Transition to a desired manpower structure

OMJ~A, The Int./l of MIImt~i., VoL 2, No. 6. 1974

Transition to a Desired Manpower Structure D SCOTT G CULLINGFORD University o f Nottingham (l~eelvcd Octaber 1975; In revlsedform Mare.k 19/4)

It is becoming increasingly common to specify preferred manpower structures for company use. Associated with such specification is the problem of achieving the desired state. The transition procedure is important both from the economic and social points of view. A Machiavellian approach to change can result in an unbalanced and dissatisfied workforce; a result which despite short term economic gains is undesirable. By taking into account the behaviour of company and workforce, together with the costs, it is possible to plan a satisfactory transition. The work reported here deals with a method of investigating the transition from the existing state to the target state. Provision is made for the consideration of all fikelycosts and constraints. By variation of the control variables, managers may investigate the effects of changes in policy. Cost is used as a measure for comparing alternative methods of transition. It is possible to predict the minimum cost transition for a given set of costs and constraints.

1 I N T R O D U C T I O N TO THE PROBLEM INDUSTRY is becoming increasingly aware of the importance of manpower planning and is beginning to take into account the findings of their manpower planners. Under stable conditions, it is possible to predict the likely results o f current policy without difficulty, but some organisations are in a position to define manning structurcs which have more desirable qualities than those which they predicted. If the advantages o f these ideal structures are thought to be sufficient to warrant their introduction, it is necessary to adapt company policy so as to bring about the required change. Although the change to a target structure could he made in a very short time, in practice the effects o f internal and external constraints on the company are such that the change is unlikely to be possible in less than 3 or 4 years. Over this time the labour demands of the company must be met. A transition which takes this length o f time requires careful 793

Scott, Cullingford--Transition to a Desired Manpower Structure planning and control. The best transition policy must be chosen from the many available using some agreed measure.

2 OUTLINE OF APPROACH In the work presented here, methods have been investigated to produce a mimimum cost transition plan-. Data have been coUected from several companies to give mathematical models of employee behaviour and in addition the real costs of using labour in these companies has been investigated. In the first stages of the work, this information was used to cost any intuitive transition policy. Subsequently it was found possible to develop optimising procedures so that given a current structure of manning and some future desired structure, a minimum cost transition plan could be developed. Cost of transition has been used as a primary criterion while allowing secondary criteria to be incorporated as constraints. It is, of course, possible to use measures of transition policy other than cost, but none is so readily understood and appreciated byall sections of management. This is an essential feature of a system which is designed as a quantitative t0ol, leaving management free to make qualitative analysis of the policies shown t o b e optimal within the alternative sets of constraints.

3 R E L A T I O N S H I P TO ASSOCIATED WORK Previous analysis of transition problems has fallen into two main categories. The first defines a target profile after which the wastage and promotion rates necessary to produce the required manpower distribution over a period of time are calculated [3]. This approach has Several obvious shortcomings, for example, the rates of wastage and promotion may not be practicable. The second type of solution takes into account an objective function. Nemhauser and Nutfle, Morgan and Purldss [5-9] have all applied this approach to various manpower problems. The major differences between the work reported here and that referred to above using objective functions lies in the use of a target structure while using a pattern of constraints which allows a great deal of flexibility when selecting feasible solutions. Another significant difference is the use of age and length of service as state parameters. Morgan arid Purkiss both report difficulty in the collection of data sufficiently accurate for their needs. With the cooperation of industry, it has been possible to collect adequate data for the work reported here. The behavioural models used are, of course, of the most basic form, any increase in their complexity would greatly increase the data collection problems. 794

Omega, Vol. 2, No. 6 4 MODEL

STRUCTURE

It is most convenicnat to consider the overall model as a set of submodels which are combined to produce the cost of a transition plan. The submodels are as follows: (a) Employee behaviour Co) Company behaviour (c) Cost submodel. When combined into a manpower costing model, optimising techniques may be used to produce a cost optimal solution.

