markov analysis details

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Human Resource Planning:Applications and Evaluation of Markov AnalysisJ. Benjamin Forbes John Carroll University

ABSTRACT

This paper briefly reviews human resource fore-casting, specifically the use of Markov Analysisand provides examples of how this technique canbe used to analyze various types of transitionswithin a large organization. Data is presentedon the stability of transition probabilities anda human resource forecast is made and testedagainst actual personnel counts.

INTRODUCTION

Human Resource Planning is a newly emerging fieldwithin the area of Human Resource Management.Certain organizations have been engaged in thistype of work for well over ten years (cf. Wikstrom,1971),while others are just beginning to show in-terest. Many textbooks completely ignore thefield while others devote substantial chapters toit (e.g., Cascio, 1982). Evidence that the fieldis becoming established include the number of booksbeing published in the area (e.g., Bur ack & Mathys,1980; Walker, 19 80) as well as the existence of aHuman Resource Planning Society which holds localand national meetings and publishes its own jour-nal.Human Resource Planning has been defined as themanagement process of analyzing an organization'shuman resource needs under changing conditions anddeveloping the activities necessary to satisfythese need s (Walker, 1980). The first part ofthis definition refers to human resource needsforecasting which can be further broken down intotwo parts. We must determine the expected demandfor various types of personnel and we must esti-mate future human resource supplies. By demandfor personnel we mean the numbers and mix of man-power needed to accomplish organizational goalsand objectives . These needs should be spelled outas part of the budgeting process and should beconsidered when planning organizational changes.Various techniques exist for forecasting person-nel demand. For example, a research and develop-ment organization might expect that its currentrate of growth will continue as in the past. Ifso,it could project its constant rate of growthin number of scientists employed into future yearsusing simple trend analysis (Burack & Mat hys,1980).A different approach involves the determination ofmanpower coeffi cients (ratio's of manpower levelsof business factors) and projecting changes in themanpower coefficient to the target year. This

technique has been used by Standard Oil of New Jersey (now Exx on) to forecast operating manpowerneeds in refinery operations based upon intensitadjusted capacity (Wikstrom, 1971).Other researchers have gone beyond ratios and havused regression analysis in manpower needs fore-casting. A manufacturing company found that fac-tory employment was predicted by the number of engine shipments but that exempt employment dependedon parts sales (Walker, 1980).It should be noted that one cannot blindly replyon the results of a ratio or regression analysissince other factors such as expected changes inproductivity may influence manpower requirements.If conditions are unstable and the future is un-certain or if little historical data is availablethe Delphi method might be considered (Burack &Mathys, 1980).With respect to the analysis of internal supplythere are basically two types of mathematical mo-dels commonly used. These are renewal models andstochastic Markov-type models. The renewal modelare sometimes referred to as pull models sincein these models promotions occur as the result ofhigher level vacancies which in effect pull lowerlevel individuals up through the organization.This process includes a ripple effect, such thaas each higher position is filled a lower openingis created. These models also assume that thenumber of personnel within a particular positioneither remains constant or changes at a constantrate.

This approach is fairly straight-forward in thatmanpower tables may be developed which can modelpersonnel flows (i.e.,promotions, turnover, andoutside hire s) using little more than simple ad-dition and subtraction. Since the desired numberin the position is known, then the number oflosses (promotions, transfers, terminations andretirements) must equal the number of replacement(promotions from below plus outside hires).These analyses are often done manually but comput-er programs have been developed which accept asinput the current distribution of personnel,anti-cipated rates of growth, and annual loss rates;and generate recruiting needs at each level of theorganization (Burack & Mathys, 1980).

