The system uses a production control
policy called CONWIP (Constant Work In Process).
The system begins empty and penny blanks are allowed
to enter the system one at a time. A reasonable plan
allows a blank to enter station 1 whenever station 1
is empty. When some predetermined number of pennies
are in the system, say K, the rule for allowing blanks
to enter changes. Now, a new blank is allowed to enter
only when a finished penny leaves. In this way the WIP
is maintained at a constant level, justifying the name
of this policy, CONWIP.
To completely describe this system one
must specify the probability distributions for the machine
times at each station and the number of coins allowed
in WIP, K. The most important output measure is the
average processing rate of finished coins, called the
throughput rate. As one might expect the processing
rate is minimized when K = 1 and increases as K increases.
Since this is a closed queueing system (the others
in this section were open queueing systems),
there can be at most 4 coins in actual production. When
processing times are constant the K equal to 4 provides
the maximum throughput and there is no point in providing
more. Because of random processing times, however, throughput
will be increased by increasing the WIP the to a value
greater than 4. Variability inevitably leads to queues
and idle times at the machines.
Another important measure is the production
cycle time. This is the time required by a single
penny to pass through the system. With constant processing
times, the cycle time is constant. With random variability
in machine times, the cycle time becomes a random variable.
It is interesting to observe the mean and standard deviation
of the cycle time. It is also interesting to observe
statistics on the queues at the stations. Of course,
for a CONWIP system, the total number or parts in the
queues and receiving processing must remain constant
after the start-up period, but it is instructive to
see the distribution of the coins among the various
Figure 15 shows an Extend model that can be used to
experiment with the parameters of the CONWIP system.
The model reports the throughput rate and average WIP
in the system. For the case shown, the material available
is equal to 10 units. Each station has a processing
time governed by the exponential distribution with a
mean time of 2. The average WIP is less than 10 because
it takes an initial startup time to fill the system.
The ten green circles in Figure 15 indicate that 10
parts were in the system when the simulation was stopped.