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Presented to: Relevant to any People Leader Date: 09/Nov/2011 Location: NA Span of Control – Quantitative Approach to Relationships Span of Control – Quantitative Approach to Relationships

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A FieryAir Venture Slide:2 Definition - RelationshipsDefinition - SOCCalculation - RelationshipsApplication - Relationships Definition of: Span of control Supervisor Subordinate The scope of activities and inter-relation between a Supervisor and the Subordinates Definition of: Span of control Supervisor Subordinate The scope of activities and inter-relation between a Supervisor and the Subordinates Agenda – Span of Control, Quantitative Approach

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A FieryAir Venture Slide:3 Definition - RelationshipsDefinition - SOCCalculation - RelationshipsApplication - Relationships Definition of three kinds of Relationships managed by a Supervisor: (DSR) Direct Single Relationships (CIR) Cross Individual Relationships (DGR) Direct Group Relationships Definition of three kinds of Relationships managed by a Supervisor: (DSR) Direct Single Relationships (CIR) Cross Individual Relationships (DGR) Direct Group Relationships Definition of: Span of control Supervisor Subordinate The scope of activities and inter-relation between a Supervisor and the Subordinates Definition of: Span of control Supervisor Subordinate The scope of activities and inter-relation between a Supervisor and the Subordinates

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Agenda – Span of Control, Quantitative Approach A FieryAir Venture Slide:4 Definition - RelationshipsDefinition - SOCCalculation - RelationshipsApplication - Relationships The Formulas to calculate the three kinds of Relationships that a Manager handles. The basic inputs being the number of Subordinates a Supervisor controls. It has been devised by Graicunas, a Management Consultant in 1933. We would discuss him at end. The Formulas to calculate the three kinds of Relationships that a Manager handles. The basic inputs being the number of Subordinates a Supervisor controls. It has been devised by Graicunas, a Management Consultant in 1933. We would discuss him at end. Definition of: Span of control Supervisor Subordinate The scope of activities and inter-relation between a Supervisor and the Subordinates Definition of: Span of control Supervisor Subordinate The scope of activities and inter-relation between a Supervisor and the Subordinates Definition of three kinds of Relationships managed by a Supervisor: (DSR) Direct Single Relationships (CIR) Cross Individual Relationships (DGR) Direct Group Relationships Definition of three kinds of Relationships managed by a Supervisor: (DSR) Direct Single Relationships (CIR) Cross Individual Relationships (DGR) Direct Group Relationships

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Agenda – Span of Control, Quantitative Approach A FieryAir Venture Slide:5 Definition - RelationshipsDefinition - SOCCalculation - RelationshipsApplication - Relationships There are various ways that the concept of SOC can be put to use for enhancing Management role and comparing current and future workload of Supervisors. We would try discussing the same as case studies. There are various ways that the concept of SOC can be put to use for enhancing Management role and comparing current and future workload of Supervisors. We would try discussing the same as case studies. Definition of: Span of control Supervisor Subordinate The scope of activities and inter-relation between a Supervisor and the Subordinates Definition of: Span of control Supervisor Subordinate The scope of activities and inter-relation between a Supervisor and the Subordinates Definition of three kinds of Relationships managed by a Supervisor: (DSR) Direct Single Relationships (CIR) Cross Individual Relationships (DGR) Direct Group Relationships Definition of three kinds of Relationships managed by a Supervisor: (DSR) Direct Single Relationships (CIR) Cross Individual Relationships (DGR) Direct Group Relationships The Formulas to calculate the three kinds of Relationships that a Manager handles. The basic inputs being the number of Subordinates a Supervisor controls. It has been devised by Graicunas, a Management Consultant in 1933. We would discuss him at end. The Formulas to calculate the three kinds of Relationships that a Manager handles. The basic inputs being the number of Subordinates a Supervisor controls. It has been devised by Graicunas, a Management Consultant in 1933. We would discuss him at end.