Employee behaviour Employee behaviour covers factors such as natural wastage and employee effectiveness. Wastage rates may be assessed using established census or cohort analysis on existing historical data [4, 10]. For the case where the workforce is grouped by age, a, and length of service, s, historical information will show that the expected proportion of the group m(a,s) carried over to the following year allowing for natural wastage (unavoidable losses) will be c(a,s) and so m(a+l, s+l) = c(a,s)m(a,s)

(1)

assuming that there is no recruitment or redundancy. Here, redundancy is regarded as those losses which are brought about at the company's initiative. Many companies make regular assessments of their employees and using the records it is possible to produce typical effectiveness curves. The methods of doing this vary from group to group and are not reported here. The transfer from assessment record to a numerical measure of effectiveness requires close cooperation from the management of the company concerned. If the number of employees with age, a, and length of service, s, is m(a,s) and the expected effectiveness of any individual in that group is e(a,s), then the contribution of the group to the total number of effectives in the company is the product e(a,s)m(a,s).

Company behaviour Company behaviour covers areas such as recruitment and early retirement patterns, growth rate and any factor which is controlled by company strategy. In the cases considered it was found that company behaviour was usually expressed in terms of limits that were imposed from without or limits that the organisation had decided to impose upon itself. This naturally led to the incorporation of company policy in the model as a set of upper and lower bound constraints. The values of the constraints may be varied to investigate the consequences of old and new company strategies. A typical use of such an investigation is to determine the cost of the hard constraints of zero redundancy. 795

Scott, Cullingford

Transition to a Desired Manpower Structure

The detailed activities of recruitment, redundancy and the maintenance of total workforce must be carried out within the overall manpower policy constraints. Recruitment and redundancy constraints are incorporated in the model as upper bounds. Total recruitment in all age and service groups in any given year, j ~< Rj. Total redundancy in all age service groups in any given year, j ~< Lj. The carryover equation (1) must be modified in terms of separation t and recruitment r to m(a+ l, s+l) = c(a,s) m(a,s) -t- t(a,s) (2) and m(a+ 1, 1) = c(a,o) m(a,o) + r(a) (3) for each age group, a, where t(a,s) is the number of redundancies for age group, a, and length of service, s, r(a) is the number of recruits age, a. The data requirements for this submodel are largely represented by constraint values. Historical data of the company behaviour in the past provides a useful basis for the evaluation of experimental changes of policy. The figures representing company best estimates of future recruitment and redundancy constraints and overall manpower requirement are assumed to be known. Cost models

The total cost of the transition is expressed as shown in equation (4) N Total Cost = Y~ [Total salary + recruitment and training costs (4) j= 1 + early redundancy costS] In some cases it was found that age could be used as the only model parameter. This simplification is valid when most of the recruitment is into the young age groups. In this case the factors influenced by length of service can be expressed in terms of age, i.e. age is equivalent to service. One of the companies had shown, prior to this work, that costs such as salary could be expressed realistically in terms of age (Fig. 1).

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Omega, Vol. 2, No. 6 Using age as the only parameter, equation (4) can be expressed as N Total Cost == ~

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(5)

where wA -- typical salary for a man age ,4 tA

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In the simplest form this cost function is linear, but in other cases, for example, where the unit costs of recruitment are related to the number of recruits, the function is non-linear. Salary information is the most easily collected and can be conveniently expressed in terms of age or length of service. Figure 1 shows a typical salary/ age curve. The costs incurred in the past by premature separation can be traced and guide lines on payment will take a similar form to that used in the past. Recruitment costs are usually available in terms of cost per recruit. This can be in the region of 30 percent of starting salary in some groups. Training costs are important and can be large, (as much as three years' salary), but are difficult to assess. Use may he made of learning curves, the training pattern of a typical recruit or any other method which gives a true picture of the training period for staff in the company concerned. Training can be expressed directly as a cost or in terms of the cost of ineffective time. Figure 2 shows a training and recruitment cost curve expressed in terms of age or recruitment as determined in a typical study.

5 TOTAL TRANSITION MODEL The behaviour models and the cost models may be amalgamated to produce the overall transition cost model. It must be emphasised that in the construction of the submodels, it is necessary to validate the derived forms both with past data and the experience of management in the company concerned. The models are all based on historical information or its projections into the future and it is essential that due account is taken of new information as it becomes available (See Fig. 3). As an example of use of the transition model in Table 1, various forms of transition are given in the first column. In the second column headed "Intuitive", the costs are calculated for fulfilling the required transition using an intuitive policy which moves at a steady rate towards the target profile. 797

Scott, Cullingford--Transition to a Desired Manpower Structure However, the form of the models derived above is particularly suited to the use of optimising procedures which are discussed in the next section.

