Printer Friendly

Holonic modelling: human resource planning and the two faces of Janus.


In the early 1970s many companies were planning significant expansion. During this period such companies were quick to realize that the key to success was an adequate supply of appropriately skilled people. This led to the emergence of human resource planning (HRP) as a personnel tool. HRP is in essence a process of ensuring that the correct numbers of human resources were available at the right time at the right place. Companies attempted to forecast their human resource requirements in the medium to long term and then to analyse their ability to achieve the forecast levels. There was a very real need for appropriate analytical tools but few, if any, were available. Much effort was devoted to developing tools and techniques to assist managers with their planning. Many of these were based on the theory of stochastic processes and, specifically, the concept of Markov chains. The academic literature since then abounds with examples of ever more complex mathematical HRP techniques based on Markov chain theory.

Much of this work was developed by D.J. Bartholomew who also wrote the definitive works on summarizing the techniques that were available (Bartholomew (1967; 1971), Bartholomew and Forbes (1979)). This research effort continued through the 1980s, resulting in a mass of published articles on the subject, e.g. Bechet and Maki (1987) Kalamatianou (1987); Raghavendra (1991); Trivedi et al. (1987).

Large organizations established HRP systems, some trying to use the emerging body of human resource techniques based on Markov chain theory, for example Charnes et al. (1972), Smith (1976), Wishart (1976). Unfortunately, the original techniques were often highly mathematical, demanding considerable mathematical sophistication for understanding. As the techniques developed, the mathematics became ever more impenetrable to anyone other than a formally trained mathematician. Unfortunately, for the successful implementation of these techniques, mathematicians tend not to become personnel managers and even fewer personnel managers subsequently study mathematics!

The recession of the 1980s and 1990s, with the readily available pool of skilled labour, resulted in much less emphasis on the need for HRP. Where such planning was in use, there was little evidence that the mathematical theories had transferred successfully into useful practice. A brief search, by the authors, of the recent non-academic literature for practical descriptions of human resource planning yielded only 24 articles. None of these descriptions involved explicit use of the mathematical tools developed by D.J. Bartholomew and his colleagues, although several of them involved the use of computer packages based on these tools.

It appears that while HRP is still used by many organizations it is less significant than it was in the heyday of the 1970s. It is also clear that despite the theoretical developments of Markov chain theory, its highly mathematical and esoteric nature has meant that the theory has not transferred into the real world of practical HRP. If the need for HRP no longer exists then the absence of practical, usable tools is of little importance.

The reality is that the current recession cannot last forever, indeed many economic indicators are showing healthy signs of growth. Even if the economy does not, however, return to the boom conditions of the 1970s there is still enormous volatility in many industries necessitating the need for HRP tools. The recent trends in "downsizing", "rightsizing" and "resizing" and the ever present "job-hopping" and "head-hunting" has increased the complexity associated with such planning. Many organizations who predominantly employ only unskilled and semi-skilled labour may be able to expect the pool of available people to persist into the future. Those industries that need specific skills, not generally available among an employment pool of unemployed coal miners and engineering workers, are likely to start to encounter increasing recruitment problems as the economy recovers. Bell predicted in 1989 that the inevitable skill shortages and changing demographic trends will cause a resurgence in the importance of HRP techniques (Bell, 1989). This view has been echoed by a number of other authors who have stressed the need for HRP in the 1990s, e.g. Evans (1991); Richards-Carpenter (1989); Walker (1989); Zeffane and Mayo (1994).

For existing human resource planners, the availability of an extensive array of techniques is of no use if those techniques cannot be converted into practical tools usable by the non-mathematician. If as predicted, the need for HRP increases then the need for appropriate, usable tools will also increase. The past 20 years has shown that expanding the array of techniques by adding more and more mathematical tools is doomed to failure. Real business problems can, at best, be described as "messes" (Ackoff, 1979) - they are complex, woolly and amorphous. They do not fit easily into the rigorous assumptions necessary for mathematical analysis - when mathematical tools are used they often "emasculate reality" (Ackoff, 1987). Even if analytical tools are suitable they are often unusable by the average practitioner. A new approach is required which combines the rich problem structuring approach of "systems thinking" with the flexible analytical power of the more traditional quantitative techniques.

