Mapower plag s gettg the rght umber of people (by persoel or le maager) wth the rght sklls, expereces, ad competeces the rght job at the rght tme [4-7]. Kowledge tesve operatos are characterzed by extesve kowledge requred for each worker. Those who complete the trag program, fd themselves valuable to other compaes that ca take advatage of the kowledge acqured by ths group of workers, ad therefore leave for better opportutes [8]. I recet tme huma resource maagers have placed emphass o cotrol of employee atttudes, feelgs ad commtmet [9-]. The stuatos may publc sectors ad prvate orgazatos the coutry are such that o coscous efforts have bee made o the quattatve determato of mapower requremet to ther advatage. The cosequeces of adequate mapower plag clude mbalace recrutmets, promoto ad uecessary sack of employee that mght lead to usatsfactory performace of the system the log ru. It s pertet to meto here that earlest attempt to forecast a classed populato was made by [,8]. But [4, 5] developed a Markova model to predct proportos of Receved: 6, Aug., 0, Accepted:, Oct. 0 Avalable ole 5, Nov. 0 workers each grade of the mapower stock. Authors lke 49

2 B. Kareem ad S.O. Akade: Kowledge graded mapower plag model for the maufacturg dustry [5] had developed a aalytc method whle [6,7] used lear programmg approach. A myrad of huma resource plag problems were addressed lterature, but ot may of them are drectly related to hrg ad trag decsos kowledge based operato wth stochastc turover rate [9-4, 7]. Lttle lterature that dealt wth learg aspect [9, 7, 5-], faled to address the ssue of how persoel ca be deoted by t. After a worker has completed trag at both A, B,, N stages (where N s the maxmum umber of producto stages) the worker s promoted to kowledge level ad respectvely. The umber of workers at tme t at ths level s deoted as as t ad at kowledge level t respectvely. Ths worker assgmet scheme s dcated Fgure. graded based o the levels of kowledge ad trag acqusto. Ths model s dfferet from aforemetoed models by takg to accout trag program, progress ad recrutmet schedule at every worker level.. Method A a t B b t N The methodology adopted cludes model developmet, testg ad valdato wth a case study.. Model Developmet t t N t N t I the curret, hghly ucerta soco- ecoomc clmate, the huma resource plag fucto s emergg as a focal huma resource actvty as t s creasgly becomg a Stage Stage Stage essetal ad very promet fucto. As such, that fucto edorses the crucal role of dealg wth the ecessary chages the volume ad make up of the workforce. There s eed for mapower plag to deal wth chages work force requremet uder stochastc codtos. Therefore, a model for mapower plag uder ucerta codtos was developed ad valdated. The varous procedures volved the model developmets cluded model formulato, model valdato, ad soluto procedure.. Model Formulato The model s a dscrete tme model whch kowledge levels of workers,,, ad producto stages A, B N a producto le s prescrbed. All ew hres always start stage A ad udergo o-the-job trag stage A durg the frst perod. Ths s kowledge level ad the umber of workers at tme t kowledge level s deoted as t. he trag the frst stage s completed for a group of ew hres, they are assged to stage B the ext perod, where they udergo trag ths stage, ths s kowledge level ad the umber of workers at ths level at tme t s Fgure Producto stages ad worker kowledge levels All ew employees go through ths career path to ga tegrated kowledge o the producto at both stages. Sce workers at stage B are expected to check the qualty of work doe at the precedg stage A, ew hres must be traed frst at stage A. Therefore, the ew hres who have completed trag at stage A are mmedately assged to stage B because the workers at stage A should kow the succeedg operatos at stage B to ehace qualty. hle t may be possble to hre a worker at termedate level, ths was ot cluded the model but t wll be cosdered later, because the emphass ow s o skll buldg practce of kowledge workers. Sce ths s a kowledge tesve operato, the mmum amout of trag ecessary for the workers who have some experece smlar settgs other operatos s large eough to warrat a complete trag program. Moreover, the avalablty of such workers may be lmted. Some level workers are assged to trag level ad 50

