As the ratio between the profits that I have here, and the investment capital that

I just squeezed in here. That is 18.25%.

Now, the reward of all this tricky calculation is that a sensitivity analysis

as quite simple. For example, the question of roots to the

case that I could shorten the time of the seat to 55 minutes by accelerating the

cleaning process. I just type this in, all the numbers we

compute, and we see this dramatic increase in ROIC.

Though, I admit, this is based on the assumption that there is really an

infinite amount of demand that, particularly, we can squeeze these extra

customers in. But, again, don't be too cautious on the

assumptions here because we're assuming that with unlimited demand, that average

time, it doesn't really mean that there's always four customers being served per

seat per night. Some will stay shorter, some stay longer.

And, as long as there's an infinite demand, we'll always get the extra guests

through the system. Anyway, you see now, draw the ROIC tree,

compute the ROIC, and then do the sensitivity analysis.

Alright. The last question is a line balancing

question. You see that there are six tasks given to

you, and a current assignment of tasks to workers.

Your job is to balance the line. In the second part of the question, you

were supposed to compute the takt time, and the target manpower calculation.

Now, a word of caution as we start the optimization here to maximize capacity

given these four workers. Besides that in class, there is a way of

mathematically formalizing a fancy mathematical optimization problem.

But, this is really overshooting it. With the numbers as small as they are

here, it's a process of trial and error. You have to just try out different

assignment combinations to see if you can further increase the capacity.

Good luck. Alright.

We have a shot here at this problem. Really, we're dealing with the process

that consists of the four resources, namely, the four workers.

The first resource is just working on task one, which gives it a processing time of

30 seconds per unit. 25 for the second worker.

And then, here, we combine three and four. So, 75 seconds per unit at station three.

And, for work number four, we have, 45 seconds per unit.

So, we've done this often enough by now in class, that we can quickly see that one

over 75, and this is now units per second, is going to be the bottleneck, and thus

this is the capacity of the current line. So, this is, again, one over 75 times

3,600 seconds in a hour. Now, let's assume the tasks are allocated

differently. You want to balance the line.

And clearly, this doesn't look like a really balanced line because there's a big

difference between the fellow working here, and the fellow working here.

So, let's see how good we can do. Now imagine, the first person here would

work on task one and task two. They would give us a 55 second processing

time. Then, the next person will just work on

this one here, 35 seconds for the next one, 40 on the next one, and then, 45 for

the third step. This will give me an activity time or

processing time at the bottleneck of 55 seconds.

How did I come up with that solution? Don't ask me.

This is a little bit of iteration, a little bit of trial and error.

I started with 30, but I doubted that I could get all the way down to a processing

time of a bottleneck of 30. Then, I tried 30 plus 25, and went from

there onward. Could I combine activities such as the

processing time at the bottleneck is 55? Yes, I could.

Again, this is trial and error as long as you don't learn mathematical programming

which could do this assignment optimally for you.

With this in mind, we have a activity time at the bottleneck of one of 55, and that's

the capacity of the bottleneck of one over five, 55 units per second.

The third question is equally tricky. In the third question, you can assume that

you can reshuffle these tasks. Now, typically, when you do these, you'd,

since you're gaining a degree of flexibility, you would be able to squeeze

down the processing time at the bottleneck further.

However, I couldn't find a combinations of activity times such that the 55 seconds

were beaten. Just try it yourself.

So, maybe you want to combine 30 and fifteen, it gives you a 45 per, per

seconds per unit activity time at the bottleneck.

Then, you could try a 55 up here, that makes it longer.

Try it yourself. I couldn't come up with anything faster.

So far, we have looked at the effect of capacity only.

We have maximized capacity. Now, we have some information about

demand. Demand here is 50 units per hour.

Since there are 3600 seconds in an hour, and we want to have 50 units, we have a 72

second between units takt time. I can quickly compute the labor content of

the process, it's simply the sum of these individual processing time and get the

labor content of 175 seconds per unit. My target manpower is then simply, these

175 seconds of work divided by the takt time of 72, which is 2.43 people.

Round this up, and you see that you should hire three workers.

Now, the last question is going to be tricky.

As we go from the target manpower to the actual staffing level, we have to, once

again, tackle the problem of assigning workers to tasks.

Let's take a look at this together. Now, here are the processing times.

They work, excuse me, I didn't want to log us out here.

30 seconds for the first, 25 seconds for the second, 35 for the fifteen and 30

seconds per unit, respectively. Let's first consider the case where we can

do the task in any order that we want. Remember, our takt time was 72 seconds.

So, I want to create bundles of tasks that are very close to 72 seconds.

I'll combine 40 and 30, that gives me 70 seconds that the worker would just have

two seconds idle time. Remember, we want to hire n = three

workers, that we know by our target manpower calculation.

That's the best we can do. Well, then, from here onwards, it's easy.

Fifteen plus 35 already gives me another 50 seconds.

I combine the first, and that gives me with n equals three workers gives me the

process staffing that I need. It's somewhat tricky, unfortunately, if I

want to keep the sequence of tasks as they were described in the questions.

Again, let's write them all down. And, let's remember that once again, we

are after a takt time of 72. So, if I combine the first two, I'm going

to get back to my assignment of 55 seconds of the cycle time, or of the processing at

the bottleneck which we saw previously that was not enough to get me down to n =

three, I have n = four. However, if I include all of these three

tasks, to [inaudible] the first worker, I'm over the 72 seconds takt time.

So, that means, first worker really has to have these two tasks assigned to them.

Same logic on the next step. If I combine tasks three and four, I'm

over my takt time, and so, that doesn't work.

And so, I have to unfortunately, hire them.

Let's just hire 35 seconds here. Then, the next person would be staffed

this way, and then the next station this way.

So, unless I can break up the tasks further and move seconds from one task to

the other. Unfortunately, in that case, I will need

four workers.