This is facilitated by harnessing modern spreadsheet technology to implement the previously esoteric tools of analysis. We call this approach "holonic modelling", named after the "holon" from Koestler (1967), having some characteristics of a whole and some characteristics of the individual parts:

intermediate structures on a series of levels in an ascending order of complexity.

Using Koestler's analogy, the "systems" and "quantitative" approaches to problem solving can be likened to the two faces of Janus:

the face turned towards the subordinate levels is that of a self-contained whole; the face turned towards apex, that of a dependent part.

Operational research

The use of a structured mathematical modelling approach to help solve business problems, started in the Second World War, when the military assembled multidisciplinary teams of scientists to work on the operational problems of modern warfare. This came to be known as operational research (OR). A wide variety of mathematical techniques have been developed and while some of them have been used very successfully, many have had little, if any, impact. The disillusionment felt by many practitioners was epitomized by R.C. Ackoff in 1979 in "The future of operational research is past" in which he said:

Managers are not confronted with problems that are independent of each other, but with dynamic situations that consist of complex systems of changing problems that interact with each other. I call such situations messes.

Crudely summarized, Ackoff (1979) maintained that problems cannot be extracted from their context and analysed in isolation. The "efficient" solutions offered by OR were not "effective" when applied back to their "messy" context.

Systems thinking

Possibly as a reaction to this approach, the last 30 years has seen the development of "systems thinking". Originally developed by yon Bertalanffy (1968) in General Systems Theory, it is now best characterized by the work of Checkland and Scholes (1990). The success of this approach is reflected in the increasing number of attempts to apply a holistic philosophy. Crudely summarized, systems thinking places the emphasis on the context in which the problem is embedded by developing a "rich picture", but provides few tools to solve the problem once the context is defined. One of the few techniques to attempt to combine the "richness" of "systems thinking" with the "effectiveness" of operational research is system dynamics.

These two competing schools of thought have now co-existed for decades, with each side appearing to learn little from the other. One side appears to concentrate on understanding the whole, the other on optimizing the parts. Good practice demands both. To quote Ackoff again:

Problems are abstracted from systems of problems, messes. Messes require holistic treatment. They cannot be treated effectively by decomposing them analytically into separate problems to which optimum solutions are sought.

Holonic modelling

Holonic modelling is not merely an alternative philosophy it is also a practical recognition that modern computer power and the flexibility of software packages allow problems to be structured in a flexible manner, recognizing the richness of their context and allowing analysis to be carried out using simple formulae or built-in, analytical and graphical tools. Non-mathematical managers can now use the armoury of techniques, which were previously the preserve of the "expert" and apply them to rich descriptions of their real problem.

This article will demonstrate the use of holonic modelling in the context of HRP showing how the power of Markov chain analysis can be implemented by decision makers who lack the mathematical abilities needed to apply Markov analysis. Indeed, this approach can be expanded to produce a richer and more flexible model, eliminating many of the limitations inherent within Markov type models. This provides the decision maker(s) with greater insights into the problem situation. An HRP system will be analysed to illustrate Markov chain analysis. The authors will then demonstrate how the identical analysis can be carried out without any mathematical knowledge, using a simple flowcharting technique based on the principles of system dynamics (Forester, 1975) and the flexible power of a spreadsheet. This is a significant improvement but still "emasculates reality" by simplifying the problem to fit a mathematical technique. The real benefit of holonic modelling can then be seen. The spreadsheet model is now simply a set of straightforward spreadsheet equations. It is no longer limited to a rigid formulation imposed by the requirements of subsequent mathematical manipulation. As formulation is no longer subject to the requirements of mathematical manipulation it can be expanded and modified to reflect the richness of the real world better.

It can be argued that the mathematical sophistication of Markov analysis is precisely that:

deprived of primitive simplicity or naturalness; rendered artificial...(The Shorter Oxford English Dictionary (1972)).

In general, system dynamics models are easier and more flexible to formulate and solve, they provide equal or greater analytical power than Markov. Additionally, such models are far superior in process terms as the models are not "black boxes" but totally understandable by the problem owner.

