dynamics of human resource and knowledge management (group-3)

13
Dynamics of Human Resource and Knowledge Management Author(s): K. Hafeez and H. Abdelmeguid Source: The Journal of the Operational Research Society, Vol. 54, No. 2, Special Issue: Knowledge Management and Intellectual Capital (Feb., 2003), pp. 153-164 Published by: Palgrave Macmillan Journals on behalf of the Operational Research Society Stable URL: http://www.jstor.org/stable/4101606 Accessed: 02/03/2009 08:33 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=pal. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]. Palgrave Macmillan Journals and Operational Research Society are collaborating with JSTOR to digitize, preserve and extend access to The Journal of the Operational Research Society. http://www.jstor.org

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Page 1: Dynamics of Human Resource and Knowledge Management (Group-3)

Dynamics of Human Resource and Knowledge ManagementAuthor(s): K. Hafeez and H. AbdelmeguidSource: The Journal of the Operational Research Society, Vol. 54, No. 2, Special Issue:Knowledge Management and Intellectual Capital (Feb., 2003), pp. 153-164Published by: Palgrave Macmillan Journals on behalf of the Operational Research SocietyStable URL: http://www.jstor.org/stable/4101606Accessed: 02/03/2009 08:33

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/action/showPublisher?publisherCode=pal.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.

JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with thescholarly community to preserve their work and the materials they rely upon, and to build a common research platform thatpromotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected].

Palgrave Macmillan Journals and Operational Research Society are collaborating with JSTOR to digitize,preserve and extend access to The Journal of the Operational Research Society.

http://www.jstor.org

Page 2: Dynamics of Human Resource and Knowledge Management (Group-3)

Journal of the Operational Research Society (2003) 54, 153-164 ?2003 Operational Research Society Ltd. All rights reserved. 0160-5682/03 $15.00

www.palgrave-journals.com/jors

Dynamics of human resource and knowledge management K Hafeezl'* and H Abdelmeguid2 'School of Computing and Management Sciences, Sheffield Hallam University, Sheffield, UK; and 2Mechanical Engineering Department, Faculty of Engineering, Nasr City, Cairo, Egypt

Recent transitions from the industrial to knowledge economy suggest an immediate and wholesale retraining scenario so that many organisations can remain at the cutting edge of technology. The dynamics of the job market is creating a challenge for many organisations in recruiting and retaining their core staff. In fact, many companies are in fear of losing critical business knowledge when their employees leave. In this paper, systems dynamics is employed to illustrate the relationship between recruitment, training, skills, and knowledge in a causal loop form. Strategies for human resource management are developed by conducting time-based dynamic analysis. We anticipate that systems dynamics modelling would help organisations to devise efficient human resource management strategies. Journal of the Operational Research Society (2003) 54, 153-164. doi: 10. 1057/palgrave.jors.2601513

Keywords: knowledge management; intellectual capital; human resource; core competence; systems dynamics

Introduction

During the last two decades a number of author1-5 have been influential in shaping the concepts of core competence. They argue that the core competence is the basis for devising business strategy and offering unique products and services to customers. We agree that core competence is often recognised in the form of intellectual capital or other intangible assets such as culture, brand name or marketing knowledge as opposed to tangible assets such as plant and

6 equipment. Owing to the work of notable social thinkers such as Handy,7 companies are recognising that their employees are their most valuable assets. Business pioneers are finding surprising ways to measure and manage the ultimate intangibles of a company, that is, skill, knowledge and information. Intellectual capital is a special form of human capital that is codified, formalised, captured and leveraged to produce a higher value asset. Many managers admit that the bulk of the value added is derived from the intellectual capital. Moreover, the intellectual capital is here to stay-it is the value of tangible or 'hard' asset, which can depreciate or vanish overtime.