A bit more interesting although also more complexare the stochastic or Markov models . These mod-els allow one to forecast flows to an from vari-ous positions based upon the past probabilitiesof such chang es. These probabilities are arrangedin a table known as a transition matrix. Inthis matrix the rows typically represent the po-sitions of Time 1, the columns the positions of


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Time2. Thetime period usedisusuallyoneyearandthepositions mightbecategories suchas job,grade,department,or acombinationofthese (e.g.,joband grade).This dataisgenerally gatheredforseveral yearsin ordertodeterminethestabilityof theproba-bilities. If thevaluesare not significantlydifferent then theymay beaveragedtoobtainanaggregate transition matrix. Thestaffing levels(includingnewhires)at the end of thenext yearmay thenbemultipliedby theprobabilitiesofvarious transitionstoobtainaforecastfor thefollowing year (Bartholomew Forbes,1979).Other matrix manipulationsmay beperformed suchas raisingthetransition matrixto the nthpowerin Qrdertoobtainaforecastfor the nthyear,orobtainingthefundamental matrix which givesthenumberofyearsonewould expecttostayin a par-ticular position (Gillespie, Leininger, Kahalas,1976).A numberof interesting applicationsofthis tech-niquehasbeen carriedout. VroomandMacCrimmon(1968) analyzedthemovementsof allcollege-trained personnelin a large manufacturing organ-ization. They presented dataonturnover, promo-tionsanddemotio.ns,andinterfunctional mobility.Forecasts were madefor afive year period. Alsopresented weretheexpected numberofyearsin po-sitionand in theorganizationaswellas theprobabilityoffirst-level entrants reaching third-level positions within either fiveor tenyears.Similar analysis have been done withinalargeCPAfirm (Gillespie, Leininger Kahalas,1976) andforall thetechnical personnel withinalargedi-visionofEaton Corporation (Hooper Catalanello,1981). Transition matrices have also been usedasan efficientandsystematic methodotestingwhether equal employmentandaffirmative actiongoalsarebeingmet(Ledvinka LaForge, 1978).The applicationsandlimitationsofMarkov Analy-sis have been reviewedbyHenemanandSandver(1977). Inadditiontoforecasting internalper-sonnel suppl ies,asdescribed above, Markov Analy-sismay beusedtoprovidea summary descriptionoftheinternal labor market. Theymayserveasan auditandcontrol device sincethetransitionmatrices reflect hiringandpromotion practicesaswellasturnover rates .The usefulnessandaccuracyofMarkov Analysisde-pendsonsuch decisionsas thechoiceof anappro-priate time intervaland thechoiceofappropriatestates (organizational levelsorunits). Statesmust contain adequate sample sizes while alsomaintaining relative homogeneity with respecttoprobabilitiesofmovement. Ofcourse,themostcritical issueis theaccuracyof theforecasts.Unfortunately,asHenemanandSandver (1977 ) pointout: Surprisinglyfewinvestigationsoffore-casting accuracy have been reportedin theliter-ative(p.5 4 1 ) .The present paper will present data illustratingthe descriptive applicationsofMarkov Analysisaswellaspresentatestof theforecasting accuracyofthetechnique. Finallythepredicted supplyofpersonnel willbecomparedto thedemandas

determined from,management planninginordertoset recruiting goals .

METHODANDANALYSIS

This analysiswasconductedin alarge rapidlygrowing natural resource company basedin the Miwest. Theemployee relations master filesfor tyears 19 78-1980 were mergedand theS.P.S.S.Cross tabulation programwasusedtogeneratetransition matrices describing movements amongdpartments,grades,and jobcode categories . Se-lected transition matrices willbepresentedanddiscussedand anaggregate transition matrixformanagement personnel only willbedevelopedandusedtoforecasttheexpected supplyofmanagemepersonnelforyear-end1981. This forecast willthenbecomparedto anactual management manpowecount.Organization-wide Transitions

The first descriptive transition matrix showsmovement amongthevariousjobclasses withinthorganization(seeTable 1 ) . This table allowstmanpower plannertomonitor movement among variojob codes, between non-exempt jobs,betweennon-managementandmanagement jobs,andamong threelevels withinthemanagement positions. Thetrasition ratesfor allcategoriesfor theentirecompany were foundto behighly consistent espe-cially during1979 and 1980. Therefore, thesewere averagedasshowninTable1. Only percentages greater thanonewere included. Itshouldnoted thatastrict hierarchyofclasses doesnoexist here since groups2 and 3 andgroups4 and5 include similar grade levels.

