Starting
in row 21, we enter data that describes the external flows and
network structure. In row 23 we see the flow of 3 per hour entering
the system at *Enter* and one per hour entering *Diagnose*.
The flows through the operations are computed using matrix algebra
and are shown in row 24. These flows are transferred to row
4 for the analysis.
The network structure is defined in the *Transfer Out*
matrix, **P**. A nonzero entry (*i*,*j*)
indicates the proportion of the flow passing through operation
*i* that is passed to operation *j*. The first
row shows the division of the entry flow to the movie and treatment
operations. All the movie participants go directly to the payment
operation. 90% of those passing through treatment go to payment,
while the remaining 10% go to the diagnosis operation. 60% of
the diagnosis patients return to treatment while the others
leave the system. Note that the entries in a row of **P**
need not sum to 1. In a case such as this where the entries
represent mutually exclusive alternatives, proportions that
do not sum to 1 imply that the missing patients leave the system.
The *Augmented Matrix* is constructed by the add-in.
Its inverse is used in the computation of the flows.
For the network structure the input and output lot sizes are
not automatically related. Although it is still logically correct
that the input lot size of an operation should equal the output
lot size of its immediate predecessors, the network option allows
an operation to have any number of successors and predecessors.
Since the lot sizes would be difficult to automatically relate,
we leave the coordination of lot sizes to the modeler.
Although it is easiest to think of the entries of the transfer
out matrix as probabilities or proportions, the entries of the
matrix can have any non-negative entries as long as the augmented
matrix is not singular.
Reviewing the results for the example, we see that the total
WIP is 9.16 patients. The average time a patient spends in the
office is 2.29 hours. A culprit in this system is the movie.
Although the movie only lasts 0.5 hours, the average time spent
in this operation is almost three hours. The problem is the
time it takes to gather the 3 patients for the movie and then
to split them up for final processing. Since patients arrive
for the movie every 45 minutes, it would be much better to use
a batch size of 1.
It is interesting to vary other parameters of the system. For
example, what is the effect of changing the maximum utilization
of the queues from 80% to 90%? This reduces the need for two
employees, but the patient time in the office more than doubles. |