Now let's continue the example of the previous slide, and imagine the case that

our marketing folks are adding a third product to the mix.

This might be a situation where our old product A is simply offered in two

versions. A1 and A2 total demand we assume for now

is staying the same. So product A1 is offering 50 units.

50 units of A2, this is our old demand of a 100 units per hour of A.

And then B, 75 units per hour. And that's all old, 175 units per hour.

The setup times are still as before, takes a half hour to switch from any one product

to another. And it is taking us P = 1/300, and that

would be, again, hours per unit. Now the production run that we're looking

for is going to look something like this. We're gonna make some a1.

So we're gonna change over, make some A2's.

We change over, we make some B's. We change over, and then we start again.

So the production run would look like this, and the batch is really a collection

of A1's, A2's and B's. The question here is, of course, how do we

choose the batch size? Well, again, we have to produce at 175

units per hour. We know that this is equal to the batch

size divided by the set-up time plus the batch size times p.

You notice now, however, that there are three set-ups in a, production run.

And for that reason, S is now no longer one but 1.5, everything

else really stays the same and just as we did before we can solve for B and I'll

leave that to you as a homework assignment.

You'll find that B = 630 units. So 630 units is set up before the whole

pattern repeats itself. From the 630 units.

630 times 50, divided by 175, equals to 180 .

Are gonna be produced on A1. The same, 630, 50 to 175.

180 will be a2. And b's will be 630 75 / 175 = to 270,

will be of product B. Now the words of production run will look

something like, like the following. 180 A1's set up, 180 of A2 set up.

And then, 270 of product b. What you see here, is its productions runs

got longer compared to the previous example.

The total amount stays the same, but by adding a third product to the mix, I have

increased the length of the production run and I'm now I am working in larger

batches. Note further that product B which really

has not been affected in terms of its demand, is also produced now in larger,

batches than before. Instead of making 180 of part B, I'm

making 270. So what we're seeing here is that more

setups force us to spend more capacity on setup.

That means we have to do bigger production runs to keep up with the total demand

rate, and that will lead to more inventory.

So, once again, you notice how variety leads to more setups, which leads to more

inventory. This is one of the biggest cost of

offering variety. Did I just squeeze it to mismatch between

supply and demand. But I just have that's a root cause for

inventory. In this session we will see how a firm

that increases its variety by, for example adding a third product to it's product

line, is going to be forced to add more inventory.

The reason for this was holding the overall flow constant.

The extra product required extra set-ups which we can only afford if we run longer

batches. The dream of every plant manager is to

produce at exactly the rate and the mix of demand.

This is what is called [inaudible]. Mixed model production.

As we will see later on in this module. This however requires that we get these

setup times reduced further and further. This is done by a technique that we will

refer to as SMET.