3 Iteratoal Joural of Egeerg Iovato ad Maagemet (0) level workers o the job. These level workers who are used for trag ew or ewly promoted workers are ot cotrbutg to the producto of the plat. Depedg upo the demad requremet ad productvty of workers kowledge levels ad, the ecessary umbers of workers from kowledge level were assged to stage B (deoted by b t Fgure. The remag umbers of workers from kowledge level, after adjustg for traers at stage B are assged to stage A (deoted by a t Fgure ). Thus, depedg upo the demad requremets ad productvty of workers kowledge levels ad, the umber to be hred level s determed. It s plaed that all workers kowledge level are to be assged to stage B. Ths s doe by desg the skll buldg practce order to keep the workers motvated ad ehace qualty. Let q ad ad workers respectvely. That s, q deote the trag fracto for level q t of level workers are used to tra level workers perod t. Smlarly t q of level workers are used to tra level workers perod t. Hece, the followg equaltes must be satsfed orkers trag costrat for level oe worker a t t q () orkers trag costrat for level two worker b t t q The demad for the product s deoted as () d t whch s a depedet, detcally dstrbuted radom varable depedet of t ad t, =,,, where s the maxmum kowledge level,t s also assume that o sgle worker wll be assged to both stages A ad B o partal assgmet bass. The productvty of workers at kowledge level s deoted as P for =,,.... Sce group s fully traed both the stages, ts productvty wll be hgher tha that of kowledge groups ad (.e P P ad P P. The objectve s to mmze the total worker related costs for whch t s amed at meetg demad by employg the optmal umber of workers at dfferet levels. The assgmet of workers was started by fulfllg the eeds for stage B frst. Frstly, all level workers level prevous perod was assged to stage B. The, based o the demad requremet ad after adjustg for the trag eeds for level workers at stage B, the ecessary umber of level workers was assged to stage B. Therefore, the producto fucto at stage B would be P Next, the assgmet for stage A. Frstly, all remag workers from level was assged to stage A. If there s suffcet umber of workers to meet demad, there s eed to recrut ew workers. hle decdg the umber of ew recruts, we must also keep md the requremet of level workers to tra the ew workers who wll ot be cotrbutg to the producto. Therefore, the producto fucto at stage A becomes t P t q t dt P a The worker balace equato for level workers s t t () (5) a b The o- egatvty codtos are t, t t, t 0, a b Summary of equatos () - (6) are equvalet to the equatos (7) - (0) that do ot clude, t ad a b t Producto fucto demad costrat at stage A Producto demad costrat for level two worker P t dt Producto fucto demad costrat at stage B No egatvty costrats (4) (6) (7) (8) (9) (0) The progresso of workers alog the kowledge levels s show Fgure. The reteto rates (complemet of turover rates) at the kowledge levels are deoted as y t P q t dt b t P P q t P P q t P t dt t P P q t P t dt P q t t, t 0, for, ad ad are defed as the probablty that a worker at kowledge level wll stay the 5

4 B. Kareem ad S.O. Akade: Kowledge graded mapower plag model for the maufacturg dustry plat after a partcular perod. Ths are estmated based o hstorcal data. After perod, a proporto level workers wll o the average leave the system. Let Z t y of to deote remag workers at the ed of the perod, who becomes level workers the ext perod ad move to stage B. After perod, a proporto y of level workers wll o average leave the system ad the t remader (deoted by Z wll become part of level worker) After perod, a proporto y wll o the average leave the system ad the remader (deoted by Z t proporto of wll stay the system). Ad after a perod K a wll o the average leave the system y ad the remader (deoted by Z t wll stay the system). It s ecessary to assume y to atta a steady state codto. The y ' s are estmated based o Let deote a restorato factor for 0. Ths restorato factor dcates the extet to whch the gap betwee the target workforce