3/5/22, 11:45 PM The Waiting Line Problem
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The Waiting Line Problem
3/5/22, 11:45 PM The Waiting Line Problem
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LO10-1
Understand what a waiting line problem is.
A central problem in many service settings is the management of waiting time. The manager must weigh the added cost of providing more rapid
service (more traffic lanes, additional landing strips, more checkout stands) against the inherent cost of waiting.
Frequently, the cost trade-off decision is straightforward. For example, if we find
that the total time our employees spend in line waiting to use a copying machine
would otherwise be spent in productive activities, we could compare the cost of installing one additional machine to the value of employee time saved. The decision
could then be reduced to dollar terms and the choice easily made.
On the other hand, suppose that our waiting line problem centers on demand for beds in a hospital. We can compute the cost of additional beds by summing the
costs for building construction, additional equipment required, and increased
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maintenance. But what is on the other side of the scale? Here, we are confronted
with the problem of trying to place a dollar figure on a patient’s need for a hospital bed that is unavailable. While we can estimate lost hospital income, what about the
human cost arising from this lack of adequate hospital care?
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The Practical View of Waiting Lines Before we proceed with a technical presentation of waiting line theory, it is useful to
look at the intuitive side of the issue to see what it means. Exhibit 10.1 shows
arrivals at a service facility (such as a bank) and service requirements at that facility (such as tellers and loan officers). One important variable is the number of arrivals
over the hours that the service system is open. From the service delivery viewpoint,
customers demand varying amounts of service, often exceeding normal capacity. We can control arrivals in a variety of ways. For example, we can have a short line
(such as a drive-in at a fast-food rest