TABLE 1Job Class Transitions

1

2

3

4

5

7

8

Hires

TO1

88

28

2

77

2

32

3

75

4

1979 19804 5

4

73

1

2

5

3

4

84

1

17

6

1

4

82

1

3

7

2

13

83

8

3

8

11

86

2

Exit9

16

15

1

9

4

4

5

Figures are average percentages moving from one stateto another.CATEGORY DEFINITIONS:1. Hourly Maintenance^ Laborers* Operatives)2 Clerical and Service3. Non-exempt Technical4 Exempt Technical/Professional5. Supervisory/Staff/Sales6. Management/Special is ts-I.ower Level7 Management/Specialists-Middle Level8. Management/Specialists-Upper Level


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This table givesanoverviewofmobility patternswithintheentire organization. We can seemove-ment fromthehourlyandclerical jobs into super-visory/staff positionsandfromthenon-exempttechnical into clerical, exempt technical,andsupervisory/staff jobs. Amongtheexempt posi-tions, movement intothelower managem ent levelsoccursat ahigher ratefortechnical/professionalperso nnel (107.) thanforsupervisory/staff person-nel (4 ). Thereis,however, movementat therateoftwopercentperyear from eachofthese groupsintothemiddle management levels. Thereis ap-preciable upward mobility withinthemanagementlevels (11-13 )and inrecent years therehasbeensome downward movement fromtheupper managementlevel. Final ly, turnover ratesand thedistribu-tionof newhiresmay bemonitored from this table .Similar analysesmay bedoneon thedepartmentallevelandmobility rates compared.Management Level TransitionsFurther analysis concentratesonmovement intoandwithinthemanagement levels. Transitions wereexaminedforconsistency overthe1978-1980 timeperiod. When reasonably consistent,thepercent-ages were averaged.Table2shows that whenallexempt personnelareconsidered therearereasonably stable tran sitionprobabilities (generallynomore than2percentvariation). Theexceptiontothiswas thefactthatalarge numberofreductionsingrade fromthe upper management group occurredin1979, whichcaused these figurestodeviatebymore thantwopercent from1978 and 1980. Since this seemedtobetheatypical pattern,itsinfluencewasdisre-garded.

TABLE3

DepartmentAAggregate Grade Transition Matrix

(1973- 1980)

TO

FROM

Non-Exempt(11-1187-1392)Lower(N-477-494)Middle(N-29-47)Upper(N-21-24)

Lower

1.5(1.2-1.5)

83(84-88)

0(0 )0(0 )

Middle

-

2(1-2)91

(36-97)2

(0-5)

Upper

-

0(0 )2

(0-3)92

(83-100)

Exit

-

11(9-13)

5(0-10)

1(0-4)

Transfer

-

2(2 )2

(0-3)3

(0-10

TABLE4

DepartmentBAggregate Grade Transition Matrix

(1973- 1930)

TO

FROM

Non-Exempt(N>1243-1400)Lower(N-424-A89)Middle(N-25-32)Upper(H-17-23)

Lower

2(2 )94

(94-95)1

(0-3)0(0 )

Middle

-

I.4-2)

88(84-91)

0(0 )

Upper

-

0(0 )5

(3-8)92

(87-95)

Exit

-

3(2-3)

1(0-3)

0(0 )

Transfer

-

2(1-2)

5(3-8)

8(5-13

Figuresareaverage percen tages moving fromonestatetoanother.NumbersInparentheses Indicate rangeof percentages averaged.

