Looking at the example we see that the simulation is governed
by three random variables. In the first period the randomly
generated capacity of station 1 is five. Station 1 has no predecessors
so all five are passed to station 2. Again station 2 has a capacity
of five so all five units are passed to station 3. Luckily,
station 3 also has a capacity of five, so in the first period
five units leave the system.
Period 2 shows some variability. Station 1 again has a capacity
of five, so station 2 receives all five units. Station 2 has
a capacity of six in this period, but only the five units are
available from station 1 to be processed. Station 3 has only
a capacity of one, so only one unit is completed in period 2.
The remaining four units remain in the WIP for station 2. This
material can be used in period 3.
In period 3, station 1 has a capacity of only two, so two units
pass to station 2. It has excess capacity of four, so the two
units progress to 3. Station 3 has sufficient capacity so it
can process the two units from station 2 and three of the units
in WIP. Five units leave the system, and one remains in the
WIP of station 2.
Reviewing the remaining periods, we see that the variability
of production at the stations has two main affects. First the
later stations do not process as many units as the earlier ones.
As a consequence of this, inventory in the form of WIP appears
in the system. The average capacity of every station is 3.5
units, however, because of the variability of production capacity,
the system output rate can never exactly reach this level.
This result is shown more clearly in a run of 1000 periods.
The output rate can never exceed the lowest average rate at
any station, which happens to be station 1. Not surprisingly,
system WIP is high. The cycle time, computed using Little's
law, is
Cycle Time = WIP/Output Rate
The average time required for a unit to pass through the system
is almost 8.5 periods. We should note that in this model, the
minimum cycle time is 0, because material does not enter inventory
if it passes through the system in a single period.
|