Employee business at various levels of a hierarchy for organisations completing case work

This article describes a model for examining the contribution of supervisors to an organization by considering the case work they complete as a production system. The average delay in case work is referred to as the service level. At a given service level, the minimization of total wages within one hour can be studied as a cost function. With this cost function, wage spending on handled-case time and idle time can be formulated. The ratio between the handled-case time and idle time of all employees at the kth level within 1 hour is defined as the ‘busy index’ at the kth level. From the optimal hierarchical structure, we find the following two properties: (1) Given any two levels i and j, the ratio between the idle times of ith and jth levels is independent not only of the service level but also the rate of arriving cases; and (2) At each level, the busy indices are proportional to the square root of each level’s wage rates. This implies that the busy indices decrease with the hierarchical level. Ultimately, when the wage rates at all levels are equal, the increment also becomes equal.