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Chapter 11 Capacity planning and control 325
only rarely will the arrival of customers match the ability of the operation to cope with them.
Sometimes, if several customers arrive in quick succession and require longer-than-average
processing times, queues will build up in front of the operation. At other times, when customers
arrive less frequently than average and also require shorter-than-average processing times,
some of the servers in the system will be idle. So even when the average capacity (processing
capability) of the operation matches the average demand (arrival rate) on the system, both
queues and idle time will occur.
If the operation has too few servers (that is, capacity is set at too low a level), queues will
build up to a level where customers become dissatisfied with the time they are having to wait,
although the utilization level of the servers will be high. If too many servers are in place (that
is, capacity is set at too high a level), the time which customers can expect to wait will not
be long but the utilization of the servers will be low. This is why the capacity planning and
control problem for this type of operation is often presented as a trade-off between customer
waiting time and system utilization. What is certainly important in making capacity decisions
is being able to predict both of these factors for a given queuing system. The supplement
to this chapter details some of the more simple mathematical approaches to understanding
queue behaviour.
Variability reduces
effective capacity
Variability in demand or supply
The variability, either in demand or capacity, as discussed above, will reduce the ability of an
operation to process its inputs. That is, it will reduce its effective capacity. This effect was
explained in Chapter 4 when the consequences of variability in individual processes were discussed.
As a reminder, the greater the variability in arrival time or activity time at a process
the more the process will suffer both high throughput times and reduced utilization. This
principle holds true for whole operations, and because long throughput times mean that
queues will build up in the operation, high variability also affects inventory levels. This is
illustrated in Figure 11.17. The implication of this is that the greater the variability, the more
extra capacity will need to be provided to compensate for the reduced utilization of available
capacity. Therefore, operations with high levels of variability will tend to set their base level
of capacity relatively high in order to provide this extra capacity.
Figure 11.17 The effect of variability on the utilization of capacity