Application of queuing theory to the "span of control"

by L. S. Hill

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A study of the supervisor-worker relationship as a waiting-line situation where the supervisor is the service unit. Generation of the waiting line is a stochastic process. If there is too much demand on the supervisor, there is an excess of worker waiting time. With too little demand, there is too much idle server time. Too many subordinates may mean loss of adequate control. Too many supervisors may be a costly extravagance and may also create too many organizational levels, thereby increasing the difficulties of communication. The idea is to seek a tradeoff between worker waiting time and supervisory costs. The cost model presented can be used to estimate the span of control for varying service times and cost inputs. Factors influencing the service time are taken into account. The model is predicated on finite queuing theory. 34 pp.

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