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Span of Control – Definition A FieryAir Venture Slide:6 Span of Control is defined as the Ratio of Subordinates to one Superior. In the following sections we would discuss the relationship between the following elements: Span of Control Relationship Management for a Supervisor Potential Relationships a Supervisor has to manage due to the Span s/he is handling Quantitative approach to the Relationship Management by a Supervisor In the following sections we would discuss the relationship between the following elements: Span of Control Relationship Management for a Supervisor Potential Relationships a Supervisor has to manage due to the Span s/he is handling Quantitative approach to the Relationship Management by a Supervisor The term Supervisor would mean an individual who: Leads a group of individuals for a certain purpose (that may change over a period) Gets reported directly by this group of individuals Has definite goals for each individual reporting to her/him and for the group as an entity The term Supervisor would mean an individual who: Leads a group of individuals for a certain purpose (that may change over a period) Gets reported directly by this group of individuals Has definite goals for each individual reporting to her/him and for the group as an entity The term Subordinate would mean an individual who: Reports to a particular superior for a particular purpose Follows defined timelines set by the superior Works towards achieving set goals individually and contributes to the team goals The term Subordinate would mean an individual who: Reports to a particular superior for a particular purpose Follows defined timelines set by the superior Works towards achieving set goals individually and contributes to the team goals

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Relationships a Supervisor handles A FieryAir Venture Slide:7 Direct Single Relationships (DSR) The relationship between a Supervisor and individual Subordinates Sup Sub1Sub2Sub3 DSR1 DSR2 DSR3 Definition (DSR) A Supervisor has to manage her/his direct relation with each individual in her/his team. Thus, the Supervisor Sup in our example is managing three relations with his subordinates, Sub1, Sub2 & Sub3. The three relations managed by Sup here are: DSR1 DSR2 DSR3 Definition (DSR) A Supervisor has to manage her/his direct relation with each individual in her/his team. Thus, the Supervisor Sup in our example is managing three relations with his subordinates, Sub1, Sub2 & Sub3. The three relations managed by Sup here are: DSR1 DSR2 DSR3

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Relationships a Supervisor handles contd… A FieryAir Venture Slide:8 Cross Individual Relationships (CIR) The relationship between each individual subordinates, in both ways. Definition (CIR) A Supervisor has to manage the inter-relations between each individual in her/his team. Thus, the Supervisor Sup in our example is managing six inter-relations within his subordinates, Sub1, Sub2 & Sub3. The six inter-relations managed by Sup here are: CIR1 CIR2 CIR3 CIR4 CIR5 CIR6 Definition (CIR) A Supervisor has to manage the inter-relations between each individual in her/his team. Thus, the Supervisor Sup in our example is managing six inter-relations within his subordinates, Sub1, Sub2 & Sub3. The six inter-relations managed by Sup here are: CIR1 CIR2 CIR3 CIR4 CIR5 CIR6 CIR1 CIR2 CIR3 Sub1 Sub2 Sub3 Sup CIR4 CIR5 CIR6

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Relationships a Supervisor handles contd… A FieryAir Venture Slide:9 Direct Group Relationships (DGR) The relationship between Superior and combination of subordinates. Definition (DGR) A Supervisor has to manage her/his group-relations between each group of individuals in her/his team. The number of groups would be a result of each possible combination that can occur with the subordinates. Thus, the Supervisor Sup in our example is managing nine group- relations within the group of subordinates, Sub1, Sub2 & Sub3. The nine group-relations managed by Sup here are: Definition (DGR) A Supervisor has to manage her/his group-relations between each group of individuals in her/his team. The number of groups would be a result of each possible combination that can occur with the subordinates. Thus, the Supervisor Sup in our example is managing nine group- relations within the group of subordinates, Sub1, Sub2 & Sub3. The nine group-relations managed by Sup here are: Sub1Sub3 Sub1Sub2 Sub3Sub1Sub2 Sup Sub1Sub2 Sub3Sub2 Sub3Sub1 Sub3Sub2 Sub3Sub1Sub2 Sub3Sub1Sub2 DGR1 DGR2 DGR3 DGR4 DGR5 DGR6 DGR7 DGR8 DGR9

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Next step after the Theory… A FieryAir Venture Slide:10 Calculation & Application After defining the theory of Relationships a Manager handles, we would discuss the practical aspect of the same. There are two aspects to Practicality of this Theory: Calculating the number of relationships of each kind a Manager handles Applying the Theory and the Calculation to Practical life in office Calculation & Application After defining the theory of Relationships a Manager handles, we would discuss the practical aspect of the same. There are two aspects to Practicality of this Theory: Calculating the number of relationships of each kind a Manager handles Applying the Theory and the Calculation to Practical life in office DSRCIRDGR

