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ABSTRACT

The human mind is amoebic in nature, responding constantly to external stimuli. For a given stimulus, the response of a human mind, or an individual for clarity, at different times may be different. Since each human mind is a unique entity, the stimulus-response equation is necessarily akin to a non-deterministic finite automaton. We shall provide reasons for such an inference later. Often, understanding the possible responses and potential problems can significantly contribute to better human resource management.

Successful human resource management is often the key to successful projects and with a bit of-management foresight, success can be ensured.

1. INTRODUCTION

The human mind is amoebic in nature, responding constantly to external stimuli. Since each human mind is a unique entity, the stimulus-response equation is necessarily akin to a non- deterministic finite automaton. We shall provide reasons for such an inference later. For a given stimulus, the response of a human mind, or an individual for clarity, at different times may be different. The set of stimuli and responses itself can be assumed without any loss of generality.

We draw heavily from the theory of automata to mathematically define the problem of human resource management. We shall' also provide an abstract solution as a framework that would attempt to streamline the solution, if not solve the problem in question.

The discussion opens up the possibility of human resource management to be treated as a central aspect of the larser issue of project management.

The discussion would however be based on managing computerisation projects per se, however, we feel that with little modification or customisation, this would address a larger interest.

The narrow view of management as striving only toward profitability is obsolete. The efficiency, productivity and effective human relations are factors that have become equally important and these bear a direct relation with individual professional satisfaction. This would eventually contribute to the profitability.

We try to provide certain objective mechanisms for approaching the problem of the human resource management issue.

To determine the actual response for a given stimulus at any instant is non- trivial. Therefore, it is simple to visualise the complication in determining a collective response from a set of individuals for the same stimulus: Mathematically though, this would seem a lot simpler. We use certain notations in the following discussion which are explained in section 2 .

Let

H = ( h I h is an individual

s = ( s I s is a stimulus 1

R = ( r I r is a response 1

We now define a transition function :

- 1

which suggests that the response of an individual for a stimulus maps to the entire set of responses as suggested earlier. Extending this definition for obtaining a collective response for the same stimulus from the set of individuals, we have :

( (H.s) 1 ---> R

( (h,sl 1 ---> R

- 2

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we further extend this notion to obtain the following :

( (Ens) 1 --> - 3

which suggests that the response of the set of individuals for the set of stimuli maps to the set of, responses. This follows from the definition of set union and 1 & 2 above. That is, the set of responses for all individuals for a given set of stimuli is the same.

Equations 1, 2 and 3 are based on the fundamental assumption that the set of stimuli is finite, and consequently the set of responses. This assumption is not unjustified because ret.1 world problems invariably fall under this category. Within the scope of real world problems, the set of stimuli would correspond to the requirements, directives and tasks to be performed. Re s p on s e s wou 1 d c o r respond to compliance, actions and goals.

The three equations reveal that with certain constraints on the individuals or stimuli, several possible responses from 1 and 2 can be eliminated, thereby facilitating the determination of a collective response. The basis for such an inference is the fact that the overall objective(s) of the project are well defined. Therefore, despite a certain amount of uncertainity about the responses, the elimination ( of most responses that tend to deviate greatly ) exercise can be conducted fairly accurately.

Management of human resources falls within the purview of the above definitions. We attempt to provide certain objective mechanisms for this management issue, and provide certain discussions on the necessity of not looking at human resource management as an isolated issue, but as a part of the larger issue of project management.

Successful human resource management is often the key to successful projects and with a bit of management foresight, success can be ensured.

2. DBFnmrIOlrS

In this section, we provide certain definitions and eplanations for the notations introduced in the previous section and those that will be introduced subsequently.

2-1 Individual : An individual is de- fined as E human mind ( a human being to be precise ) that would participate in the project and which needs to be manaqed .

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2.2 Stimulus : A stimulus is defined as an input, provocation or directive ( generated by the environment or a project manager ) to which the individu- al has to respond.

2.3 Req"? : A response is.defined as an output, reaction or action that the individual takes as a consequence of receiving a stimulus.

2.4 Mon-deterdnistic F i n i t e =ta ( "FA ) : This phrase is borrowed from the theory of computation and is defined in section 3. The definition of the Deterministic Finite Automata ( DFA ) also follows from the same.