TABLE2Exempt Personnel

Aggregate Grade Transition Mstrlx(1978- 1980)

FROMNon-Exempt(N-6045-6313)L.owerManagement( N - 2 9 4 1 - 4 0 0 2 )MiddleManagement(N-306-561)UpperManagement*(N-308-416)

LowerManagement

3(2-4)89

(87.7-89.4)

2.9-3.5)

1.3-1.0)

TOMiddleManagement

3(2.2-3.1)

33(81.7-83.3)

4(3.2-4.1)

UpperManagement

.1

.1)

11(10.2-12.7)

90(90.1-90.3)

Exit

3(6.9-8.0)

4(3.0-5.2)

3(4.3-4.6)

Figuresareaverage percenta ges movi ng fromonestatetoanother.NvunbersInparenthese Indicate rangeofpercentagesaveraged.

This line basedon 1978 and 1930data onlydue tonumerousdemotionsIn 1979.

Similar tables were generatedforeach majorde-partment withinthefirm. These couldbeusedtomonitorandcompare mobility patterns withindif-ferent areasof thecompany. Forexample. Table3and Table4presentthetransitions withintwo

similarly sized departments. Inthese tableswehave distinguished between exits (fromthe com-pany)andtransfers toother areasof the com-pany). Some differencescan benoted betweende-partments. Turnover (exits)ishigherinDepart-mentA,especiallyin thelower level ma nagementlevels. Thismay berelatedto thefact thattherearegreater promotion rates within Depart-mentB andalso higher ratesoftransfertootheareas. Itshould alsobenoted thatinbothde-partments transfer rates increase with managementlevel. Apparen tly these departmentsarebeingtapped (althoughatdifferent rates )toprovidemanagement personnelforother area s.Management Personnel Supply ForecastComparisonofTable2with Tables3 and 4indi-cates that althoughthetransition matricesarehighly consistenton acompany-wide basis , deparmental transition probabilities vary considerablThisis afunctionof thereduced sample sizeandthe growthandvolatilityof thecompany. There-foreit wasfelt thataforecast basedonaggre-gate transition probabilitiesfor theentirecom-pany wouldbefairly accuratebut thedepartmentforecasts wouldnot bereliable.Therefore,aforecastfor 1981 for allexemptpersonnelwasprepared. SeeTable 5 ) . Theforecawas calculatedbymultiplyingthenumberineach


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categoryat the end of 1980 by theprobability(orthe propor tion)ofthat category expectedto be ineachof thethree categoriesby the end of 1981.The numberineach category w ere then suiranedtodeterminetheinternal supply forecastfor 1981.This forecast includes only those from withinthecompany.The accuracyof thecompany-wide forecastwascheckedbyobtainingacountof thenumberof em-ployeesin themiddleandupper management levelswho werenot newhires. AsseeninTable5,thesefiguresarehigher thantheforecastsbyonly4.5and3percent.Finallya forecastfor 1982 wascomputedinorderto illustratehow thetechnique couldbeusedtodetermine recruiting needs. Thiswasdonefor allexempt personnel. Theestimated yearendcountsfor1981fromthecompany's Manpo wer Planni ngPro-gram were usedas thebase. These were multipliedbythetransition probabilitiesandsummedto ob-tainthe 1982internal supply forecasts. The sup-ply forecasts were comparedto the 1982demandforecasts fromtheManpower Planning Programandthe differences then were comparedto the 1982 re-cruiting plans .

TABLE3Hanpower Forecasc- 1981

TRAKSITION RATESAHDCOUNTS

CATECOK?Non-Exempt

LowerManagementMiddleManagementDpperManagement

Tear-EndCount19SD6292

4322

701

440

Lover.03)18 9.89)3847.02)

14.01)

4

Middle

.03)13 0.83)58 2.04)

18

Dpper

.001)4

.11)77.90)39 6

Internal Supply Forecastfor Year-End1981:

Actual Year-End1981notnewh lreo ) :

Difference:

4054 730

34+4.51)

15+31)

Table6indicates that theremay be noneedforadditional recruitingon acompany-wise basisforthe upper management group. In theother catego-riesthesupply-demand differencesand the re-cruiting goalsarevery close. Further analysisrevealed, howeve r, that these company-wid e figuremaybemisleading. Forexample, although supplyand demandforupper management personnel wereinbalancefor theentire company there were short-agesandsurpluses within specific areas. Thesewere relatedto theratesofgrowthofthesede-partments. Furthermore, surplus managersin onearea werenotnecessarily transferabletootherareas. Therefore, therewas aneedforrecruit-mentofupper level managers.

