The Sequence Solution: Maximising Throughput In Mixed-Model Assembly Operations

A mixed-model assembly line is a type of production system that can manufacture multiple product models / variants simultaneously on the same line. Products are assembled continuously without stopping the line for changeovers between different variants.

In this article, I discuss a worked example of a mixed-model production system, and present the optimal sequence results in the end for maximum throughput.

A custom PC (Personal Computer) manufacturer offers the following options to their customers:

• CPU - Standard CPU, or High Performance CPU
• Storage - Single SSD, or SSD & HDD with RAID Configuration
• Grpahics - Basic GPU, or High-end GPU with power connectors & bracket

This results in 8 PC variants listed in Table 1.

PCs are assembled in a 10-step process, with a sequence common to all the 8 PC models:

Based on the proportion of the annual demand for the PC variants, we can calculate the daily demand for individual models as 20, 13, 3, 1, 11, 3, 2, 3 units per day. We arrive at these figures by dividing the annual demand per model by 240 (working days), and rounding off the results to the nearest integer. This gives us a total of 56 units.

Now the interesting thing about mixed-models problems like this is that the time taken to produce these 56 units depends upon the sequence in which these units are produced.

Let's say, if we follow the natural order and produce 20 units of Model-A, followed by 13 units of Model-B, etc, and end with 3 units of Model-H, we will need a total time of 817 minutes to produce them. This duration is called makespan. The following figure shows the Gantt chart for our chosen sequence, which we call FIFO (first in first out). The sequence of units is indicated on the y-axis. They are ordered from 1 to 56.

But how do we know whether 817 minutes of makespan is good or bad? Thankfully, we have a way of determining the lower bound, which in our case is 669 minutes. So it means the processing time taken by our sequence is over 22% longer than the best possible. However it is impossible to tell whether there is any sequence that could give us a makespan of 669.

So how are we going to obtain the best sequece? Now 56 jobs could be sequenced in 1E+115 different ways. That is 1 followed by 115 zeros. Using a brute force approach, one has to work out all these sequences and calculate the makespan for every possibility to identify the optimal sequence. This is simply impossible, given the enormous size of the problem. Instead we use what are known as "heuristics" to come up with certain intuitive sequences that could give near optimal results.

Some of the simplest heuristics available are indicated below:

• FIFO - First In First Out. This is the order in which orders arrive.
• SPT - Sequenced according to the Shortest Processing Time
• LPT - Sequenced according to the Longest Processing Time
• SPTF - Sequenced according to the Shortest Processing Time for the First Step

None of these are particularly efficient, but they are widely used, to get a fairly decent solution. The figure below shows the Gantt chart for an LPT sequence. This turns out to be worse than the earlier choice (FIFO). Note the sequence indicated on the y-axis.

Thankfully there are many other methods. However they are computationally intenstive, and not well known to people who actually plan the operations. In this article I will share the results for a well known heuristic known as NEH (Nawaz-Enscore-Ham), a Hybrid-NEH (with local search), as well as my own "Random Search" approach.

But before that let us consider the number of units to sequence. In the earlier example, we sequenced 56 units of daily demand. We could sequence a much smaller lot, by dividing the total demand profile with minimum demand (307 for Model D), then round the results to the nearest integer. This gives us a total of 45 units, 16,10, 3, 1, 8, 3,2, 2 units each for Models A to H respectively. We can follow the same approach to calculate lot size for 2 days, or for 1 week, depending on how much inventory we are allowed, and how much lead time we have.

The table below shows various splits of lot sizes by their models:

And the following table shows the Minimal, Daily, Two Days and Weekly lot sizes (for sequencing), and their corresponding makespan values for various heuristics used.

In the table above, the column LB indicates the Lower Bound. The heuristic STAT (uses a random search approach) performs significantly better than NEH and Hybrid NEH methods, though it takes more time to calculate, which turns out not more than 30-60 seconds. The column Mins Saved is the difference between the worst case and the best case.

The results show that about 100 minutes per day could be saved when using the best sequence (when compared to the worst), which turns out to be 8-9 additional PCs produced in a 2 shift day.

Using the STAT method, a makespan of 732 is achieved by sequencing 56 units (daily lot) as shown in the figure below. Notice there is no repeating pattern.

Don't settle for sub-optimal solutions using spreadsheets and inefficient methods. Get in touch with me for a custom designed solution, specifically for your operations. Contact, Moses Gummadi at [email protected], or send a DM in my LinkedIn profile.