Abstract
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.
Highlights
For managing service, production and supply chain systems, understanding queueing systems is critical
The research method used in this study involved the modification and addition of assumption conditions in the queuing theory; the conditions were modified to imitate the concepts behind the ‘production function’ and ‘cost function’ in microeconomics
Hierarchy parameters H: organization level, with Hth representing the top level of the organization. s: average case completion rate, defined as the service level of an organisation. k: average number of cases received in the organization per unit time, representing the average case arrival rate. wk: wage rate of an employee at the kth level. lk: number of cases completed by an employee at the kth level, k 1⁄4 1, 2, . . . , H. hk: average proportion of a kth case relative to all cases in the inventory, k 1⁄4 1, 2, . . . , H
Summary
Production and supply chain systems, understanding queueing systems is critical. This study applied queueing theory in the context of operations research to present the production and cost functions of an organisation implementing case work. The research method used in this study involved the modification and addition of assumption conditions in the queuing theory; the conditions were modified to imitate the concepts behind the ‘production function’ and ‘cost function’ in microeconomics. This method was used to establish the production and cost functions for the ‘optimal hierarchical structure of the case work implementation organization’
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