ad curret workforce the subsequet levels s affectg the decso o the recrutmet level at level the very ext perod [4,5]. A value of 0 dcates that we dsregard the gap betwee the curret ad target workforce the upstream levels whle hrg for level. A value of dcates that we allow the complete gap to effectg hrg decso. Therefore usg the cocepts of restorato factor ad target values troduced [6-9] (whch s also called the proportoal cotrol the cotrol theory lterature), the followg lear cotrol rule s therefore troduced t t t t t t t t (4) Equato (4) s the decso rule. The decso rule mples hstorcal data. that, at the begg of every perod, the requred umber of Z t Z t Z t Z t workers to be hred kowledge level, t, would be calculated usg equato (4). Ths decso wth the turover t t t t rates at all kowledge levels at the ed of that perod, wll determe the work force levels at ext two kowledge levels the begg of ext perod. Uder ormal codto based o the tal assumpto the decso makers the compay y y y y are ot suppose to hre workers drectly to level or ay other level of the kowledge workers as a result of skll buldg practce of kowledge workers. Fgure Flow of workers through kowledge levels A hrg polcy s developed le wth [] whch relatoshp betwee the steady state levels of workers at dfferet kowledge levels was establshed. Frst, the target levels are set, ad for t, t, t ad t respectvely. The followg costrat relatoshp s set betwee the target levels: y () y () The target level for level workers s gve as: y () From equato (4) we ca see that the umber of workers at a kowledge level s adjusted every perod depedg upo a umber of factors, amely the turover rates, the restorato factor, the target worker levels ad curret worker levels. Ths equato takes to cosderato the ucertaty turover rates ad regulates the umber of workers at each kowledge level. The followg worker related cost parameters are used for dervg the objectve fucto. c :age of a worker kowledge level, for =,,.. r : Trag cost of oe worker level, for =, ad. 5

5 Iteratoal Joural of Egeerg Iovato ad Maagemet (0) The focus s o log term work force plag of kowledge worker for whch the above cost are relevat. The overtme cost was ot cluded the model sce t s cosdered to be a short-term correcto. The, the objectve fucto s c h r t c r t c r c t M (5) Subject to the costrats equatos gve prevously as equatos (7)-(0) teamg up wth expereced workers; ad last, solo resposblty. The worker kowledge levels are measured by the type of ut of products that they ca assemble wth respect to tme. A ut s a complete assembly of product e.g. a seed plater s a ut. The ma ssues the staffg decsos are twofold: to determe how may workers to hre at the begg of each perod; ad to develop a approprate trag schedule for hgher productvty ad flexblty. The cycle tme of the plat s 60 mutes, whch meas gve as Productvty of labour as poted out by [5,6] s that a worker eeds to lear 60 mutes worth of work cotet a work stato. A worker takes 5 weeks to complete Productvty of labour P TP TO (6) trag ether of stages A ad B. The trag schedule s such that each worker wll be ready to move from smple buld statos to complex buld statos 5 weeks. A perod TP s Total Producto/day of a skll level, as appled to the formulato wll be legth of 5 weeks. Therefore, Cycle tme s 60 mutes, a perod s 5 weeks ad,, ad TO workers of a skll level,. Soluto Procedure s Total umber of Operators or, The soluto processes for determato of optmum umber of workers s gve as: Total Trag Cost: TC r r r (7) here TC s Total Trag Cost,, s umber of level oe, level two workers hred to level, r s Trag cost of oe worker level.4 Model Valdato Data were,, ad collected from a agrcultural equpmet maufacturg compay based Lokoja, Ngera. The compay performs assembly le operatos for cassava grater, palm ol extractor, seed plater, rce trasplater, fertlzer shft legth s 8hrs. The data for the product demad uts for each thrtee weeks of a quarter of a year was collected. The producto for eght hour shft per day was calculated for each year by dvdg the total producto uts for each year wth total umber of weeks of the year (5 weeks) ad umber of producto days per week (5 ths