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Calculating DSR A FieryAir Venture Slide:11 Calculating Direct Single Relationships DSR is the easiest to calculate. It is equal to the number of Subordinates a Supervisor has. Assumption: Number of Subordinates = n Formula: DSR = n Calculating Direct Single Relationships DSR is the easiest to calculate. It is equal to the number of Subordinates a Supervisor has. Assumption: Number of Subordinates = n Formula: DSR = n

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Calculating CIR A FieryAir Venture Slide:12 Calculating Cross Individual Relationships CIR calculation is not tricky, and the formula finds out the exact number of cross relation a manager handles in her/his team. Assumption: Number of Subordinates = n Formula: CIR = n x (n-1) Calculating Cross Individual Relationships CIR calculation is not tricky, and the formula finds out the exact number of cross relation a manager handles in her/his team. Assumption: Number of Subordinates = n Formula: CIR = n x (n-1)

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Calculating DGR A FieryAir Venture Slide:13 Calculating Direct Group Relationships DGR calculation is little tricky, and the formula finds out the exact number of group relation a manager handles in her/his team. Assumption: Number of Subordinates = n Formula: DGR = n x (2n/2-1) Calculating Direct Group Relationships DGR calculation is little tricky, and the formula finds out the exact number of group relation a manager handles in her/his team. Assumption: Number of Subordinates = n Formula: DGR = n x (2n/2-1)

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Sum of all Relationships A FieryAir Venture Slide:14 Total number of relationships The total number of relationships handled by a Superior would then be a sum of DSR, CIR & DGR. However, there is another formula to calculate the total number of relationships without calculating DSR, CIR & DGR separately, if required: The formula is: n*(2 n /2+ n -1) Calculating the figures using an example… Total number of relationships The total number of relationships handled by a Superior would then be a sum of DSR, CIR & DGR. However, there is another formula to calculate the total number of relationships without calculating DSR, CIR & DGR separately, if required: The formula is: n*(2 n /2+ n -1) Calculating the figures using an example… To view the live example of above theory, please open the embedded Excel file at right to have the formulas and calculations already set up for you in an Excel File… To view the live example of above theory, please open the embedded Excel file at right to have the formulas and calculations already set up for you in an Excel File… A chart in the embedded Excel File based on the table demonstrates that, as the number of subordinates increases past four, the complexity of the relationships increases exponentially. This owes primarily to an increase in the number of DGR created by adding a member to an existing group. For example, adding a fifth subordinate roughly doubles complexity, increasing the total direct plus cross relationships from 44 to 100. Adding a sixth subordinate more than doubles complexity again, increasing the number of relationships from about 100 to 222. For 12 subordinates, the total number of relationships that might demand a superior's attention is an astounding 24,708!

