Mixed Model Sequencing – Complex Example Sequencing 1

Sequencing products due to different workloads of different products at different workstations is tricky. This is now the sixth post on Mixed Model Sequencing, and we finally start with our sequence! Wohooo!

Sequence the First Product

The first product to be sequenced is usually easy; it is the biggest rock you have (i.e., the part that has the largest cycle time at any station). In the example we used so far, this would be product number 2437, since it has the largest cycle time for the mounting of the sunroof of 112 seconds. This is our biggest rock. I have marked this in red in the table below.

The sequence for this part 2437 is easy. We want to produce 5,500 of this type out of 17,732 parts in total. Hence our sequencing interval S for our product k with a quantity Qk out of n products in total is:

\[ {  S_k =\frac{\sum_{m=1}^{n} Q_m }{Q_k} } \]

or for our case:

\[{  S_{2437} =\frac{17 732 }{5500 } = 3.22} \]

Hence, every 3.22 items in the sequence should be this product 2437. If we start at position 1 with this type, then the next one should be at 1+3.22 = 4.22. The next one afterward should be at 4.22+3.22 = 7.45, then at 10.67, at 13.90, and so on. Since this is the first product, all slots are still available, and we can simply round to the nearest integer, giving us this product 2437 at positions 1, 4, 7, 11, 14, etc. in our production sequence. The first 30 slots are visualized below.

Sequence the Second Product

Now comes the ambiguous part: Which product should we sequence next? Should we take product 2434 because it has the second-biggest cycle time, also at the sunroof mounting? Or should we take some of the products that have no sunroof to offset the excessive sunroof time of 2437? If so, it could be product 2436, which also has a similar quantity to product 2437, which we just sequenced (grayed out in the table below). Or should we go for something completely different by sequencing 2435, because it has the largest cycle time for the door mounting?

There is no single right answer here. Depending on which aspects you look at, you may pick a different product for sequencing. I go for product 2434 here, since it has the second-largest cycle time overall due to the 111 seconds for the sunroof mounting, but this is just a hunch. The sequencing interval is 6.41, hence every 6.41 slots I would like to have this product.

\[ {  S_{2434} =\frac{17 732 }{2766 } = 6.41} \]

The first slot is already occupied, hence we cannot start this sequence with the first slot. The second slot would not be good either, because then we have two sunroof mountings directly adjacent to each other in slot 1 (product 2437) and slot 2 (product 2434). This would require even more buffer before the sunroof mounting to decouple two excessively long cycle times in sequence. So we move to the third slot … and have the same problem again since the fourth slot is another sunroof again.


This is a tricky situation. We seem to have always two sunroofs adjacent to each other in the sequence. I picked the second slot to start the sequence, giving me product 2434 at slots 2, 8, 15, 21, and so on. If the sequence arrives at a slot that is already occupied, then you simply take the nearest available slot. The result is visualized below, and we have lots of sunroof mountings adjacent to each other in the sequence. This is a problem!

However, this is not yet the final sequence. I can shuffle both the initial product 2437 (our biggest rock) and the second product 2434 (our second-biggest rock) around. I cannot remove any product, but I can move them within the sequence. And, lo and behold, we can get a sequence where there is always at least one slot free between sunroof mountings!

While this kind of shuffling is time consuming and hard to automate, it can save you a lot of problems later. The updated sequence is shown below.

Generally speaking, if you have no more than 50% of the products with one certain aspect, you can always keep a slot free between them. In our example, we had a total of 8,266 products with sunroof (across two product variants), representing 47% of all products. Hence we can make a series of alternating sunroof – no sunroof, sometimes even with two empty slots in between.

However, this can only be guaranteed if you start with an empty sequence. If the sequence has been already filled with other products, our options are limited, and we may not be able to keep a nice alternating sequence without breaking some other sequence benefit. This is the idea of always putting in the biggest rock firsts, so if you run into conflicting sequences later, you already have the biggest problems out of the way.

Sequence the Third Product

So, what should be our third-biggest rock? The largest deviation from the average of the not-yet-sorted products are now all models without a sunroof. However, since this means all remaining available slots will be filled with “no-sunroof” vehicles, there is no priority to assign them. Instead, we would go for the next biggest deviation which we have in the door-mounting process with product 2435.

Since we make only 121 products of this type, the sequencing interval is 146.55 hence only every 146.55 slots, I would like to have this product.

\[ {  S_{2435} =\frac{17 732 }{121 } = 146.55} \]

Now, I could start the sequence at the first free slot, slot number 2 as shown below.

However, looking into the data in more detail, this would give me a four-door vehicle 2435 directly adjacent to another four-door vehicle 2437. Again, I would have two longer cycle times in sequence for the door-mounting station. There are not many options left, but I could move this product from slot 2 to slot 22, where it is adjacent only to a two door-vehicle 2434.

The resulting sequence is visualized below:

So far we have taken care of our thee biggest rocks, and so far we have been lucky. We were always able to find a nice spot somewhere for all of our products, where we did not have an excessive accumulation of sequential cycle times.

However, as you can see in the sequence above, now we have only slots left that are adjacent on both sides. It is going to be tight! But this has to wait for the next post. Now go out, look again for your biggest fluctuations, and organize your industry!

P.S. Many thanks to Mark Warren for his input.

Series Overview

  1. Mixed Model Sequencing – Introduction
  2. Mixed Model Sequencing – Just Make the Problem Go Away
  3. Mixed Model Sequencing – Adjust Capacity
  4. Mixed Model Sequencing – Basic Example Introduction
  5. Mixed Model Sequencing – Basic Example Workload and Buffering
  6. Mixed Model Sequencing – Basic Example Sequencing
  7. Mixed Model Sequencing – Complex Example Introduction
  8. Mixed Model Sequencing – Complex Example Data Basis
  9. Mixed Model Sequencing – Complex Example Sequencing 1
  10. Mixed Model Sequencing – Complex Example Sequencing 2
  11. Mixed Model Sequencing – Complex Example Verification
  12. Mixed Model Sequencing – Summary

Here is also the Sequencing Example Excel File for posts 7 to 11 with the complex example. Please note that this is not a tool, but merely some of my calculations for your information.

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