case), the resultg data s show Table. The wages, hrg cost ad trag cost r c for three kowledge levels per worker per year was collected ad s show Table. Nara N, s the symbol of Ngera Currecy ( USD s equals to N50). The data for umber of workers for each kowledge level per year ad umber of workers that was egaged trag was collected ad the trag fractos was computed by dvdg sprayer, ad rce husker. The assembly operatos are the umber of workers that was egaged trag for each categorzed accordg to ther complexty as Smple buld or Complex buld operatos. A ew worker s ormally assged to the smplest of the operatos amog the smple buld stages, whch s geerally the frst operato. Trag level wth the total umber of worker at respectve level for each year. The resultg data s show Table. orkers states at the compay betwee 004 to 006 whch clude the umber of workers employed, umber of workers that left the s mostly o the job: the form of tal observato; compay ad umber that was promoted was collected ad 5

6 B. Kareem ad S.O. Akade: Kowledge graded mapower plag model for the maufacturg dustry show Table 4. Table Demad level per uts of product at the plat for each 5 weeks ad producto for eght hour shft per day Quarter (wks)/year Demad ( Uts) st d rd th d t Capacty) Eght shft (prod. hour Total (mea) Table ages ad Trag cost for the three kowledge levels kowledge level c N/year/ worker 6,000 60, ,000 r /worker/yr 4,000 4,500 - Table Number of workers ad ther trag fracto for three years (kowledge level) Years (Number of workers) Number of level workers egage Trag Trag fracto q 44% % - 4% 40% - 50% 50% The data for total cotrbuto of each kowledge level worker to reveue geerated by the compay for each moth was collected for each year. The mea was the computed for each level per year, the resultg output s show Table 5. Table 4 orkers Status at the plat from 004 to 006 year Kowledge level Number of workers employed: Number of workers that left: Number promoted: Table 5 Cotrbuto of Each Kowledge Level orker Mllos Nara to Reveue Geerated By the Plat Years 004 Tota l Years 005 Total Years 006 Tota l Kowledg e level Moth Average 5.,6., ,7.4, ,8.6,.5 6. The productvty of labour for each kowledge level uts of product produced per shfts of 8hrs/day was calculated usg equato (7) ad data Tables, ad 4. The productvty for ffty two (5) weeks was the computed by multplyg the productvty per shft of 8hrs/day by umber of producto days (5 ths case) ad umber of producto weeks (5) for each year cosdered. The resultg 54

7 Iteratoal Joural of Egeerg Iovato ad Maagemet (0) computato results are show Table 6. Reteto rates (y ) whch s the probablty that a worker at kowledge level wll stay the compay after a partcular perod as show Fgure. s computed by subtractg the probablty of workers at ay kowledge level leavg the compay from oe (.e. Probablty of stayg = Probablty of leavg). The resultg computato s show Table 7. Table 6 Productvty of the three kowledge level uts of product produced (kowledge level) year P (Productvty of each worker per shft of 8hrs/day) P uts) for 5 weeks ( t t t Z M Subject to t t t 05 t t t t, t 0, t t ad teger Equatos reduce to t.56 t. t 6. t 6 t.5 t t 0. 0 t t, t 0 ad teger, The optmum soluto was determed by usg the brach-ad boud method of teger programmg [40] ad t s represeted Fgure 6. Table 7 Reteto rate of worker from oe kowledge level 7.76, 5.98, 6.86, Z to aother betwee Kowledge level Year y , 6, 7.4, Z , 6, 7, Z Upper boud (optmum) 006, umber of level oe workers hred s, Number of level two workers hred s ad umber of level workers hred = Also from Table, hrg cost h /worker s N6000, trag cost per worker for level oe worker r s N4000 ad Trag cost per worker for level two workers r s N4, 500. Total trag cost s calculated usg equato (7) thus: 7 7, 7.54, 7 Z , 6, 7.4, Z , 6., Z , 6, Z , TC = N6, 500 Therefore, the objectve fucto ad costrats are developed based o equatos ()-(0) as Fgure 6 Determato of the optmum soluto usg Iteger programmg 55