2.5 X = ( x I x is a ... ) : This state- ment stands for "X is set of all x such that x is ...". 2.6 (x ,y ) --> z : This statement stands for the item x subjected to the stimulus y yielding response z. By extending this we have { (x,y) ) as the set of all possible pairs of

2.7 W ( h ) : The weight associated with every individual. This weight has to be assigned by the project manager and can be altered over time as the project manager's interaction with the individual lets the manager judge the individual better. Weights necessarily have to take into consideration the individual's qualifications, expertise, inter-personal relations, experience and other attributes such as dedica- tion, confidence level etc.

2.8 W ( h ) ( r ) : The weight associated with a specific response for each individu- al. This weight would be determined only as the interaction between the individ- ual and the manager continues. As above, this also hlust undergo change over time .

x and y.

The cumulative response for a given stimulus for the set of individuals would be :

Sum( W ( h ) ( r ) for all h ) - 4

2.9 W ( p ) : The weight associated with the project manager. In case of a technical manager, this weight can be judiciously self-assigned, judicious because the weights would normally be not revealed by anyone. In case of a non-technical manager, this could be the highest weight assigned to any of the individuals.

2.10 State : A state can be defined as a situation where the exact staus of the project s progress can be quantified in some form. Also, indirectly this would refer to the sequence of re-

sponses already obtained from the indi- viduals for the sequence of stimuli encountered. This would also mean that any response forced on an individual to keep the project interests would get reflected. Refer section 4.

2.11 Transition Function : The transi- tion function can be defined as the progress of the project from one state to another state.

3. THE PROBLEM DEFINITION

We had stated earlier that the .set of responses for all individuals for a given set of stimuli is the same without giving an explanation or sufficient justification. The statement is not true in general. If the question is restricted to project management alone with its avowed goals acting as constraints, the statement can safely be regarded as true.

Because, the ultimate aim is to sustain the progress of the project, despite individual responses tending to differ. Further, the stimuli can be mapped to the various actions and alternatives available to the project team. The responses can be mapped to the various decisions, milestones and goals or deliverables. These responses can be termed for our purpose as states ( see 2.10 ) where the project initiation would act as initial state. From among these states, some ( corresponding to deliverables ) can be considered as final states or terminal responses. Some of these states may correspond to certain milestones, we would term them intermediary responses or states. If the equations 1-4 can be regarded in some crude form as a grammar, we have the following definition of the question at hand as an NFA, as a 5-tuple :

( States, Stimuli / Inputs, Transition F’unction, Initial State , Final states ) - 5

Several bottlenecks are apparent from this definition. Identifying the states and from them the final states may seem simple as they could correspond to the milestones and deliverables of the project . The non-determinism in the context of project management arises from the inherent human factors as explained while arriving at equations 1-3.

The solution therefore is to remove this non-determinism to some extent by formulating the transition function so as to obtain, on the right hand side of the equations 1-3. a unique value,

instead of a set of values. Ironically, this transition function is not easy to arrive at, fior can it be a unique universal function. This, for the same reasons emphanised in eplaining the non-determinism. Often, circumstances and experience would be the key to identify the solution.

4. Aw W C T SOIJJTION

At the outset, it is essential to untlerstand that a concrete solution is not possible, but We attempt to provide a frarevork which could be adapted to form solutions, albeit on a case to case basis. Often, circumstances and experience would be the key to identi- fyirig the solution.

As mentioned section 3 , the solution exists in removing the non-determinism, atleitst to some extent by formulating the transition function to obtain a unique response for a given stimulus from the set of individuals, or the project team. This unique response may have to be forced on certain dissentlng individuals in certain cases as explaifled below.

The approach we propose would be similar to that followed in converting an NFA to a OPA. The set of original states are converted into a different set of states. But unlike in the case of the NFA conversion in computation theory, we introduce the concept of new states as distinct subsets or groups of individuals. In the original approach, a state can be part of more than one of the new states. We exempt the project manager from this restriction and make him a part. of all the subsets. Recall the definition of a state ( section 2.10 ) . How does this approach remove the non- determinism as the responses of individuals within these subsets may differ? Or more import.antly, how does it ensure that a ( new ) state would give a unique response as required. This seems to be the original problem with reduced number of individuals to deal with.

Recall that the fundamental aim is to sustain the progress of the project . Therefore, from the possible different responses from the individuals within a group, or this new state we have formed, we have to select one response which would be the representative response.

This representative response would thus give US a single response for a subset

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of the original team. This exercise can be replicated by forming thQs second level subset of individuals 8yom the first level subsets of individua4g.

The representative responses are qxrived at on the basis of the weights associated with the individual responses. In case the cumulative weights for different responses causa a tie, the manager's response from a m q g these responses would form the representative response.