Markov models

Markov analysis is named after a Russian mathematician to whom to its development was attributed in 1907. It is a descriptive technique that falls within the family of mathematical modelling techniques known as stochastic process models. The technique is used to describe the behaviour of a system in a dynamic situation over time and has numerous applications including replacement analysis, HRP, brand loyalty, investment evaluation and stock market analysis. Markov analysis is highly mathematical in nature, being a derivative of probability theory. However, despite this mathematical underpinning, it purports to be part of the practising manager's portfolio of techniques and is taught as part of undergraduate and postgraduate curricula in both business studies and mathematics.

Markov analysis is one type of discrete time stochastic process, a sequence of random events for which the probability of each event is determined by the nature of the preceding event. Markov analysis attempts to describe a system as a series of stocks and flows (states and transitions). For example, in a human resource system the number of staff in each grade of the system at any one time are the states. Staff can flow from one state to another over time with a transition probability. The system is considered to be uncertain, but all the probabilities of movement from state to state are known. By describing the movement of the system, this allows management to evaluate the effectiveness of various decisions or scenarios.

Implicit movement through time is achieved using matrix algebra. Markov models are a means to analyse the behaviour of dynamic systems to identify, steady-state values by using probabilities to predict the movement of the elements of the system over time. Models are developed and analysed using a transition probability matrix. The solution is normally in the form of a steady-state transition matrix and a vector of system states. The way in which the system reached that steady rate is normally given scant attention or ignored after the solution is reached.

Most Markov models are closed systems, they do not interact with the environment of which they are a part. Some interaction can be modelled by treating entities which leave the system as entering an absorbing state. The mathematics become even more complex and messy where entities also enter the system and a source term is needed. Models very soon reach the point where they can only be analysed by converting the complex mathematical equations into a special purpose computer program.

Human resource planning

Organizations tend to be hierarchical with a finite number of job grades where individuals can stay in their existing grade, leave or be transferred to another grade (normally a higher grade). The number of staff in any grade is known from personnel records and the probabilities of leaving or transferring to another grade can be estimated reasonably accurately from past data.

Most organizations feel the need to predict future human resource levels in order to forecast recruitment and training needs and to ensure that sufficient experienced people are rising through the ranks to fill vacancies at higher levels. The nature of the problem seems ideally suited to the use of Markov analysis as it clearly involves probabilistic transitions from a set of known initial states. So, it is hardly surprising that HRP is the subject of many academic publications on Markov processes.

Of course Markov type models can be easily solved using a variety of application software, such as Percom, and evidence suggests that the use of such software is increasing in popularity, especially since the later part of the 1980s (Raghavendra, 1991). Zeffane and Mayo (1994) discuss more complex models based on Markov. There are also a number of articles such as Lee and Biles (1990) and Carolin and Evans (1988) illustrate how simple planning models can be developed using a spreadsheet.

A simple, hypothetical HRP model will be used to demonstrate Markov analysis and replicate the analysis using a much simpler approach combining the principles of system dynamics flowcharting with the convenience and flexibility of spreadsheet power. This approach can achieve the same results as Markov analysis much more easily and effectively. Of even greater importance, the suggested approach avoids the crippling simplifications and assumptions which limit the use of Markov analysis and which have provided an irresistible intellectual challenge to generations of mathematical researchers, largely to no practical avail. As Ackoff said in 1979,

OR has been equated by managers to mathematical masturbation.

Application of Markov analysis in a simple HRP example

The definition and analysis of a human resource system, using Markov chain theory, is best demonstrated with a small example. The example (slightly modified) has been taken from the definitive text on HRP models (Bartholomew et al., 1991).

In the example staff are divided into three grades, probationer, staff and senior staff; can be promoted from one grade to the next higher grade but are never demoted. Promotions are automatic, there is no requirement for vacancies to exist before recruitment takes place. This is often called a push system as the pressure for promotion results because of push pressure from lower grades in the system. Staff leave the system from all grades, so it is a normal to show an "absorbing state" (A). This is the simplest form of a Markov chain and it can be solved using simple and elegant matrix algebra (if you can understand it!). But, as new staff are not allowed to enter the system, it is only useful for looking at the behaviour of the initial cohort, i.e. staff in the system at time (0).

If staff are also recruited into the system there needs to be a source term. Markov analysis with a source term means that straightforward matrix multiplication is no longer possible, at each step there must be either a manual or computer intervention. This reduces the simplicity of the mathematical formulation and means that only a computer-based solution is feasible. Taking the example (Bartholomew et al., 1991), the data used in the model are summarized in Table I.

