Markov Analysis Details 471r2m

Human Resource Planning: Applications and Evaluation of Markov Analysis J. Benjamin Forbes, John Carroll University

ABSTRACT

technique has been used by Standard Oil of New Jersey (now Exxon) to forecast operating manpower needs in refinery operations based upon "intensity adjusted capacity" (Wikstrom, 1971).

This paper briefly reviews human resource forecasting, specifically the use of Markov Analysis and provides examples of how this technique can be used to analyze various types of transitions within a large organization. Data is presented on the stability of transition probabilities and a human resource forecast is made and tested against actual personnel counts.

Other researchers have gone beyond ratios and have used regression analysis in manpower needs forecasting. A manufacturing company found that factory employment was predicted by the number of engine shipments but that exempt employment depended on parts sales (Walker, 1980). It should be noted that one cannot blindly reply on the results of a ratio or regression analysis since other factors such as expected changes in productivity may influence manpower requirements. If conditions are unstable and the future is uncertain or if little historical data is available, the Delphi method might be considered (Burack & Mathys, 1980).

INTRODUCTION

Human Resource Planning is a newly emerging field within the area of Human Resource Management. Certain organizations have been engaged in this type of work for well over ten years (cf. Wikstrom, 1971), while others are just beginning to show interest. Many textbooks completely ignore the field while others devote substantial chapters to it (e.g., Cascio, 1982). Evidence that the field is becoming established include the number of books being published in the area (e.g., Burack& Mathys, 1980; Walker, 1980) as well as the existence of a Human Resource Planning Society which holds local and national meetings and publishes its own journal.

With respect to the analysis of internal supply there are basically two types of mathematical models commonly used. These are renewal models and stochastic Markov-type models. The renewal models are sometimes referred to as "pull" models since in these models promotions occur as the result of higher level vacancies which in effect pull lower level individuals up through the organization. This process includes a "ripple" effect, such that as each higher position is filled a lower opening is created. These models also assume that the number of personnel within a particular position either remains constant or changes at a constant rate.

Human Resource Planning has been defined as the management process of "analyzing an organization's human resource needs under changing conditions and developing the activities necessary to satisfy these needs" (Walker, 1980). The first part of this definition refers to human resource needs forecasting which can be further broken down into two parts. We must determine the expected demand for various types of personnel and we must estimate future human resource supplies. By demand for personnel we mean the numbers and mix of manpower needed to accomplish organizational goals and objectives. These needs should be spelled out as part of the budgeting process and should be considered when planning organizational changes.

This approach is fairly straight-forward in that manpower tables may be developed which can model personnel flows (i.e., promotions, turnover, and outside hires) using little more than simple addition and subtraction. Since the desired number in the position is known, then the number of losses (promotions, transfers, terminations and retirements) must equal the number of replacements (promotions from below plus outside hires). These analyses are often done manually but computer programs have been developed which accept as input the current distribution of personnel, anticipated rates of growth, and annual loss rates; and generate recruiting needs at each level of the organization (Burack & Mathys, 1980).

Various techniques exist for forecasting personnel demand. For example, a research and development organization might expect that its current rate of growth will continue as in the past. If so, it could project its constant rate of growth in number of scientists employed into future years using simple trend analysis (Burack & Mathys, 1980).

A bit more interesting although also more complex are the stochastic or Markov models. These models allow one to forecast flows to an from various positions based upon the past probabilities of such changes. These probabilities are arranged in a table known as a "transition matrix." In this matrix the rows typically represent the positions of Time 1, the columns the positions of

A different approach involves the determination of "manpower coefficients" (ratio's of manpower levels of business factors) and projecting changes in the manpower coefficient to the target year. This

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Time 2. The time period used is usually one year and the positions might be categories such as job, grade, department, or a combination of these (e.g., job and grade).

determined from, management planning in order to set recruiting goals.

METHOD AND ANALYSIS This data is generally gathered for several years in order to determine the stability of the probabilities. If the values are not significantly different then they may be averaged to obtain an aggregate transition matrix. The staffing levels (including new hires) at the end of the next year may then be multiplied by the probabilities of various transitions to obtain a forecast for the following year (Bartholomew & Forbes, 1979).