However, in the present business climate of job opportu- nities, companies are always under the constant threat of losing their core people, and therefore essential business knowledge. This, in our view, is reflected in the recent developments in the competence management field.8'9 We

have proposed an Analytical Hierarchy Process (AHP) method in order to help companies to identify their core capabilities using both financial and non-financial measures such as learning and innovation.10 Staff turnover issues have reached to such a level that many industrial, service and consulting organisations are investing a big slice of their resources under knowledge management initiatives.',2

In our view an efficient human resource or intellectual capital investment strategy demands a good understanding of the dynamics of recruitment and training issues. In this paper, recruitment, training, and skill and knowledge management are illustrated more explicitly in a causal loop form. Strategies for human resource management are developed in the form of a systems dynamics model. Simulations are conducted to illustrate the time-based dynamics of skill attrition, recruitment and training programmes. We anticipate such a modelling exercise would serve as useful aid for devising an effective medium to long-term intellectual capital management strat- egy for organisations.

Human resource and knowledge management

A good knowledge management (KM) definition is given by Swan et al,13 who defined it as "any process or practice of creating, acquiring, capturing, sharing and using knowledge, wherever it resides, to enhance learning and performance in organisations". Johannessen et a114 have given a fuller account of various types of knowledge, namely systemic, explicit, tacit, hidden, and relationship knowledge. Systemic knowledge is learned by studying patterns such as those

*Correspondence: Khalid Hafeez, School of Computing and Management Sciences, Sheffield Hallam University, City Campus, Howard Street, Sheffield S 1WB, UK. E-mail: [email protected]

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154 Journal of the Operational Research Society Vol. 54, No. 2

from scenario planning exercises or computer simulations. Explicit knowledge is relatively easy to attain and commu- nicate through listening and reading. Relationship knowl- edge is learned via interaction and is relatively difficult to communicate. The most difficult forms are tacit knowledge and hidden knowledge, because these are difficult to comprehend and communicate. Hidden knowledge is the way of organising ideas and mental models and is usually learned by socialising. However, the most valuable form of knowledge is tacit knowledge. Johannessen et a114 refer to it as "know how," which is acquired or "learned by using, doing and experimenting". Tacit knowledge is usually very subjective and resides inside one's head, and is, therefore, difficult to communicate, comprehend and quantify. For this reason organisations are struggling to discover how to motivate their people to share tacit knowledge, which is recognised as a strategic asset. In our view many companies attempt to achieve this via employee training (apprentice- ship) and competence development (job shadow) programmes.

1

We illustrate the KM process in the form of a 'knowled•g

flywheel' effect as shown in Figure 1.15 Human beings have the amazing capacity to elicit and enrich existing knowledge while simultaneously receiving and interpreting different forms of data and information through various knowledge embodiment receptacles. Demarest9 has explained that when knowledge is (explicitly) embodied, it may reflect in the form of raw materials, products, services, machinery, mechanisms, business practices and processes, environment and culture. Note that in our view environment and culture embodies both tacit as well as explicit forms of knowledge. The challenge for a company is to develop appropriate policies and procedures in order to reflect 'knowledge flywheel' effects, where the knowledge enrichment process is taking place via the interchange between tacit and explicit knowledge, and knowledge codification is in operation to enhance 'organisation memory'.

There are many examples where companies are resorting to information technology tools to devise a kind of KM system in order to store explicit knowledge. For us, infor-

Knowledge Sharing

TACIT * Individual * Environment and culture

EXPLICIT * Written repositories

KNOWLEDG Raw materials and services

TACIT * Machinery and

FORMATI mechanisms * Business practices and

processes * Environment and culture

DATA ---- -

* KNOWLEDGE PROCESSING

SYSTEM Individual knowledge process

(Knowledge Creation) Knowledge repositories

(Knowledge Embodiment)

Figure 1 Knowledge creation and embodiment 'flywheel' within an organisation.

