use the graicuans formula to calculate the number of relationship when there are 4 subordinate in a department?
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In this article we will discuss about the Graicunas theory on the span of management.
V.A. Graicunas a French management Consultant, made a study on superior-subordinate relationship, however, not based on empirical observations. He developed a mathematical formula to analyse this relationship. He suggested that the number of possible relationships increases with the number in the number of subordinates.
Graicemas has identified three specific kinds of superior-subordinate relationships in every organisation and leading to the question as to the number of subordinates which a superior can effectively manage.
They are:
1. Direct Single Relationship:
This refers to relationships that are easily and clearly recognized by the individuals who are his immediate subordinates. They are equal to the number of subordinates supervised. For example, if A has three subordinates, there would be three direct single relationships. This has been identified as Number of direct relationships = n.
2. Direct Group Relationships:
This means the group relationships between the superior and each possible combination of subordinates. A manager has occasions to consult, confer, advise, inform or discuss with every subordinate or any number of them or all of them in attendance. This type of relationship arises between the superior and his group of subordinates in all possible combinations.
Example: A manager having three subordinates would have three direct group relationships.
Formula = n (2n-1 -1) where n represents the number of subordinates.
3. Cross Relationship:
Cross relationships are mutual relationships among subordinates necessary for working under the same superior. This result from the need of the subordinates of a common superior to consult with one another.
Resulting from the above analysis of the three kinds of relationships, Graicunas developed the following formula to give the total number of all the three kinds of relationships where n = number of subordinates.
n(2n/2 + n + 1)
The significance of Graicunas contribution is that he initiated the principle of restriction of the span of delegated authority on account of maximum limit to the potential burdens set up simply by innate limitations of the capacity of human mind. From this analysis he deduced a ‘reasonable span’ restricted to five or six subordinates. Thus he stimulated thinking on this aspect of organisation structure which, later on, became the subject of much discussion in management literature.
Though Graicunas gave mathematical formula for finding out the number of relationships, his approach suffers from the following shortcomings:
(a) Mathematical precision of the formula is debatable. Relationships increase with the increase hi the number of subordinates but not in a precise formula.
(b) Graicunas has ignored the frequency of relationships and the strain they generate.
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