At the Foreign step, this situation is different, because only the foreign units,

3 units per hour are going to arrive at this department.

There's no demand from the regular units and the easy units.

In Department one, we have the 3 units arriving from the Foreign Department, the

foreign units. We have the 11 regular ones, but we

don't have any ones from the easy. In Department two, however, we have no

foreign, no regular, just easy ones at a rate of 4 units per hour.

Finally, everybody shows up at printing, and the total demand there is 3 plus

11 plus 4 equals to eighteen. So, you notice here that a nice process

for diagram ideally using different colors to illustrate the different flows is going

to be very helpful as you do these calculations.

Finally, we can compute the ratio between the demand and the capacity as a sense of

busy-ness. We will call this measure the implied

utilization. Notice that this measure is different from

our utilization, which we defined as a flow rate divided by capacity.

Flow rate, by capacity, by definition, has to be less than 100%, less or equal to

100%. In contrast, implied utilization can well

exceed 100 % if there's more demand for a service than we have capacity.

In this case, we notice that 18 divided by 20 is the implied

utilization for filing. 3 divided by 6, it's a Foreign

Department. 14 divided by 12, it's

Department one. 4 divided by 15 at Department two,

and 18 divided by 30 at Department three.

We see that there's highest implied utilization, 14 divided by 12,

which is roughly 116.6%. This highest implied utilization makes the

Department one the bottleneck. The first approach was based on simply

adding up the flows at the various resources, computing a total flow, and

using that as our demand rate. The second approach I want to illustrate

is slightly different. Think about work flowing through the

system. At each of the resources, we have a

certain amount of work that the various resources can provide.

For example, at the Filing Department we are able to provide 60 minutes per hour of

time. And so, Foreign Department, we have two

persons working there and together their able to provide 120 minutes of work.

At Department number one, we have 3 people, creating a total amount of time

available of a 180 minutes, a 120 minutes for Department two, and then, a total of

60 minutes at the Printing Department. Now, ask yourself, how much work time will

be required by each of the flow units? Similar to the previous calculations,

we'll look at the 3 flow unit types. So, foreign ones, the regular ones, and

the easy ones. Now, we know at the Filing Department, we

have 3 units per hour arriving. Each of them will take 3 minutes of

work. Regular units, we have 11 units

arriving, each of them requiring 3 minutes of work.

And easy ones, we have 4 units arriving every hour, requiring 3 minutes of

work each. This creates a total workload of 54

minutes. So, the units here are really minutes of

work per hour. In the same way, we can compute that in

the Foreign Department, we have 3 units arriving, just as before, 3 units

arriving. Each of them corresponding to 20

minutes of work. This creates is a total workload of 60

minutes. There's no workload created in the Foreign

Department by regular units and the easy units.

Department one, we have 3 times 15 minutes caused by the foreign

cases, 11 times 15 minutes caused by the regular cases, and no work caused

by the easy cases. In Department two, we have only the work

from the easy cases of which there are 4 units an hour times 8 minutes per

unit. Finally, everybody shows up at printing.

Creating a workload of 3 times 2 minutes for the foreign cases, 11

times 2 minutes for the regular cases, and 4 times 2 units for the easy

cases. So, if we total these various rows, we see

that the workload in the Department one is 210 minutes.