Queues and Hierarchies

Abstract

This paper examines the optimal structure of hierarchies when workers differ in the range of tasks they can perform. A hierarchical system may reduce costs by allowing most tasks to be handled by unskilled workers. This may however increase delay for those tasks which must pass through several layers before reaching the appropriate level. The paper characterises an optimal hierarchy when such a trade-off exists. Organizations typically have a hierarchical structure. In recent years, economists have investigated a number of explanations for this, for example the need to monitor workers,' the desire to exploit parallel processing by having agents work simultaneously on a project,2 the need to coordinate decisions,3 and so on. This paper explores another explanation for the prevalence of hierarchies: the desire to economize on skilled workers. A firm typically has many problems flowing in that require decisions, many of which do not need the attention of senior management. By employing relatively unskilled workers to deal with tasks initially, one may therefore be able to employ relatively few senior managers. For example, in a shop most customer queries can be dealt with by low-paid assistants, with only the more important problems passed on to supervisors. The drawback of such a hierarchy is that it may delay some decisions by making them pass through more than one layer of control rather than being dealt with immediately. The paper aims to explore the implications of this trade-off between cost and delay for the structure of hierarchies. There are of course many aspects of hierarchies. This paper focuses on a particular one which has been previously neglected. In the model considered, workers differ in their ability to make decisions. Abler workers are capable of making (good) decisions in a wider range of tasks than less able ones. There is no horizontal specialization into different jobs and so the only motivation for employing less able workers is that they command lower wages. Tasks pass through the levels of the hierarchy until they can be dealt with. Software support fits this framework well. Typically, when one contacts a company because of a problem with a package, the enquiry is initially dealt with by low-level staff. If they cannot solve the problem, they hand it on to the next level, who in turn hand it on to the next level if they cannot solve it and so on until it is dealt with. A large number of levels may create considerable delay. Similarly in hospitals in the U.K., routine deliveries of babies are usually dealt with by mid-wives. A junior doctor will be brought in if there is a problem and he in turn will call