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K Hafeez and H Abdelmeguid-Dynamics of human resource and knowledge management 155

Table 1 Some characteristics of a knowledge management system

Term Definition Author

Skill Skill is the ability to master the Sanchez et al"6 concepts of a discipline or domain, and to apply this knowledge appropriately in new situations

Knowledge Knowledge is information Collins Cobuild17 and understanding about a subject which a person has in mind

Competence The set of skills and knowledge Baker et a 18 that an individual needs in order effectively to perform a specified job

Learning The process of improving Fiol and Lyles9' actions through better knowledge and understanding

mation technology solutions rather relate to explicit knowl-

edge and organisation memory. However, an appropriately devised and implemented human resource management system (that emulates 'knowledge flywheel' characteristics has a lot to offer with rewards to managing in tacit knowl-

edge in the organisation. Also, a good knowledge manage- ment system (KMS) should be able to attract company employees as well as other stake-holders voluntarily to get involved in some kind of knowledge sharing and learning activities. Often such communities-of-practice (COP) act as a medium to enhance individuals' knowledge and skills, and therefore facilitating informally via participating members the organisation's competencies. A summary of some char- acteristics of KMS and their inter-relationships is presented in Table 1.

Systems dynamics

Jay Forrester20 conducted some pioneering work by combin-

ing the fields of feedback control theory, computer and

management sciences as early as 1961 in order to shape the systems dynamics discipline. More recently tools such as systems thinking have made many gains in 'soft' systems problem structuring as advocated by Senge.21 In other

examples, Morecroft22 has used systems dynamics to exam- ine the management behavioural resource system to analyse a diversification strategy based on core and non-core busi- ness. Winch23 has used systems dynamics to introduce a skill inventory model to manage the skill management of

key staff in times of fundamental change. Coyle et a124 have used systems dynamics to manage and control assets and resources in major defence procurement programmes. Warren25 defines tangible and intangible resources for

systems dynamics model development. Hafeez et a126 have used systems dynamics modelling to re-engineer a supply chain. In this paper we make use of an Inventory and Order

Based Production Control Structure (IOBPCS) based on

systems dynamics as described by Coyle27 and Towill28 to

develop a skill inventory pool model.

Causal loop analysis

Causal loop diagrams (or influence diagrams) are used to

develop cause and effect relationships between the main variables of a system.27 In our view, key components of a

simple KM model should represent an inter-link between

knowledge, skill, and training/learning processes as identi- fied in Table 1. Figure 2 illustrates the causal loop format of a simplistic KMS. In reality, existing knowledge (if not

updated) becomes obsolete with time due to the instability of the market or product portfolio changes. Also, corporate knowledge erodes when employees leave the company, taking away the important knowledge within their heads. These influences are represented using feed-forward and feedback loops. Clearly, the higher the knowledge erosion rate, the faster the corporate knowledge pool depletion or

'memory loss'. The management needs to take appropriate actions through recruitment and/or training employees to maintain the minimum reasonable knowledge level to conduct essential business operations. Also, strategic knowl-

edge and competencies (through recruitment and training) need to be developed for long-term competitiveness and

sustainability of the business.

Skill pool model (SKPM)

Skill, knowledge and competence are identified as the essential resources of the knowledge economy. These cannot be bought and/or delivered instantly. Usually it takes a considerable amount of time to develop and support the required infrastructure to nurture required skills and

competencies. The causal loop illustrated in Figure 2 is very involved, comprising a number of inter-linked feed-forward and feedback loops. A computer simulation model and

subsequent dynamic analysis is possible, but is of limited use as the individual parameter changes (eg, recruiting rate) cannot be isolated easily. Also full-scale sensitivity analyses for the entire organisation would be prohibitive due to the

large number of variables involved. Therefore we propose a

simplistic model based around the key variable-skill-to reflect the dynamics of intellectual capital and organisation knowledge.