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Omega, Vol, 2, No. 6

6 COST OPTIMAL TRANSITIONS In determining the cost transition, it is assumed that the length of the planning horizon is fixed. To determine the global optimum, the costs on a selection of transition period can be investigated. The type of optimising procedure to be used depends on the form of the cost function, i.e. linear or non-linear. Linear programming procedures have been found to give the best performance for linear problems. Gradient techniques have been used successfully with non-linear forms. Taking into account the nature of the data and with the basically linear form of the constraints and transition equations in practice it is most realistic to use the linear form of the problem. Figure 4 shows a typical result in terms of age profiles. tA'. l r " . .

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7 RESULTS The cost/man produced by the model depends on the transition period and growth rates, together with constraints on hiring and firing. Therefore, each result must be looked at in the context of its imposed poficies and constraints. In order to establish a datum the concept of the "intuitive" policy has been introduced. This policy is one which takes the manpower profile from the existing to target profile in equal steps (rather like linear interpolation between

points). Two alternative methods of using the transition model are, either to compare the cost/man for two different policies and assess one against the other, or to cost an actual policy prepared by other methods. 799

GO

(

) saving on intuitive policy

1% p.a. decrease of nos. in service No change in numbers 10% p.a. increase of nos. in service Fall and rise of 10% over 5 years

Form of transition Gradient solution 2348 (34%) 2364 (32 %) 2505 (4.3 %) 2321 (10%)

3567 3498 2618 2581

2138 (40%) 2237 (39 %) 2330 (11%) 2125 (17%)

Linear programming solution

Recruitment and separation restricted

Total transition cost over five years

OF COST OPTIMAL SOLUTIONS U S I N G DIFFERENT MODELS

Intuitive

TABLE 1. COMPARISON

2102 (41%) 2032 (42 %) 2329 (11%) 2124 (18~o)

Relaxed linear programming solution

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Omega, VoL 2, No. 6 Table 1 shows the performance of three types of model using a linear cost function over a five year transition. The improvements in cost over the "intuitive' policy are shown. In the columns headed "Recruitment and separation restricted", results are presented from the use o f gradient methods and linear programming on the various transition problems under typical company restrictions on recruitment and separation presented in the model by upper bound constraints. In the last column~ these restrictions have been removed and the cost differences between the constrained and unconstrained solutions will give a measure o f the need for changes in self imposed company constraints. In most of the companies Studied, their forecast change in total manpower was no greater than 1 percent per annum rise or fall. The situation o f 10 percent growth or 10 percent fall and subsequent rise for which the results are given in Table 1 can be looked on as outer bounds in most circumstances. TABLE2. COSTPER MAN-YEA~OF TRANSITION(NO REDUNDANCY) No. of stages in transition

No. of man-years

Cost of transition

Cost/man-year

7 8 9 10

847 1042 1256 1492

2,139,400 2,646,400 3,180,800 3,767,700

2520 2540 2540 2520

TABLE3. COSTPingMAN-YEAROF TRANSITION(WITHRBDUNDANCY) No. of stages in transition 2 3 4 5 6 7 8

No. of man-years

Cost of transition

Cost/man-year

110 231 363 509 670 848 1042

260,232 489,975 746,000 1,038,286 1,390,380 1,818,430 2,323,660

3270 2130 205O 2040 2080 2160 2230

In some industrial circumstances it is not possible to allow redundancy in one section while recruitment is taking place in another. Under these conditions it is necessary to reduce to zero the upper bound on redundancies. Tables 2 and 3 show the costs o f transition with and without the redundancy option. There is a significant difference in cost/man between the two (-"- 15%) which is caused by the impmition of a "recruitment only" regime. Although this type o f transition c o r n more to maintain, it may be argued that it is worth the cost penalty, especially since the saving o f the two policies is practically the same when compared with the cost o f the "intuitive" policy. The point is debatable but serves to illustrate the use o f the model as a tool and not as a decision making 801