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Practicality & Applicability A FieryAir Venture Slide:15 There is nothing which rots morale more quickly and more completely than poor communication and indecisiveness -- the feeling that those in authority do not know their own minds. And there is no condition which more quickly produces a sense of indecision among subordinates or more effectively hampers communication than being responsible to a superior who has too wide a span of control - Lyndall F. Urwick (Pg 43 of article, "The Manager's Span of Control" published in May-June 1956 issue of Harvard Business Review) There is nothing which rots morale more quickly and more completely than poor communication and indecisiveness -- the feeling that those in authority do not know their own minds. And there is no condition which more quickly produces a sense of indecision among subordinates or more effectively hampers communication than being responsible to a superior who has too wide a span of control - Lyndall F. Urwick (Pg 43 of article, "The Manager's Span of Control" published in May-June 1956 issue of Harvard Business Review) Practicality of quantifying SOC SOC affects the cost A wider SOC, as in the above statement, at times creates unrest among the subordinates. However, a wider SOC ensures lower cost of management. Though, the significance lies is comparing the cost of poor quality of output of the team against cost of maintaining thinner SOC. Because, as a thumb rule, thinner SOC ensures lesser number of relations that a superior manages and therefore, efficient output. SOC affects subordinate morale As discussed above, a wider SOC at times creates unrest in subordinates as the superior has a visible span of large number of subordinates and it exposes her/his ability to do People Management. Even a Super Efficient supervisor would have a hard time to handle 10 subordinates where s/he is actually handling a total of 5210 relationships (DSR+CIR+DGR). SOC behaves typically for different industries Affording a wider or a thinner SOC depends on the kind of industry as well. In an industry where the output is co-dependent on machines (for e.g. manufacturing), a wider span of control can be afforded. However, in service industry as ours, thinner SOC results better as in service industries, the output is dependent on the human resource only. Therefore, managing human relations and inter-relations are more significant SOC varies with hierarchy For any kind of industry, the general approach should be thinning the SOC towards the bottom of hierarchy. The justification being, at the top of hierarchy, the superior has to manage fewer number of ancillary tasks and major number of human relations. Thus, the people management becomes easier. However, at the lower levels, the transaction management also becomes as important as human resource management. Thus, managing the total number of relationships (DSR+CIR+DGR) becomes difficult. SOC is highly dependent on the culture of the kind of organization and industry. It can be used judiciously to control the cost and output of the organization and define the optimum mix so that there is a maximization in earning. Practicality of quantifying SOC SOC affects the cost A wider SOC, as in the above statement, at times creates unrest among the subordinates. However, a wider SOC ensures lower cost of management. Though, the significance lies is comparing the cost of poor quality of output of the team against cost of maintaining thinner SOC. Because, as a thumb rule, thinner SOC ensures lesser number of relations that a superior manages and therefore, efficient output. SOC affects subordinate morale As discussed above, a wider SOC at times creates unrest in subordinates as the superior has a visible span of large number of subordinates and it exposes her/his ability to do People Management. Even a Super Efficient supervisor would have a hard time to handle 10 subordinates where s/he is actually handling a total of 5210 relationships (DSR+CIR+DGR). SOC behaves typically for different industries Affording a wider or a thinner SOC depends on the kind of industry as well. In an industry where the output is co-dependent on machines (for e.g. manufacturing), a wider span of control can be afforded. However, in service industry as ours, thinner SOC results better as in service industries, the output is dependent on the human resource only. Therefore, managing human relations and inter-relations are more significant SOC varies with hierarchy For any kind of industry, the general approach should be thinning the SOC towards the bottom of hierarchy. The justification being, at the top of hierarchy, the superior has to manage fewer number of ancillary tasks and major number of human relations. Thus, the people management becomes easier. However, at the lower levels, the transaction management also becomes as important as human resource management. Thus, managing the total number of relationships (DSR+CIR+DGR) becomes difficult. SOC is highly dependent on the culture of the kind of organization and industry. It can be used judiciously to control the cost and output of the organization and define the optimum mix so that there is a maximization in earning.

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Graicunas. A FieryAir Venture Slide:16 The Graicunas formula is named after V.A. Graicunas, who gave a mathematical formula to explain the complexity of span of control if more subordinates are added to the executive. Every executive 'always measures the burden of his responsibility to control the subordinates in terms of single relationship between himself and his subordinates. Graicunas feels that in any group, the relations between executive and his subordinates cannot just be calculated based on single relationship alone. According to him, there also exists cross relationships which increase in mathematical proportion. The direct single relationship always increase in the same proportion as the number of subordinates. In such a case each addition to t h ~ I, group would only create a single direct relationship. But according to Graicunas there also exists direct group and cross relationships which increase very rapidly than the 1I1 increase in the number of subordinates. This is n~a because the addition of each \ !/ individual results in many cross and drrett group relationships as there are persons already in the group. Therefore, the number of relationships increases in exponential proportion. Based upon his studies, Graicunas develops a formula to calculate the /I/ number of relationships to enable the executives to-examine the complexity of span of control. According to these formula, in any organization if there are three subordinates direct single relationships would be three, cross relationships six and direct group relationships nine. But if one more member is added there would nor be any change in the direct single relationships which would be four, but the cross relationships would increase to 12 and direct group relationship, however, rise exponentially to 28. This explains that addition of each member to the group under the control of the executive would increase the number of direct group relationships to such an extent that direct contribution becomes difficult in some cases even impossible. Graicunas also added that for subordinates it is clhite easy to grasp and remember every combination of groups. But from five on, it is not possible to remember because the relationships become more of confusion. When the x principle enunciated by Graicunas is valid or not, whether the formulae has empirical validity or not, the problem that any increase in the number of subordinates would lead to complexity in the relationships between the individual and groups has aptly been brought out by Graicunas. It is this factor that needs to be carefully considered in any discussion on how many subordinates an executive can effectively control. www.nickols.us/graicunas.pdf http://en.wikipedia.org/wiki/Graicunas_formula http://en.wikipedia.org/wiki/Span_of_control www.jstor.org/stable/254987 www.bus.lsu.edu/bedeian/articles/VGracunias-AMJ1974.pdf

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K. S. Alok Ranjan +91 9810 77 5457 | +91 124 4118792 A FieryAir Venture Slide:17

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