A Skill Pool Model (SKPM) is developed to help under- stand the dynamics of skill acquisition and retention, parti- cularly during times when a company is planning some major changes in its product/service portfolio. There is an implicit link with the organisation environment to reflect how new skills can improve the organisation productivity and innovation process. The present and future recruitment and training needs are represented as a function of present skill loss rate in a feed-forward path. Also the skill pool

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156 Journal of the Operational Research Society Vol. 54, No. 2

Desired

knowledge

New ideas/

implementation-'

l+Knoledge +kn ledge applicable to the

knowledge company acquisition Actual +

rate knowledg Average +-

ve level knowledge

K>\ -+

erosion

+Knowledge "+ Learning ining

in process t knowledge rate erosion + rate

Desired - Knowledge knowledge in

in process process adjustment p

+

Figure 2 Causal-loop diagram of knowledge management in an organisation.

level and recruitment and training performance are managed by introducing a feedback loop.

The Skill Pool Model (SKPM) is derived by translating the concepts of IOBPCS. The IOBPCS model has been identified by Coyle27 as representing much of the UK's industrial practice associated with industrial systems, which also involves human experience. Towill128 has shown how the IOBPCS model can be shaped to satisfy those conditions under which analogous linear control systems for other applications have been regarded as optimum. Cheema et a129 have developed an extension of this model by making use of feed-forward information with regards to ordering trends and targeting customer service levels, and the feed- back of information on finished goods stock, and production lead-time variances. Ferris and Towill30 have shown how IOBPCS forms the basis of a generic family of production control systems representing the performance of many industrial sectors. Hafeez et a126 have shown its usefulness for modelling a multi-echelon supply chain. Mason-Jones et

a131 have extended this work to show its applicability in an Efficient Consumer Response (ECR) environment by link- ing point-of-sale to instigate inventory triggers.

Influence diagram

The influence diagram for SKPM is shown in Figure 3 using the standard Ithink software package. (The software allows

one with no or only elementary control theory knowledge to construct an equivalent model to represent time-based dynamics.) In order to anticipate the skill loss replacement requirements, some kind of averaging is useful. The present skill loss rate is exponentially averaged over a time (Ta) and added back to the original training rate to reflect the skill loss history in the recruitment planning.

Figure 3 illustrates that the company-training rate comprises two parts, one the present skill deficit/gap, and the other the averaged (forecast) skill loss rate. Training rate is therefore effectively controlled via Ta (the average time to determine the forecast skill loss rate), and Ti (the time over which the present skill gap is to be recovered). The difference between the present skill loss rate and recruitment or skill development rate is accumulated to give the present actual level of the skill pool. Therefore the model as shown in Figure 3 consists of two parts; feedback control based on the skill gap and feed-forward control based on the forecast skill loss rate. In order to analyse the dynamic response of the skill pool, recruitment (training) process delay is repre- sented by a time delay Tr (training lead-time), and the time over which skill loss rate is averaged by Ta. Towill28 suggests using exponential delay for industrial dynamics simulation. We have used the discrete version of exponential delay in SKPM. Details of the discrete-time feed-forward and feedback difference equations giving the relationship between the major variables are presented in the Appendix.

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K Hafeez and H Abdelmeguid-Dynamics of human resource and knowledge management 157

0 Trainees

ecruatmen

Recruitment skill pool Present Skill

raecompletion Loss rate rate rate

Recuitment

Lead time (T,) Desired

level of skill Skills gap -

pool +

Skills shortage Skill loss

Skilsorer / averaging time (Ta)

Recovery

Time (Ti) Forecast skill loss rate

Figure 3 Influence diagram of Skill Pool Model (SKPM).

It is important to recognise how to manage the actual level of the skill pool. To reach the desired value, a simple and appropriate policy is proportional control, where infor- mation concerning the magnitude of the level (actual level of skill pool) is fed back to control the training rate. The

training rate is calculated by dividing the discrepancy between the desired and actual value of the level by a time factor, which represents the average delay in perform- ing the training rate.