This analysis was conducted in a large rapidly growing natural resource company based in the Midwest. The employee relations master files for the years 1978-1980 were merged and the S.P.S.S. Cross tabulation program was used to generate transition matrices describing movements among departments, grades, and job code categories. Selected transition matrices will be presented and discussed and an aggregate transition matrix for management personnel only will be developed and used to forecast the expected supply of management personnel for year-end 1981. This forecast will then be compared to an actual management manpower count.

Other matrix manipulations may be performed such as raising the transition matrix to the nth power in Qrder to obtain a forecast for the nth year, or obtaining the fundamental matrix which gives the number of years one would expect to stay in a particular position (Gillespie, Leininger, & Kahalas, 1976).

Organization-wide Transitions A number of interesting applications of this technique has been carried out. Vroom and MacCrimmon (1968) analyzed the movements of all collegetrained personnel in a large manufacturing organization. They presented data on turnover, promotions and demotio.ns, and interfunctional mobility. Forecasts were made for a five year period. Also presented were the expected number of years in position and in the organization as well as the probability of first-level entrants reaching thirdlevel positions within either five or ten years. Similar analysis have been done within a large A firm (Gillespie, Leininger & Kahalas, 1976) and for all the technical personnel within a large division of Eaton Corporation (Hooper & Catalanello, 1981). Transition matrices have also been used as an efficient and systematic method o£ testing whether equal employment and affirmative action goals are being met (Ledvinka & LaForge, 1978).

The first descriptive transition matrix shows movement among the various job classes within the organization (see Table 1 ) . This table allows the manpower planner to monitor movement among various job codes, between non-exempt jobs, between nonmanagement and management jobs, and among three levels within the management positions. The transition rates for all categories for the entire company were found to be highly consistent especially during 1979 and 1980. Therefore, these were averaged as shown in Table 1. Only percentages greater than one were included. It should be noted that a strict hierarchy of classes does not exist here since groups 2 and 3 and groups 4 and 5 include similar grade levels. TABLE 1 Job Class Transitions (1979 & 1980

TO

2

1

The applications and limitations of Markov Analysis have been reviewed by Heneman and Sandver (1977). In addition to forecasting internal personnel supplies, as described above, Markov Analysis may be used to provide a summary description of the internal labor market. They may serve as an audit and control device since the transition matrices reflect hiring and promotion practices as well as turnover rates.

1

The usefulness and accuracy of Markov Analysis depends on such decisions as the choice of an appropriate time interval and the choice of appropriate states (organizational levels or units). States must contain adequate sample sizes while also maintaining relative homogeneity with respect to probabilities of movement. Of course, the most critical issue is the accuracy of the forecasts. Unfortunately, as Heneman and Sandver (1977) point out: "Surprisingly few investigations of forecasting accuracy have been reported in the literative (p. 541)."

3

4

88

5

6

7

8

Exit

2

9

5

16

4

3

15

4

73

4

10

•2

10

5

I

84

4

2

9

1

82

13

4

1

83

11

4

8

86

5

3

2

2

77

3

2

75

i 7 8

Hires

28

32

4

10

17

3

Figures are average percentages moving from one state to another. CATEGORY DEFINITIONS: 1. 2. 3. 4. 5. 6. 7. 8.

The present paper will present data illustrating the descriptive applications of Markov Analysis as well as present a test of the forecasting accuracy of the technique. Finally the predicted supply of personnel will be compared to the demand as

288

Hourly (Maintenance^ Laborers* Operatives) Clerical and Service Non-exempt Technical Exempt Technical/Professional Supervisory/Staff/Sales Management/Special is ts-I.ower Level Management/Specialists-Middle Level Management/Specialists-Upper Level

This table gives an overview of mobility patterns within the entire organization. We can see movement from the hourly and clerical jobs into supervisory/staff positions and from the non-exempt technical into clerical, exempt technical, and supervisory/staff jobs. Among the exempt positions, movement into the lower management levels occurs at a higher rate for technical/professional personnel (107.) than for supervisory/staff personnel (4%). There is, however, movement at the rate of two percent per year from each of these groups into the middle management levels. There is appreciable upward mobility within the management levels (11-13%) and in recent years there has been some downward movement from the upper management level. Finally, turnover rates and the distribution of new hires may be monitored from this table. Similar analyses may be done on the departmental level and mobility rates compared.