The example is shown below using standard Markov chain notation, for a Markov chain with a source term (recruits) and an absorbing state (leavers):

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

R(T)r = (52 15 3 0).


The calculations necessary to carry out the first time step, from time (0) to time (1) are (Bartholomew et al., 1991):

[n.sub.1](1) = [n.sub.1](0)[p.sub.11] + R(1)[r.sub.1] = 180 (0.70) + 52 = 178

[n.sub.2](1) = [n.sub.1](0)[p.sub.12] + [n.sub.2](0)[p.sub.22] + R(1)[r.sub.2] = 180 (0.10) + 145 (0.85) + 15 = 156.25

[n.sub.3](1) = [n.sub.2](0)[p.sub.23] + [n.sub.3](0)[p.sub.33] + R(1)[r.sub.3] = 145 (0.05) + 35 + (0.85) + 3 = 40

As Bartholomew states "...the first few values of T these (the calculations for each step) could be carried out with a pocket calculator". When the calculations are carried out for 100 time periods (presumably using a computer program) the results summarized in Table II are obtained.

As recruitment is fixed at a level higher than total wastage, in the first few years the workforce tends to increase until wastage becomes equal to recruitment. This is known as "limiting, steady-state" behaviour. It is also clear that in reaching the steady state the proportion of staff in the lowest grade has fallen and the proportion in the two higher grades has increased. This is to be expected in a push system as staff are promoted whether or not vacancies exist at the next level. This may not sound like a very sensible recruitment policy, but examples do exist, e.g. pyramid selling, apprentice recruitment based on training policy rather than anticipated vacancies, students in further education.

This problem can be overcome by replacing the push equation with a pull equation, here staff will only be promoted when there is a vacancy at a higher level. The Markov chain analysis is then based on the revised equation:


[Mathematical Expression Omitted]

This is a more suitable formulation for most organizations but assumes that the overall size of the organization remains static. These may apply to some organizations but they are unlikely to be the organizations that feel the need to take HRP seriously!

A system dynamics model

System dynamics was used for human resource modelling extensively over a ten-year period, within Lucas Industries plc. The authors have drawn on this experience in developing an alternative approach to Markov chain analysis for HRP. Although the models are based on these experiences, the Bartholomew model developed above will be used to compare the two different approaches.

System dynamics modelling is one of a family of continuous system modelling techniques. The technique derives from engineering control theory and, while there is a body of theoretical literature (Forester, 1975); it is almost totally devoid of mathematical content. Models generally use Euler integration, a simple integration method whereby time is advanced in fixed steps and simple arithmetic operations are used to simulate changes deterministically over time. This allows highly complex models to be constructed and solved without the complexities and limitations of differential calculus or matrix algebra. This simple but effective method, using difference rather than differential equations, has been a source of much criticism over the years by mathematicians because of the fixed time step. This is despite the fact that a fixed time step is precisely the mechanism used by the same mathematicians when analysing a Markov chain.

Models are conceptualized and developed using a variety of easy-to-understand flowcharting techniques known as causal loop and level and rate diagrams. Causal loop diagrams are a method of sketching out what causes what in the system. The emphasis is on understanding the overall behaviour of complex systems in terms of stability, robustness, response time, etc. Although the final result will be a mathematical computer model the modelling process is much closer to a "systems" approach than to any form of mathematical analysis. This integration of mathematical rigour and "systems" richness is an example of holonic modelling, i.e. having some characteristics of the whole and some characteristics of the individual parts.

The partial causal loop diagram in Figure 1 shows that probationers leaving a system are part of a negative feedback system. As the number of probationers increases, the number leaving increases which in turn causes the number of probationers to fall. If nothing else happened this would cause the number of probationers to approach zero progressively. However, as probationers fall, the discrepancy between actual and desired probationers will increase causing the hiring rate to increase. This kind of negative feedback loop is at the heart of all management control systems. A target is set, the actual is compared with the target and appropriate remedial action taken.

Having understood the basic nature of the system the diagram is redrawn using levels and rates.

Levels represent the stocks or states within the system. Rates are the flows or transitions which cause the levels to change. Entities enter the system from a source and leave via a sink.

