Calculating Optimal Crew Size in Mixed Model Cells

I have a question for you. How would you staff a cell that produces multiple products, all with varying cycle times?

In this article I will offer my thoughts and am excited to hear your comments as to how you would (or do) approach it in your organization.

Cycle Time Assumptions

Let’s assume, hypothetically speaking, we have developed a u-shaped cell were material flows counter-clockwise.

Let’s also assume, for the sake of this example, there are 5 similarly sized products produced in the cell.

The total manual cycle times (e.g. the time operators are needed) to produce each product are as follows,

– Product A : 5.1 minutes – Product B : 6.8 minutes – Product C : 4.9 minutes – Product D : 7.9 minutes – Product E : 3.9 minutes

We’ll also assume there is no auto or machine time required to assemble these units. Therefore, the average cycle time for the 5 products is 5.72 minutes.

Demand and Takt Time Assumptions

Now then, let’s also assume that on this particular day our “make to order” model cell is asked to produce the following.

– Product A : 23 units – Product B : 26 units – Product C : 3 units – Product D : 94 units – Product E : 14 units

In total, the cell must produce 160 similarly sized units.

Assuming 8 net working hours (480 minutes) are available in the full day, so our takt time comes to 3 minutes per unit (480 minutes / 160 units).

For the sake of this example, we will also assume no changeovers are required as we switch between products.

Calculating the Crew Size

Let’s get to the million dollar question. How should the team determine the optimal crew size for this particular day?

We know that the formula for optimal crew size is the sum of manual cycle time / takt time.

However, since we are not producing one product (like most of the lean books present us with) it’s not quite as straight forward.

If they use the average cycle time for the units our optimal crew size comes to 1.91 operators, which they round to 2 (5.72 minutes / 3 minute takt).

Using this approach the team would staff the cell with 2 people, splitting the work up evenly.

Would this work out? I vote no.

Weighted Average Cycle Time

Since the team is not working with an even number of units averaging is the wrong thing to do, in my opinion.

Asking these two people to succeed (without overtime) is the perfect example of MURI.

Instead of taking the average, the team would be better served by taking a “weighted average” of the cycle times. This is easy to do in Excel using the “SUMPRODUCT” command. Here is how this particular example is being worked out in MS Excel.

– Product A : 5.1 minutes x 23 unit – Product B : 6.8 minutes x 26 unit – Product C : 4.9 minutes x 3 unit – Product D : 7.9 minutes x 94 unit – Product E : 3.9 minutes x 14 unit

When we take the weighted average, which accounts for the fact the team is asked to produce far more product D’s than anything else, we learn the weighted average cycle time is 6.91 minutes (total sumproduct/total product).

Weighted Average Crew Size

If we use the weighted average cycle time in the formula our optimal crew size comes to 2.3 people (6.91 minutes / 3 minutes takt).

This is to say that more than 2 people are needed in the cell on this particular day.

Or, at a minimum, more than 2 people will be needed for parts of the day.

So, we can not expect 2 people to get the job done in the available time until some waste is eliminated and we are able to reduce the total cycle times.

What do you think? Do you (or would you) handle similar situations the same way? Or do you (or would you) approach it differently?