A Production Function for Organizations Doing Case Work - Beckmann, Martin J. (Management Science, 1982)
This paper examines the contribution of supervisors to an organization's output by constructing a production function in which supervisors' time and case workers' time enter as inputs. There is a quality variable associated with output: average delay. The functional form of the production function is derived for the simplest possible type of queuing model, but the method can be applied to other specifications of the queuing process and of the quality variable. Such a production function can be used to determine the most cost effective span of control. The model is extended to obtain a multi-factor production function for multi-level organizations. Numbers from a welfare agency are used as illustrations but no empirical validation is attempted.