From the level and rate diagram, equations are developed to describe the system in a straightforward, transparent and non-mathematical way. Analysis of the equations was historically completed utilizing a special purpose simulation language (Dynamo, Dynastat, Microdyn "B", Stella); however, medium sized models can now be constructed easily using a spreadsheet, such as Microsoft Excel. The solution is normally presented in the form of tables and graphs showing behaviour over time, possibly to a steady state. Emphasis is, very often, on gaining insights into how that final state is reached rather than the end state itself.

System dynamics can model closed systems so it can model particular cohorts as part of a larger system, but it is more commonly used to model open systems which do interact with their environment. Entities can be modelled in such a way that they leave the system without having to resort to the artificial device of an (Markov) absorbing state. More importantly, it is easy to model entities entering the system so it becomes possible to model the behaviour of the overall system over time rather than just the particular cohort that was in the initial state.

The absence of mathematical symbols and the simple flowcharting techniques mean that models are very easy to formulate and interpret. Such models also provide a very powerful communication tool. Of almost equal importance, they help to ensure that assumptions and quantification are explicit, consistent, communicable and hence understood by all of those involved. The integration method of a fixed time advance is conceptually easy to grasp and maps readily on to most problem owners' conceptual framework of weekly, monthly reports, etc. The best known applications are industrial, urban, world and economic models. There are few practitioners in the UK and the majority of articles are published overseas, especially in the USA. Like the classic system dynamics studies mentioned above, articles tend to be based on real world applications.

A simple level and rate diagram for the above human resource example is given in Figure 2.

A description of the symbols used in a level and rate diagram are given below. When combined to represent the overall system, the diagram produced is graphic and clearly understandable. As a communications tool, it is clearly superior to any form of mathematical matrix, yet still retains all of the information:

* Levels are shown as rectangles, they represent the current state of the system.

* Rates are shown as valve symbols, they show flows around the system.

* The direction of movement between states is shown with arrows.

* Sources and absorbing states (sinks) are outside of the system; these are shown with a cloud symbol.

* Intermediate calculations which are neither stocks nor flows are shown, when needed, as circles.

* Any additional constants or values are added to the diagram as required.

Developing the level and rates diagram is not merely a programming step, it is a vital part of the model building process. Conceptualization and definition of the system evolves through the freedom of sketching out interactions in a causal loop diagram, to the level and rates diagram where relationships are made more explicit and their definition more rigorous. Throughout this process, the emphasis is on understanding how the overall system behaves and how the parts of the system interact together. No constraints have been imposed on the conceptualization of the model by any mathematical requirements of formulation and subsequent analysis.

If the result of this process was the model discussed earlier then it could be analysed using nothing more sophisticated than a spreadsheet and ordinary arithmetic. A spreadsheet model for the above system is shown in Table III. The results are identical to those in the Markov analysis, as they must be. The interactions are the same; it is only the method of describing them which is different.

The same results are shown graphically in Figure 3. The graph shows the final steady state but of equal importance it shows how and why the workforce is changing over time.

The spreadsheet formulations for the first two columns are shown in Figure 4; subsequent columns are simply copies of the equations. All of the calculations are straightforward, using only four-function arithmetic, and will be obvious to anyone with even a smattering of spreadsheet knowledge.


Advantages of holonic modelling over Markov analysis


Using a level and rate diagram to describe the HRP example produces a diagram which anyone with even limited spreadsheet skills can convert into a spreadsheet model. But this is only one of the formulations which Markov analysis can produce. The spreadsheet model can easily be modified to replicate these.

Analysis of a single cohort. One use of Markov analysis is following the original labour force over time to look at the way in which employees leave or progress through the grading structure. Markov analysis does this through repeated matrix multiplication. The above spreadsheet can carry out the same analysis, very simply, by setting the hiring rates in cells B6, B7 and B8 to zero.


Push models. The above example is a push model where staff are promoted to the next higher grade whether or not there are vacancies. This will normally produce expansion or contraction of the workforce, over time. It has been shown that the spreadsheet model reproduces this kind of analysis exactly. The final size of the workforce is determined by the rates of recruitment, promotion and leaving. This appears to be realistic, as human resource levels change over time, but it is in fact naive. In practice changes in the size of the workforce do not just happen, they are managed and normally designed to achieve a target workforce dictated by the strategic plan.