The only bottleneck in this mechanism would be the number of discrete responses that would emerge from within a group. In any case, this should not be our original set of responses R.

The following observations are important:

- In case the manager has subjected more than one group to the same stimulus, one response is chosen from each group as described above, and from these responses a representative response is chosen.

- The major constraint therefore is to identify cohesive groups, so that the number of individual responses from within each group remains restrict- ed. This is a temporal issue.

Once the conflict ( of individual interests ) is solved, all those individuals with a different response must be reset to the reflect the representative response, thereby altering the state in which the individual would have been otherwise.

The reasons that make this solution an abstract one are :

- It is not a universal solution. - The partitioning of the set of individuals into disjoint groups is not definite or fool-proof, nor can there be a universal deciding factor. This partitioning would depend on the manager's knowledge of the individual response factors, and consequently from the original argument of an amoebic mind, temporal.

This implies that cohesive groups would get formed over time depending on the changing weightage factors mentioned before. This in turn necessitates that the weightage factors must undergo change and hence the groups.

- Assigning the different weights is non-trivial, though a thumb rule for initial assignment can take the form :

W(h) Risk / Respamsibility on the individual - 6

Snr( W ( h ) ( r ) = 1 - 7

Equation 7 indicates the possibility of considering the weights as probabilities, which opens up several avenues for experimentation.

The abstract solution we have presented is not concrete as mentioned earlier. However, it identifies a broad framework with ample scope for experimentation. The subject of human resource management is not a definite science, and hence subject to several interpretations and consequently results.

m e issue that has been highlighted khough is the formation of cohesive grqups. The next section deals with this in slightly more detail.

5 - a x x " G A n D T A s K ~ m

The principal problem highlighted in the previous section, that of judiciously forming the groups can usually be solved with a lot of reflection on individual behaviourial aspects such as ethical and professional values along with the inter-personal relations of the individuals. Often, these issues would becvme clear after a couple of sensitive discussions and individual perspectives become clear.

It would then be a trivial exercise to identify potential grouping of the individuals. An elementary mechanism would be to analyse the responses of the individuals to a fixed set of stimuli, say in the form of a questionnaire. This can be a potential deciding factor. It is ironical though that in modern management based on the scientific management philosophy, ethical and professional are not given enough importance.

Tne emphasis of the scientific management philosophy is on the prosperity of business. Our suggestion deviates from this philosophy, in that we try to achieve this through other means by shifting the emphasis from the prosperity factor alone.

We lay a lot of emphasis on the issues of ethics and professional values, even though this may not be to business interests per se. However, this promotes the individual interests and provides motivation and satisfaction which would eventually lead to improved productivity.

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The formation of groups, as mentioned is a temporal function and is dependant not only on the information gathered ( by the project manager ) over time as emphasised before, but also on the other factors as mentioned above.

Task allocation should be the next stage of grouping, though both these activities complement each other. Task allocation would depend upon the background, expertise of individual members etc. This information would aid in deciding the nature of activity that a particular group or individual is better suited for, with sufficient provisions made to avoid the monotony of working on similar things too often.

The above facts would ensure the proper participation of the entire project team, thereby increasing the overall productivity of the team. This in turn, would lead to achieving the goals and make the business a success. The above discussion tends to be more philosophical, but its significance cannot be overlooked.

6. CONC.UlSION

Our discussions and proposals can be widely contested. We admit that the solution proposed is abstract , and leaves a lot of room to indentify loopholes and modifications. Our aim was just to provide the framework for such an exercise, as the issue of human resource management is very subjective. And any attempt to streamline such an important field, several viewpoints are to be considered.

On one hand is the scarcity of well trained, high quality workers and on the other is the deteriorating motivation and commitment factors. Add to this the uncertainities involved. The solution to this problem is the biggest challenge for human resource managers. A number of old paradigms of management need to discarded or reoriented to meet this challenge.

REFERENCES

[l] Francois Lustman, Managing Computer Projects, Reston Publishing Company Inc, 1985.

Engineering - A Practitioner's Approach, McGraw Hill, 1987.

[ 3 ] C. A. Ellis etc., "Groupware : Some Issues and Experiences" , Communications Of The ACM, Vol 34, No 1, pp 38-58.

[2] Roger S. Pressman, Software

[ 4 ] Thomas D. Clark Jr, "Corporate Systems Management : An Overview and Research Perspective" , Communications Of The ACM, Vol 35, NO 2, pp 60-75.

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