8 B. Kareem ad S.O. Akade: Kowledge graded mapower plag model for the maufacturg dustry cost of N7,775,000. The dustry over-estmated the umber The optmum soluto s therefore t, t 6, t 8 Z Smlar procedure was used to evaluate the system for years 004 ad 006 usg data Tables ad 4, respectvely.. Result ad Dscusso 7, The results of the optmum umber of workers at each level ad the cost mplcato s show Table 8 usg smplex method [40]. The optmal umbers of workers were foud to be 9.07 for level oe worker, 5.98 for level two workers ad 7.67 for level three workers at the total cost of N8, 7, I order to elmate fractoal estmate of mapower, the optmal umbers of mapower through teger programmg approach were 8, 6 ad 7, respectvely, wth attedat total cost of N7,775, 000. Ths outcome from teger programmg showed mprovemet over the use of fractoal based smplex method. The optmum mapower requremet ad cost of mapower for the dustry that was obtaed based o the developed teger programmg based model are summarzed Table 9 for the years 004, 005, ad 006, respectvely. The outcomes geerally showed a mapower cost reducto over the use of smplex approach. Table 8 Mapower requremet based o the model for 004 orkers level Smplex method Iteger programmg Z(cost) N8,7, N7,775,000 If the outcomes from the model Table 9 are compared wth what were obtaable the compay as show Table 0, t ca be deduced that the cost of operatg the mapower was cosderably hgh as compared to the outcomes from the ew scheme. Explctly, the results Tables 9 ad 0 show that 004 the curret worker rato 9:6:7 for level oe, two ad three, respectvely wth labour cost of N, 40,000 s expesve compared wth the model calculated results of 8:6:7 for level oe, two ad three, respectvely wth labour of workers for the levels. Smlar stuato was foud from the outcomes of 005 ad 006 as show the table Therefore, the results showed a msmatch mapower requremet ad utlzato the dustry whch must have cotrbuted to hgh cost of producto. Table 9 Optmum Mapower Requremets ad Cost of Mapower from 004 to 006 Mapower/year Level oe Level two Level three Total 7 Cost (Z) N7,775,000 N6,04,500 N7,775,000 Table 0 Mapower Utlzato ad Cost of Mapower from 004 to 006 Mapower/year Level oe Level two Level three 7 Total 6 Cost(Z) N,40,000 N0,6,500 N9,54, Cocluso The Lear programmg (LP) - model was developed for determg the optmum umber of workers at each kowledge levels for the dustral case study, wth the objectve fucto of mmzg worker related cost ad also meetg demad wth the requred level of relablty. The varous procedures volve the model developmets clude model formulato, model valdato. I the developmet, maagemet of kowledge mx, workers dfferet kowledge levels such as usklled (level oe), sem- sklled (level two) ad sklled levels (level three) was focused. Based o these levels, seres of models were formulated was based o drect recrutmet of mapower 56

9 Iteratoal Joural of Egeerg Iovato ad Maagemet (0) to frst level oly, ad the movemet of mapower from oe kowledge level to aother based o trag ad kowledge acqusto. Producto ad labour data were collected from the agrcultural equpmet maufacturg compay, Lokoja, Ngera based o the parameters of the Market Growth o Kowledge orker Product Productvty Qualty. orkg Paper, Maagemet Departmet. Uversty of Texas at Aust, 997. [9] R. Zeffae ad G. Mayo, Plag for Huma Resources the 990s: Developmet of a Operatoal model ad that data after aalyss were used to test the model. The applcato of the model showed that the optmal mx of Model, Iteratoal Joural of Mapower, Vol. 5, 994, pp No.6, workers at dfferet kowledge levels was qute dfferet [0] J.. alker, Huma Resource Roles for the 90s, from the prevously appled covetoal method the plat. As a result of ths, there s eed for reducto umber of workers that are curretly egaged by the compay to reduce the labour cost. Refereces: [] F.I. Ugwuowo ad S.I. Mcclea, Modelg heterogeety a mapower system: a revew, Appled stochastc models ad data aalyss, Vol. 6, No., 000, pp [] S. Bswas, ad S. K. Adhkar, Modelg ad realzato of a grade structure o the bass of promoto ad recrutmet polcy, Mapower Joural, Vol., No. 4, pp [] V. Subramaya, Optmal promoto rate o mapower model, Iteratoa Joural of maagemet ad systems, Vol., 996, pp [4] S. Chadra, Attaablty of a two characterstcs mapower structure, Oper. Research, Vol 7, No., 990, pp [5] A.F. Forbes, D.J. Bartholomew, The Cotrol of a Grade Structure a Stochastc Evromet Usg Promoto Cotrol, Advace Appled Probablty, Vol., 979, pp [6] A.C. Igboaugo ad K.E. Erobo, A Markova Study of Huma Resource Plag, Vol. No., 989, pp [] R. C. Carpeter, Mapower Plag Makes a Comeback, Persoel Maagemet, Vol. No. 7, 989, pp [] A.J. alker, New Techologes Huma Resource Plag, Huma Resource Plag, Vol. 9 No. 4, 004, pp [] F. Hassma ad S.. Hess, A lear Programmg Approach to Producto ad Employmet Schedulg. Mgmt Tech. Vol., No. 4, 960, pp [4] L. Gog, ad H. Matsuo, Cotrol Polcy for Maufacturg System wth Radom Yeld ad Network. Joural of Optmzato Theory ad Applcato Vol. 95, No., 997, [5] M.A. Guerry, Profle-based push models mapower plag, Appled Stochastc models ad data aalyss, Vol. 4, No., 007, pp. -0. [6] G.B. Datzg Lear Programmg Uder Ucertaty. Mgmt Sc. Vol., pp. 97. [7] R.C. Grold, Mapower Plag wth Certa Requremets. Operato research Vol. 4, No., 976, pp [8] O. Ukwosa: A Markova Model of Mapower Mapower Plag I a Large Ol Compay, Ngera Plag the Cvl Servce, M.Sc. Uversty of Be, Egeerg Joural of Maagemet (NEJM), Vol. 5. No, 004, pp [7] V.G. Jorsse, Plag for Mapower Requremets: 00. [9] C.C. Holt, F. Modgla, J.F. Muth, ad H.A. Smo, Plag Producto, Ivetores, ad orkforce, Eglewood STAFFPLAN - A Aalytcal Model, Iteratoal Joural Clffs, NY of Mapower, Vol.0 No.4, 989. pp. 4. [8] E.G. Aderso, Maagg Software Implemeters the Iformato Servce Idustry: A Example of the Impact of [0] R.J. Ebert, Aggregate Plag wth Learg Curve Productvty, Maagemet Scece, Vol., No., 976,

10 B. Kareem ad S.O. Akade: Kowledge graded mapower plag model for the maufacturg dustry [] A. Chares,.. Cooper, R.J. Nehaus, A. stedry, Statc ad Dyamc Assgmet Models wth Multple Objectves ad some Remarks O Orgazatoal Desg. Maagemet Scece Vol. 5, No. 8, 969, B65- B75. [] A. Chares,.. Cooper, R.J. Nehaus, A Geeralzed Network Model For trag ad recrutg decsos mapower plag, I: Mapower ad Maagemet Scece. The Eglsh Uversty press, Lodo, 970. [] C. Gamo, G.L. Thompso, A Dstrbuted Parameter Cohort Persoel Plag that Uses Cross sectoal Data. Maagemet Scece, Vol. 0, No. 6, 994, [4] V.S.S. Yadavall, K.M. Setlhare, ad S.S. Rajalakshm, A aalyss of a optmal promoto polcy for a mapower system usg a queug approach, Maagemet dyamcs, Vol. 5, No., 006, pp [5] M.V. Murthy, R.V. Srvasa ad R.K. Srvasa, Three mapower systems, Iter. Jour. of Systems Assurace Egeerg ad Maagemet, Vol., No., 00, pp [] O.E. Charles, Academc Staff Performace Measuremet Model. Ngera Joural of Idustral ad Systems Studes. Vol., No.4, 004, pp. -. [4] A. Martel ad A. Ahmed, Tactcal Mapower Plag Operato Research Socety Jourals, Vol., 006, pp [5] E. Deardo, C.S. Tag, Lear Cotrol of a Markov Producto System. Operato research Vol. 40 No., 99, [6] M. Telsag Idustral Egeerg ad Producto Maagemet, S. chad & Compay ltd New Delh pg 8, 00, pp [7] L. Greehalgh. A.T. Lawrece, ad R.I. Sutto, graded mapower plag model, proceedg of APORS, Determats of orkforce Reducto Strateges 000, pp [6] Y. P. Gerchak ad M. S.S. Segupta, O Mapower Plag the Presece of Learg. Egeerg Cost ad Producto Ecoomcs Vol. 0, 990, pp [7] V.M. Murthy, Some flueces of Markova mapower plag models, IJMAS, Vol., No., 996, pp [8] J.R. Dorroh, T.R. Gulledge, N.K. omer, Ivestmet kowledge: A Geeralzato of Learg by Experece Maagemet Scece Vol. 40, No. 8, 994, Declg Orgazatos, Academy of Maagemet Revew. Vol. No., 00, pp [8] J. Alevras, ad A. Frger, Pckg Up the Peces after Dowszg, Trag ad Developmet Joural, Vol. 4 No. 9; 988, pp. 9. [9] M. R. Spegel ad L. J. Stephes, Schaum s outle Of Theory ad Problems of Statstcs rd edto, McGraw Hll New York, 999. [40] H. A. Taha, Operatos Research A Itroducto 7 th Edto, Pretce Hll of Ida, 00. [9] C. Gamo,. Plag Iformato Techology-kowledge orker system. Maagemet Scece, Vol. 4, No. 9, 997, [0] A.O. Maz, Itegratg Huma Resource Plag ad Developmet: The Ufcato of Strategc, Operatoal, ad Huma Resource Plag Systems, Huma Resource Plag, Vol. No., 988, pp [] C.R. Beam, Europea Uemploymet a Survey, Joural of Ecoomc Lterature, 994, pp [] P. T. Rao, P.R.S. Reddy ad A.V.S. Suhas, Optmal mapower recrutmet by stochastc programmg graded 58