Dynamic analysis

As shown in Figure 3 the policy parameters Ti, Ta and Tr are varied to determine their optimum settings using simulation results. Once selected, the system operates with the recruit skill rate automatically governed by Ta and Ti for a present skill loss rate and skill gap. During normal operation, the

management would observe skill gap and training comple- tion rate to meet the organisation's requirement.

The system dynamics model and simulation analyses presented in this paper relate to a hypothetical IT company employing 400 staff. The company is going through a major diversification strategy needing one-quarter of the total workforce to undergo a recruitment and/or training programme. Also, the company has to cope with, on

average, 5% employee turnover at any time. Therefore the simulation model is subjected to some 20% increase in the

present skill re-training rate (as per 100 employees) as shown in Figure 4. Figures 4(a) and (b), respectively, show the response of actual skill pool, and training (recruit- ment) completion rate for a range of Ti values. The larger the Ti values, the larger the skill pool drop, indicating the

company is unable to recover from the skill shortages over a

period of time. With the worst case scenario (in Figure 4(a)), the company faces skill shortages for about 50 months if

Ti = 16 months). On the other hand, a small Ti value would allow recovery of the skill deficiency much more quickly (eg, note the actual skill pool values for Ti ranging from 1 to

4). However, very small Ti values induce unwanted oscilla- tions about the required skill pool value over a longer period. (Clearly, in control theory terminology this is a bad system design.) In reality, this shows a very aggressive hiring and firing human resource policy, showing inap- propriate management of human capital and associated cost implications. Under such circumstances, the company would be forced to introduce short-term employment contracts to avoid offering redundancy or golden handshake

packages. The aggressive hiring and firing policy would reflect in low staff morale and a realistic risk of more staff

leaving the company while voting with their feet. Conse-

quently, there would be serious implications on productivity and customer service level, and, ultimately, on the bottom- line performance. For a pure training scenario, these tran- sients reflect excessive-training or under-training issues, again an undesirable situation. Also, while selecting Ti, training pace has to be adjusted in line with workforce

background and individual learning capacity. Figure 5 illustrate the influence of Ta, the averaging

parameter, to control the extravagant hiring and firing and

training policy. Figure 5(a) shows that as the value of Ta is

gradually increased, say from 0 to 16 (months), the actual skill pool overshoot and therefore (hiring and firing) oscilla- tions are well managed. However, this would dictate the

corresponding skill pool recovery only after 30 months-a

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158 Journal of the Operational Research Society Vol. 54, No. 2

450

* 400

350 16.5

aa 12.5 300

~< 8.5

250 4.5

40 0 20 40 60 80 100 0.5 80

Time (months)

(a)

130 -

120

o E -),16.5

8.5

100 4.5 1

20 r,: 0

60 0.5 80

1 100

Time (months)

(b)

Figure 4 Step response of SKPM for varying values of Ti: (a) Skill level behaviour (Tr = Ta = 4 months); (b) Recruitment completion rate behaviour (Tr = Ta = 4 months).

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K Hafeez and H Abdelmeguid-Dynamics of human resource and knowledge management 159

450

S-400

4A 350

316.5

12.5 ? 300

8.5

250 4.5 o 20 &q• 40 60 0.5

Time (months) 80 100

(a)

130

5 *

120

" c Eo

SE 16.5

?, 1 10 12.5

100 4.5

20 40

: •

0 20 40 60 0.5 80

Time (months) 0

(b)

Figure 5 Step response of SKPM for varying values of Ta: (a) Skill level bahaviour (Tr = Ti = 4 months); (b) Recruitment completion rate behaviour (Tr = Ti = 4 months).

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160 Journal of the Operational Research Society Vol. 54, No. 2

500

S450

400

0.5 350-

4.5

< 300f 8.5

250

12.5 o1.