Scott, Cullingford--Transition to a Desired Manpower Structure

device. Policies may be compared but the balancing of costs and non-quantifiable factors must be left to the manager involved. It can be seen (Tables 2 and 3) that cost/man-year is a function of the length of transition, but variations are small and from experience transition length usually depends on company policy rather than minor cost variations. Restrictions on recruitment and redundancy place a lower bound on the transition length. Using a shorter period will violate one of the company constraints. The shortest transition period for a given set of constraints is found by experiment. No hard and fast rules can be given for the type of transition which will consistently give minimum cost/man. Different costs, constraints and policies are bound to give different results. There are, however, several characteristics which have become apparent. Any recruitment at the young end of the age scale tends to be in preparation for the target profile, taking into account natural wastage in the intermediate years. In general, natural wastage and and retirement is allowed to act in the older groups for as long as possible before major changes are made in the final year in order to achieve t h e objective profile. During the transition it is likely that cost patterns and external circumstances will change. In addition, the response of employees to the internal changes will become apparent. This could cause the company to modify its target profile although a return to steady conditions may involve a return to former employee behaviour patterns. With improved information, however, the form of the transition can be modified to remain cost optimal. For this reason it is essential that all data is continuously updated and that the validity of the models is frequently checked.

8 USE OF THE MODEL The model is designed to assist management. Any of the constraints or costs can be varied. This gives an opportunity to discover the likely effects of changes in company practice (such as introducing early retirement) and to investigate increases in costs (e.g. salary revisions). Cost/man/year provides a convenient yard stick for comparing different types of transition, but additional measures such as recruitment or number of redundancies can be used. Experience has shown that this type of model is most useful when a group of managers can themselves run a series of tests. The changes in the values of costs and constraints are made in the light of the results of previous tests. This approach allows the managers to learn more about the problem and design a solution. The way of achieving a satisfactory manpower profile is a matter for company decision. If the transition is to be cost optimal, there are at least two methods. 802

Omega, Vol. 2, No. 6

The first involves setting a transition period. The optimising procedure is repeated annually until the target year. This allows the continuous up-date of data as more information becomes available, and for allowance to be made for deviations from the desired policy in the previous year. The second approach involves the repeated use of a fixed transition period. This is not as rigid in its definition of the real transition period and makes use of the moving horizon concept, and allows the user to modify data and respond to changes in company requirements.

9 PRESENT USE OF THE MODEL This model is now being used in a large company. The cost optimal manpower profile [1, 2] is used as the target profile and various policies for transition and their implications are investigated. The model is used very much as a tool to test response to various policies, transition periods, growth rates etc. Although this technique only takes into account quantifiable aspects of the transition, it provides a starting point for the formulation of management policy.

ACKNOWLEDGEMENTS We would like to thank the British Manpower Society for the opportunity to discuss the ideas and results presented here, and various organisatiom, without whose cooperation and help no meaningful results would have been produced.

REFERENCES 1. CULLINOFORDG and ScoTT D (1973) Optimality and manpower planning. Personnel Rev., 2 (3). 2. CULLINOFORDG, SCOTTD and Bem~ON M (1973) Target manpower holding in a large company. Proceedings of Anglo-French Manpower Conference. Le Touquet, May. 3. Fom~s AF (1969) . . . policies for control o f . . . hierarchical systems. Proceedings NATO Conference: Mathematical Models for the Management of Manpower Systems. Oporto. 4. I-Im)am~oM (I961) The turnover of labour in industry, an actuarial study. Aeta Sociologlea, 5, 129-143. 5. MORGANRW (1969) Manpower planning in the R.A.F. NATO Conference. Oporto. 6. NlZMHAU~RGL and NuTr~ HLW (1965) A quantitative approach to employment planning. Mgmt Sci., 11 (8). 7. PURKIM CJ Approaches to recruitment, training and redeployment planning in an industry. BISRA Open Report. OR/35/107. 8. PURKI~ CJ and RICHARD~NJZ Planning recruitment and training in the steel industry. BISR,,I Open Report. OR/41/68. 9. ~ C3 (1969) Models for examining the optimising manpower deployment. N.ATO Conference. Oporto. 10. Sn.cocE H The phenomenon of labour turnover. J. R. Statist. Soc., All7 429-440. 803