SUMMARYANDCONCLUSIONS

This paperhasshown that Markov Ana lysiscan bevery usefulas amethodfordescribingand ana-lyzing personnel movement into, withi n,and out oa firm. It can beusedtomonitorandauditper-sonnel practicesbyproviding usefu l summariesofmanpower transitions. Andevenin arapidlyex-panding organizationit canprovide ac curate forecastsof theinternal supplyofpersonnel. Theseinternal suppliesmaythenbecomparedtodemandforecastsandrecruiting needs identified.Problems withthetechnique includethelackofstabilityoftransition probabilities withincer-tain depa rtments. AsCascio (1982)haspointedout: Acritical assumption. . . isthat transition probabilitiesarestable over time(p. 8 4 ) .However, blind relianceonmathematical modelsinplanningisunwarrentedas iscomplete faithinpast data. Evenif thepast transitionsareinconsistent,themodelmay beusedtosimulatethechangesininternal supplies under va rious hypo-thetical conditions(cf.Bartholomew&Forbes,1979). Aslongasmanagementandhuman resourceplannersareawareof thelimitationsof thetechniquesit canproveto be avery usefu l partof ahuman resourse planning effort.

TABLE6Manpower Forecaat- 1982

TRANSITION RATESANDCOUNTS

CATEGORYNon-Exempt

LowerManagementMiddleManagementUpperManagement

Y

Internal Supply Forecafor Year-End1982:

Manpower Demand Forecafor Year-End1982:

Difference:1982 Recruiting Flan:

lar-EndCount19817361

5184

988

552

atlat

Lower.03)22 0.89)4614.02)20.01)

6

4862

5669809)861

Middle

-.03)156.83)82 0.04)

22

9981112114)117

-.001)

5.11)10 9.90)49 7

611603

831

REFERENCES

Bartholomew,D. J., and A. F.Forbes, StatisticalTechniquesforManpower Planning. NewYork:Wiley,1979.Burack,E. H. and N. J.Mathys, Human ResourcePlanning APragmatic ApproachToManpowerStaffingAndDevelopment. Lake Forest,111.:Brace-Park Press,1980.Casio,W. F.,Applied PsychologyinPersonnelManagement(2nd.ed .) . Reston,VA.: RestonPub-lishing,1982.Gillespie,J. F., W. E.Leininger,and H.Kahalas"A Human Resource PlanningandValuation Model, "AcademyofManagement Journal,1976, 79,650-656.


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Heneman , H. G., III ., and M. G. Sandver, MarkovAnalysis in Human Resource Administra tion: Appli-cations And Limit ation s, Academy of ManagementReview, October, 1977, 535-542.Hooper, J. A. and R. F. Catalan ello, Markov Anal -ysis Applied to Forecasting Technical Personnel,Human Reso urce Plann ing, 1981, 4 ,41-54.Ledvinka, J. and R. L. LaForge, A Staffing ModelFor Affirmativ e Action Planning , Human ResourcePlanning, 1978, 1, 135-150.Vroom, V. H. and K. R. MacCrimmo n, Towards aStochastic Model of Management Career s, Adminis-trative Science Quarterly, 1968,3_ 26-46.Walker, J. W., Human Resource Planning. New York:McGraw-Hill, 1980.Wikstrom, W. S., Manpower Planning: Evolving Sys-tems. New York: The Conference Board, 1971.


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