TABLE 3 Department A Aggregate Grade Transition Matrix (1973 - 1980) TO

FROM Non-Exempt (11-1187-1392)

Lower

Middle

Upper

Exit

Transfer

1.5 (1.2-1.5)

-

-

-

-

83 (84-88)

2 (1-2)

0 (0)

11 (9-13)

2 (2)

Middle (N-29-47)

0 (0)

91 (36-97)

2 (0-3)

5 (0-10)

2 (0-3)

Upper (N-21-24)

0 (0)

2 (0-5)

Lower (N-477-494)

92 (83-100)

1 (0-4)

3 (0-10)

TABLE 4

Management Level Transitions

Department B Aggregate Grade Transition Matrix

Further analysis concentrates on movement into and within the management levels. Transitions were examined for consistency over the 1978-1980 time period. When reasonably consistent, the percentages were averaged.

(1973 - 1930) TO

FROM Non-Exempt (N>1243-1400)

Table 2 shows that when all exempt personnel are considered there are reasonably stable transition probabilities (generally no more than 2 percent variation). The exception to this was the fact that a large number of reductions in grade from the upper management group occurred in 1979, which caused these figures to deviate by more than two percent from 1978 and 1980. Since this seemed to be the atypical pattern, its influence was disregarded.

TO

Non-Exempt (N-6045-6313) L.ower Management

3 (2-4) 89 (87.7-89.4)

Exit

' 3 (2.2-3.1)

.1 (.1)

3 (6.9-8.0)

(N-2941-4002)

Middle Management (N-306-561) Upper Management * (N-308-416)

2 (.9-3.5)

33 (81.7-83.3)

11 (10.2-12.7)

4 (3.0-5.2)

1 (.3-1.0)

4 (3.2-4.1)

90 (90.1-90.3)

3 (4.3-4.6)

Transfer

-

-

-

-

I (.4-2)

0 (0)

3 (2-3)

2 (1-2)

Middle (N-25-32)

1 (0-3)

88 (84-91)

5 (3-8)

1 (0-3)

5 (3-8)

Upper (H-17-23)

0 (0)

0 (0)

92 (87-95)

0 (0)

8 (5-13)

similarly sized departments. In these tables we have distinguished between exits (from the company) and transfers (to other areas of the company). Some differences can be noted between departments. Turnover (exits) is higher in Department A, especially in the lower level management levels. This may be related to the fact that there are greater promotion rates within Department B and also higher rates of transfer to other areas. It should also be noted that in both departments transfer rates increase with management level. Apparently these departments are being tapped (although at different rates) to provide management personnel for other areas.

(1978 - 1980)

Upper Management

Exit

Numbers In parentheses Indicate range of percentages averaged.

Aggregate Grade Transition Mstrlx

Middle Management

Upper

Figures are average percentages moving from one state to another.

TABLE 2

FROM

2 (2)

Middle

94 (94-95)

Lower (N-424-A89)

Exempt Personnel

Lower Management

Lower

Management Personnel Supply Forecast Figures are average percentages moving from one state to another.

Comparison of Table 2 with Tables 3 and 4 indicates that although the transition matrices are highly consistent on a company-wide basis, departmental transition probabilities vary considerably. This is a function of the reduced sample size and the growth and volatility of the company. Therefore it was felt that a forecast based on aggregate transition probabilities for the entire company would be fairly accurate but the department forecasts would not be reliable.

Nvunbers In parenthese Indicate range of percentages averaged. •This line based on 1978 and 1930 data only due to numerous demotions In 1979.

Similar tables were partment within the monitor and compare ferent areas of the and Table 4 present

generated for each major defirm. These could be used to mobility patterns within difcompany. For example. Table 3 the transitions within two

Therefore, a forecast for 1981 for all exempt personnel was prepared. (See Table 5 ) . The forecast was calculated by multiplying the number in each

289

category at the end of 1980 by the probability (or the proportion) of that category expected to be in each of the three categories by the end of 1981. The number in each category were then suiraned to determine the internal supply forecast for 1981. This forecast includes only those from within the company. The accuracy of the company-wide forecast was checked by obtaining a count of the number of employees in the middle and upper management levels who were not new hires. As seen in Table 5, these figures are higher than the forecasts by only 4.5 and 3 percent. Finally a forecast for 1982 was computed in order to illustrate how the technique could be used to determine recruiting needs. This was done for all exempt personnel. The estimated year end counts for 1981 from the company's Manpower Planning Program were used as the base. These were multiplied by the transition probabilities and summed to obtain the 1982 internal supply forecasts. The supply forecasts were compared to the 1982 demand forecasts from the Manpower Planning Program and the differences then were compared to the 1982 recruiting plans. TABLE 3 Hanpower Forecasc - 1981

Tear-End Count 19SD

CATECOK?

