The Optimum Span of Control in a Pure Hierarchy

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Abstract
This is a model of a pure hierarchy which oversees a given number of productive units. Its aim is to minimize costs, which are the sum of wage costs and costs caused by delays in decision making. The advantage of the model is that it permits the calculation of an optimum formal structure of the hierarchy in terms of the span of control at different levels. The general result is that spans of control should increase as one goes down the levels of the hierarchy. However, when time savings become more and wage costs less important, the difference between the optimum spans of control shrinks; in the limit, when wage costs are not considered at all, they become equal. These results support the findings of some empirical studies: there is evidence for increasing spans of control in business organizations, while in armies, where cost considerations are secondary, spans of control tend to be more uniform.

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