0 20 s 40 60 t6.5 80

Time (months) 100

(a)

140

k: 130

E 120

0,5

, 10 u8.5

100 12.5

o? 0 20 40 60 80 100

T m 60n16.5

Time (months) 1

(b)

Figure 6 Step response of SKPM for varying values of Tr: (a) Skill level behaviour (Ti = Ta = 4 months); (b) Recruitment completion

rate behaviour (Ti

= Ta- 4 months).

Page 10: Dynamics of Human Resource and Knowledge Management (Group-3)

7--

CtD cD N

:q I sw cD

VD

4-b

3

CD

•r

C2,

3

CD

o

UQ

CD

o

3

3 cb

Table 2 A summary of the performance index for the optimum human resource policy design parameters

Performance index for the optimum

SKPM design parameters Ideal design parameters performance (7Ti = Tr and

Performance index Ta Ti T index Ta = 2Tr = 8)

Skill pool Initial skill pool Increasing Ta increases Increasing Ti increases Increasing Tr increases Minimum the 20.37% of the measurements drop (representing the initial skill pool the initial skill pool the initial skill pool better nominal value

skill shortages) drop drop drop Duration of the skill Increasing Ta increases Increasing Ti increases Increasing Tr increases Minimum the 22 months

pool deficit the settling time the settling time the settling time better Peak skill pool Increasing Ta decreases Increasing Ti decreases Increasing Tr increases Minimum the 0.46% of the

overshoot (ie, the peak skill pool the peak skill pool the peak skill pool better nominal value redundant skills) overshoot overshoot overshoot

Recruitment (training) Rise time (time for Increasing Ta increases Increasing Ti slightly Increasing Tr increases Quicker the 8 months

completion rate recruitment policy to the rise time increases the rise the rise time better measurements make an impact on time

the pool) Peak overshoot (or Increasing Ta decreases Increasing Ti slightly Increasing Tr increases Minimum the 6.94% of the

over recruitment) the peak overshoot increases the peak the peak overshoot better nominal value overshoot

Duration of Increasing Ta increases Increasing Ti slightly Increasing Tr increases Shorter the 16 months overshoot the duration of increases the duration the duration of better

(over recruitment) overshoot of overshoot overshoot

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162 Journal of the Operational Research Society Vol. 54, No. 2

totally unacceptable scenario in many situations. Also, there is a marginal improvement in the recruitment overshoot rate, for higher values of Ta.

Figure 6 illustrates the skill pool and recruitment comple- tion rate response for varying recruitment (training) lead- time Tr. Clearly, the smaller the Tr, the quicker the skill pool inventory recovers while avoiding any over-recruitment. If required skills are scarce in the marketplace and recruitment delay approaches 16 months, for example (an extreme scenario), the company could suffer from an agitated hiring and firing policy for well over a 5-year period in order to recover from present skill needs.

In order to devise a good human resource policy, that is, which values of Ti, Ta related to Tr yield the best recruitment (training) performance, we have made use of the well documented IOBPCS model 'trade off' procedure (Towill128). The optimisation guidelines taken under consid- eration include:

(i) Good skill pool recovery in response to changes in skill loss rate, and

(ii) Good recruitment (training) completion rate in response to skill loss changes, including the ability to attenuate fluctuations that lead to increased cost.

As with Towill,28 the SKPM optimum was found to be

Ti = Tr and Ta = 2Tr at Tr = 4 months. Table 2 gives the overall summary of the effect of varying Ti, Ta, and Tr on the human resource policies.

Conclusions

Many organisations have realised that proper management of their skill and competence base is key to their survival and profitability in the knowledge economy.6'32 Therefore, they need to understand the dynamics of their intellectual capital and human resource management policy. The Skill

Pool Model presented in this paper allows organisations to maximise the value of their intellectual assets and work- force. By tweaking human resource policy parameters Ti, Ta, and Tr, management should be able to optimise desired recruitment patterns while looking at current workforce shortages. Also, it is possible to minimise the current and future (desired) skill gap by devising appropriate recruit- ment and training programmes.