Pull models. As mentioned earlier Markov analysis can also be used to represent recruitment and promotion policies aimed at maintaining a constant workforce size by limiting recruitment and promotion to levels determined over time by vacancies. This is far more realistic in most organizations, but the assumption of a constant workforce is again very naive in the context of HRP. The spreadsheet model can easily be modified to a pull model by specifying the desired workforce as a total or by grade. At each point in time the spreadsheet can be made to compare actual people to the constant number of desired people and hire the discrepancy.

Mixed push and pull models. Some organizations will have a mixture of pull and push systems. Probationers, in the example, may be trained for a fixed period and then automatically promoted to staff or possibly dismissed if they fail to meet target standards. Promotion from staff to senior staff is more likely to be based on filling senior staff vacancies as they occur. This combination of push and pull can be easily incorporated into the spreadsheet model.

Strategic models. Whether recruitment and promotion is based on push or pull, it is unrealistic to believe that any organization using HRP will have any real use for a model which assumes constant workforce size or a workforce which grows or declines almost at random because recruitment and turnover are out of balance. Most HRP involves investigating policies aimed at achieving changing levels of workforce which are known or predicted into the future.

Changing levels of desired workforce can be set in the spreadsheet model by setting target levels for each time period, either explicitly or by using a Lookup function. At each point in time the model calculates actual against target and recruits or promotes accordingly.


Advocates of Markov analysis would argue that all of the above situations can be modelled using existing theory and they would be correct. The problem with Markov models is that as more reality is incorporated to capture the richness of the problem the analysis becomes mathematically more and more complex. Using the approach outlined above, the model just becomes bigger!

Having released ourselves from the necessity of limiting the formulation based on the requirements of subsequent analysis, the real richness of this "holonic" approach can be appreciated. The emphasis can switch from what is mathematically analysable in terms of the solution to what is important in terms of the problem. For example:

* Three grades of staff were modelled; if it was subsequently realized that this was too aggregate then the number of grades could be increased by little more than copying and editing spreadsheet cells.

* The level of economic activity affects both recruitment and retention. Leaving rates, which are currently set as constants, can be reformulated to increase or decrease with predicted changes in the labour market using a spreadsheet Lookup function, driven by time.

* Hiring rates can also be made to vary over time based not only on the state of the labour market but also by adding a limit on the number of recruits based on the organization's capacity for recruitment and training.

* The time period used can be reduced to say a week so that, inevitable, delays in filling vacancies can be incorporated into the model using, for example, exponential or fixed lag functions.


The holonic modelling approach provides a means of describing rich, complex problem situations in a way that ensures all assumptions are consistent, explicit and easily communicable, as well as providing the analytical power to process this rich model without complex mathematics. The use of simple flowcharting techniques and spreadsheet models avoids all the problem of alienation and distrust associated with "black box" techniques. This not only produces better models but encourages a healthy modelling process with a close relationship between modeller and decision maker. This results in an improved intuitive understanding and conceptualization of the system under investigation. The insight and the active involvement of the decision maker, which is made possible by the transparency and accessibility, greatly enhances decision-making effectiveness.


Human resource planning is about ensuring that the correct number and mix of employees is available at the right place at the right time. The success of HRP is paramount to the survival of the organization and the complexities associated with the planning process are enormous.

There is no doubt that quantitative techniques can enhance problem-solving abilities and hence improve decision-making effectiveness. Unfortunately, such techniques often require mathematical knowledge far beyond that of the practising manager. This has often resulted in the tools being considered to have no practical applications. Descriptive techniques such as those associated with soft systems provide tools enabling the practitioner to conceptualize the "rich picture", but exclude analytical power to facilitate solution. The approach suggested by the authors combines the descriptive power of the soft systems approach with some of the analytical techniques associated with quantitative methods, and by harnessing the power of modern technology provides a series of new tools which managers can easily understand and make use of. This new approach can be applied in a number of areas, but one obvious application area would be HRP.

This article has compared and contrasted two alternative methodologies for solving a simple HRP problem. The traditional approach, using Markov analysis is shown to be complicated, communicating little to the decision maker. The holonic, systems dynamics approach on the other hand proves easier to build and provides a richer picture for the decision maker. The benefits of the holonic approach includes improved formulation ability, greater flexibility and an intuitive process which provides extensive insight to the decision maker. The approach combines the richness of a systems approach with the rigour and computational power of operational research. These advantages and the improved insight enable decision makers to have greater understanding resulting in an improvement in decision-making effectiveness.