SUMMARY AND CONCLUSIONS

This paper has shown that Markov Analysis can be very useful as a method for describing and analyzing personnel movement into, within, and out of a firm. It can be used to monitor and audit personnel practices by providing useful summaries of manpower transitions. And even in a rapidly expanding organization it can provide accurate forecasts of the internal supply of personnel. These internal supplies may then be compared to demand forecasts and recruiting needs identified.

TRAKSITION RATES AHD COUNTS

Lover

Middle

Dpper

Non-Exempt

6292

(.03) 189

Lower Management

4322

(.89) 3847

(.03) 130

(.001) 4

Middle Management

701

(.02) 14

(.83) 582

(.11) 77

Dpper Management

440

(.01) 4

(.04) 18

(.90) 396

Internal Supply Forecast for Year-End 1981:

Table 6 indicates that there may be no need for additional recruiting on a company-wise basis for the upper management group. In the other categories the supply-demand differences and the recruiting goals are very close. Further analysis revealed, however, that these company-wide figures may be misleading. For example, although supply and demand for upper management personnel were in balance for the entire company there were shortages and surpluses within specific areas. These were related to the rates of growth of these departments. Furthermore, surplus managers in one area were not necessarily transferable to other areas. Therefore, there was a need for recruitment of upper level managers.

Problems with the technique include the lack of stability of transition probabilities within certain departments. As Cascio (1982) has pointed out: "A critical assumption . . . is that transition probabilities are stable over time (p. 8 4 ) . " However, blind reliance on mathematical models in planning is unwarrented as is complete faith in past data. Even if the past transitions are inconsistent, the model may be used to simulate the changes in internal supplies under various hypothetical conditions (cf. Bartholomew & Forbes, 1979). As long as management and human resource planners are aware of the limitations of the techniques it can prove to be a very useful part of a human resourse planning effort.

730

4054

Actual Year-End 1981 (not new hlreo): 34 (+ 4.51)

Difference:

15 (+ 31)

TABLE 6

REFERENCES

Manpower Forecaat - 1982 TRANSITION RATES AND COUNTS

Y lar-End CATEGORY

Count 1981

Non-Exempt

Bartholomew, D. J., and A. F. Forbes, Statistical Techniques for Manpower Planning. New York: Wiley, 1979.

Lower

Middle

7361

(.03) 220

-

Lower Management

5184

(.89) 4614

(.03) 156

(.001) 5

Middle Management

988

(.02) 20

(.83) 820

(.11) 109

Upper Management

552

(.01) 6

(.04) 22

(.90) 497

-

Internal Supply Foreca at for Year-End 1982:

4862

998

611

Manpower Demand Forecalat for Year-End 1982:

5669

1112

603

Difference:

(809)

(114)

8

861

117

31

1982 Recruiting Flan:

Burack, E. H. and N. J. Mathys, Human Resource Planning! A Pragmatic Approach To Manpower Staffing And Development. Lake Forest, 111.: Brace-Park Press, 1980. Casio, W. F., Applied Psychology in Personnel Management (2nd. e d . ) . Reston, VA.: Reston Publishing, 1982. Gillespie, J. F., W. E. Leininger, and H. Kahalas, "A Human Resource Planning and Valuation Model," Academy of Management Journal, 1976, 79, 650-656.

290

Heneman, H. G., III., and M. G. Sandver, "Markov Analysis in Human Resource istration: Applications And Limitations," Academy of Management Review, October, 1977, 535-542. Hooper, J. A. and R. F. Catalanello, "Markov Analysis Applied to Forecasting Technical Personnel," Human Resource Planning, 1981, 4^, 41-54. Ledvinka, J. and R. L. LaForge, "A Staffing Model For Affirmative Action Planning," Human Resource Planning, 1978, 1, 135-150. Vroom, V. H. and K. R. MacCrimmon, "Towards a Stochastic Model of Management Careers," istrative Science Quarterly, 1968, 3_, 26-46. Walker, J. W., Human Resource Planning. McGraw-Hill, 1980.

New York:

Wikstrom, W. S., Manpower Planning: Evolving Systems. New York: The Conference Board, 1971.

291