From the simulation results, it is evident that the propor- tional control achieved through Ti in the feedback path is more influential than Ta in the feed-forward path. Also, an adherence to the given recruitment time (assumed 4 months in this case) is absolutely essential to minimise unwanted transients in the system impacting on staff morale or scheduling required customer service level. Also, knowl- edge of unnecessary recruitment (training) delay transients would allow management to estimate the incurred losses due to an acute hiring and firing policy. In some situations management may decide to meet some staff shortages by moving towards a multi-skill policy and offering training to existing employees. Here, systems dynamics simulations can help to provide training/learning time estimates against the required skill shortages and associated costs.

Appendix: Transfer function of SKPM

Notation

Ti: Time over which the present skill gap is to be recovered Ta: Skill loss rate averaging time Tr: Training/recruiting lead-time

Figure Al shows the block diagram representation of the key variables of the model and their interactions.

Equations (1) to (5) outline the main structure of SKPM in terms of its variables. Equation (1) calculates the skill gap

Forecast 1 Present skill skill loss I + T . S loss rate

rate

Desired _Training Actual level of Skill Training completion

level of Skill pool gap 1 + rate rate skill pool + 7a+Tr'.S I

Figure Al A block diagram representation of SKMP.

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K Hafeez and H Abdelmeguid-Dynamics of human resource and knowledge management 163

as the difference between a fixed or constant desired level of skill and the actual level of skill pool.

Equation (5) shows the forecast skill loss rate as a

smoothing function, [1/(1 + TaS)], of the present skill loss rate. The latter is then used to derive the scheduled training rate in Equation (2). The schedule aims to meet the forecast skill loss rate but adjusts this target to take into account the current skill gap. The adjustment is given by function (1/Ti), representing a control algorithm as shown in Equation (3). The training completion rate is given as the result of the

delaying function [1/(1 + TrS)] of the schedule training rate in Equation (3). Finally, in Equation (4) the actual level of skill level is shown as the accumulation onto its previous level, function (1/S) of the training completion rate less

present skill loss rate. These equations can be written down

directly from Figure Al using the difference equations.

Equations

SKG = DLSKP - ALSKP (1)

where SKG = current skill gap; DLSKP = desired level of skill pool; and ALSKP = actual level of skill pool.

TRATE = SKG. () + FSKLR (2)

where: TRATE = training rate; and FSKLR = forecast skill loss rate.

TCRATE = TRATE 1 +

Tr S (3) (I1 + Tr S

where TCRATE = training completion rate.

ALSKP = (s) . (TCRATE - PSKLR) (4)

where PSKLR = present skill loss rate.

FSKLR = PSKLR . 1 ) (5) (1 + Ta

- S)

Equations (1) to (5) are solved to develop the actual level of the skill pool/present skill loss rate transfer function (Equa- tion 6), and actual level of skill/training completion rate

(Equation 7) as shown in the following: Actual level of skill pool

Present skill loss rate

T[ r ? rTa) " S

r TaS2 ](6) - (1 + TaS)(1 +

TiS +

TiTrS2)J (

Training completion rate Present skill loss rate

1 + (Ti + Ta) '

S

(1 + TaS)(1 + TiS + TiTrS2)

Equations (6) and (7) are extremely useful in understanding how the two parameters Ti and Ta, to be set by the system

designer, interact and affect the actual level of skill loop dynamic recovery pattern. If the feed-forward component is removed, so that the control law is actual level of skill pool, the application of the Final Value Theorem shows that there is a steady-state skill deficit of Ti for a sudden unit change in

present skill loss rate. With the feed-forward component added, it may be similarly shown that this deficit is elimi- nated. Equations (6) and (7) are the form required if the

recovery is to be calculated via standard Laplace Transform Tables.

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Received July 2001; accepted August 2002 after one revision