Ackoff, R.C. (1979), "The future of operational research is past", Journal of the Operational Research Society, Vol. 30 No. 2, pp. 93-104.

Ackoff, R.C. (1987), "President's symposium: OR a post mortem", Journal of Operational Research, Vol. 35, pp. 471-4.

Bartholomew, D.J. (1967), Stochastic Models for Social Processes, Wiley, London.

Bartholomew, D.J. (1971), "The statistical approach to manpower planning", The Statistician, Vol. 20, pp. 3-26.

Bartholomew, DJ. and Forbes, A.F. (1979), Statistical Techniques for Manpower Planning, Wiley, Chichester.

Bartholomew, D.J., Forbes, A.F. and McClean, S.I. (1991), Statistical Techniques for Manpower Planning, 2nd ed., Wiley, Chichester.

Bechet, T. and Maki, W.R. (1987), "Modelling and forecasting focusing on people as a strategic resource", Human Resource Planning, Vol. 10 No. 4, pp. 209-17.

Bell, D. (1989), "Why manpower planning is back in vogue", Personnel Management (UK), July, pp. 40-43.

Carolin, B. and Evans, A. (1988), "Computers as a strategic personnel tool", Personnel Management, Vol. 20 No. 77, pp. 40-43.

Charnes, A., Cooper, W.W. and Niehaus, R.J. (1972), Studies in Manpower Planning, Office of Civilian Manpower Management, Department of the Navy, Washington, DC.

Checkland, P.B. and Scholes J. (1990), Soft Systems Methodology in Action, Wiley, Chichester.

Evans, R. (1991), "Surviving the skills shortage: equal opportunities in recruitment and selection", Library Management, Vol. 12 No. 2, pp. 4-14.

Forester, J.W. (1975), The Collected Papers of Jay W. Forrester, Wright-Allen Press, Boston, MA.

Kalamatianou, A.G. (1987), "Attainable and maintainable structures in Markov manpower systems with pressure in the grades", Journal of the Operational Research Society, Vol. 38, pp. 183-90.

Koestler, A. (1967), The Ghost in the Machine, Picador, London.

Lee, A.S. and Biles, G.E. (1990), "A microcomputer model for human resource planning", Human Resource Planning, Vol. 18 No. 4, pp. 35-9.

Raghavendra, B.G. (1991), "A bivariate model for Markov manpower planning systems", Journal of the Operational Research Society, Vol. 42, No. 7, pp. 565-70.

Richards-Carpenter, C. (1989), "Manpower planning makes a comeback", Personnel Management, Vol. 21 No. 7, pp. 55-65.

(The) Shorter Oxford English Dictionary (1972), Oxford University Press, Oxford.

Smith, A.R. (Ed.) (1976), "Manpower planning in the civil service", Civil Service Studies No. 3, HMSO, London.

Trivedi, V., Moscovice, I. and Bass, R. (1987), "A semi-Markov model for primary health care manpower supply prediction", Management Science, Vol. 33, pp. 149-60.

von Bertalanfy, L. (1968), General Systems Theory, Braziller, New York, NY.

Walker, J.W. (1989), "Human resource roles for the '90s", Human Resource Planning, Vol. 12 No. 1, pp. 55-61.

Wishart, D. (1976), "Guide to MANSIM," in Smith, A.R. (Ed.), "Manpower planning in the civil service", Civil Service Studies No. 3, HMSO, London.

Zeffane, R. and Mayo, G. (1994), "Planning for human resources in the 1990s: development of an operational model", International Journal of Manpower, Vol. 15 No. 6, pp. 36-56.
COPYRIGHT 1996 Emerald Group Publishing, Ltd.
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1996 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Parker, Brian; Caine, David
Publication:International Journal of Manpower
Date:Aug 1, 1996
Previous Article:Differential teamwork performance: the impact of general and specific human capital levels.
Next Article:The labour market in Nigeria under regulation and deregulation: a comparative study.

Terms of use | Privacy policy | Copyright © 2021 Farlex, Inc. | Feedback | For webmasters |