Can you increase efficiency and throughput by slowing down?

I recently had a discussion with a customer and an engineering firm about increasing throughput by slowing down the rate of a labeler from 400/minute to 380/minute. They recorded an improvement in efficiency to justify the change.  I questioned the decision from a thruput standpoint and wanted to come up with a good way to determine if an increase in efficiency actually increased the thruput or not.

Is slower better?

Efficiency is calculated using the following formula:

MTBF / (MTBF + MTR)

MTR = Mean Time to Repair
MTBF = Mean Time Between Failure

A properly buffered line should have capacity to handle the longest MTR on the line. The difference in maximum rates should be such that the table can go from full to empty in less time than the MTBF. For example, if you have a line like this:

Your labeler must have a MTR of 3 minutes or less and an MTBF of 9.9 minutes or more, giving us a minimum labeler efficiency of 77%. So what if I decrease my max rate in an effort to improve efficiency?

My minimum required MTR is the same since I’m still filling the buffer at 330 bpm, but my minimum required MTBF is now 19.8 minutes. This gives us a way to measure whether the decrease in rate has affected throughput. My labeler efficiency must now remain above 87% (19.8 / (3+19.8)) to keep the filler running and maintain throughput.

As the labeler slows down, its efficiency must go up to maintain throughput for the packaging line.

The formula can even more simply be expressed like this:

e = (Fr / Lr)

Where e = the minimum efficiency needed to maintain throughput
Fr = the max rate of the constraint
Lr = the max rate of the machine in question

If I run the labeler at 400 bpm I need to maintain a labeler efficiency of 77%. If I run it at 380bpm, I must maintain an efficiency of 87%. So if slowing the max rate of the labeler resulted in improving the efficiency from under 77% to something over 87%, then yes it will have improved throughput. If they were already running above 77% prior to the rate change, then throughput will be unchanged. If efficiency is under 87% after the rate change, then throughput will decrease.

In practice you have to find the right balance between rate and efficiency. It may be tremendously more difficult to maintain 87% than 77%, due to inconsistent materials or operator error.

A puck system is used to move unstable products through a packaging line. They’re popular in the cosmetics and personal care industries and can be purchased from a number of vendors such as Advantage Puck. The pucks and the products are separated at the end of the line and the pucks must be conveyed and reintroduced back to the beginning. A puck system provides a unique challenge for our line analysis calculation because stoppages in the line affect the flow of pucks upstream and downstream simultaneously.

Let’s look at a simple example of three machines.

Three machines in a packaging line with a puck return system.

Like any normal packaging line, this line has a constraint. Machine A runs at 300 products per minute (ppm) and the line can’t go any faster than that. Machine B accepts products from Machine A and sends them to Machine C. Machine C performs some sort of operation on the product, removes the product from the puck, and returns the empty back back to Machine A. If any machine malfunctions, all other machines must also shut down. Normally we can add an accumulation to help protect the constraint from the downtimes on other machines like this:

We added an accumulation table between Machines A and B to improve throughput, but does it help?

Unfortunately, Machine A requires a steady stream of empty pucks from Machine C to run. Downtimes on Machines B and C interrupt this stream, so despite having an accumulator downstream to allow A to keep running, line production shuts down anyway.

Downtime on Machine C cuts off the flow of empty pucks to Machine A, shutting down the whole line.

The same thing happens for downtime on Machine B.

We solve this problem by placing a second buffer upstream from the constraint in the empty puck return conveyor.

A second accumulator primed with empty pucks will allow the constraint to keep running.

If we have downtime on B or C, the second accumulator that was pre-primed with empty pucks will start emptying out and the original accumulation table will start to fill up at a rate of 300ppm. If the malfunctions on B or C are corrected before these tables empty out or fill up, then no production has been lost and throughput has been increased.

If B or C malfunctions, the first accumulator starts to fill up and the second starts to empty out, but the important thing is that Machine A keeps going.

Some important notes and questions:

How big should the accumulation tables be?
Both tables should hold enough products to handle the longest average repair time of any non-constraint machine, plus the number of pucks in transit.

Do the tables have to be the same size?
If you have two tables, they must be the same size because they are emptying out and filling up at the same time.

Does the second accumulator have to be in the empty puck return section?
No, but for the majority of cases it is the best place. Otherwise you will have to remove all the empty pucks from the system at the end of a shift or allow empty pucks to pass through machines without products in them. It makes sense from throughput standpoint and an operations perspective to accumulate all the empty pucks on accumulator 2 at the end of the shift.

How many pucks should I put on the system?
Fill the accumulation table prior to Machine A with empty pucks and don’t put any more on. Adding more pucks will decrease the line’s throughput.

We can't see the light behind the column

This happens when designers and engineers work inside of a bubble. They worked on a perfectly useful feature that is rendered less useful in the context of the structure around it. This happens all the time in our industry where a typical automated packaging line consists of machines designed by many different vendors. How can we make sure our features are still useful in the context of where they’ll be installed? What are some good design practices to use to achieve this?

George turned the packaging line up to Extra Fast

The newest casepacker model from Douglas Machine or Standard Knapp?

I have a theory that George and the Man with the Yellow Hat have a Fight Club type of relationship. It would explain a lot.

Remember that game show the Weakest Link?

The first step in maximizing your throughput is identifying your constraint, or bottleneck. Take the efficiency of each machine and multiply it by its maximum rate. This will give you the net rate of each machine. The machine with the lowest net rate is your constraint and your goal should to keep it running as fast and as often as possible.

Example:
A simple packaging line: (ppm = products per minute)

Some interesting notes:

• Each machine runs 92% or higher, but the line net efficiency is only 83.9%. This is because downtime on just one machine shuts down the whole line (ie. if the Casepacker jams, the Filler and the Labeler also shut down). The net efficiency of the line is calculated by multiplying the efficiencies of each machine in sequence:
  0.94 * 0.97 * 0.92 = 0.839 = 83.9%
• To get the overall line speed, multiply the net efficiency by the max rate of the slowest machine: 0.839 * 200 = 167.7 ppm
• The machine with the lowest net rate is the labeler (194 ppm), making it the constraint. 194 ppm is the upper limit of what we can achieve on this line.

So how do you achieve the upper limit of 194 products per minute? By making sure downtime on the Filler and Casepacker don’t ever cause the Labeler to shut down. By adding an accumulation table in between the Filler and the Labeler, you are segregating the line into two separate systems. This breaks the compounding effect of the machine efficiencies.

Since the line is now in two sections, we have to calculate their throughput separately. The throughput of the first section is 282ppm (0.94 * 300 ppm = 282 ppm). The throughput of the second section is 178.5 ppm (0.97 * 0.92 * 200 ppm = 178.5 ppm). We are still limited by the bottleneck of the second section, so the throughput of this line is 178.5 ppm, a 6.4% increase over our previous line.

Since we haven’t reach our upper limit of 194 ppm we should add another buffer between the Labeler and the Casepacker.

Now we’ve broken the line into three sections with each machine running independently. We have no compounding of efficiencies, so all we have to do is pick the lowest net rate of the machines. In this case, the Labeler’s net rate is 194 ppm and this is throughput of the line, a 15.7% increase over our original throughput of 167.7 ppm.

What does 15.7% mean to a company’s bottom line?

If you are having trouble meeting market demand for a product it could be huge.
Let’s say the line is running:
2, 8 hour shifts per day
7 days a week
Profit is a conservative 50 cents per product

2 shifts * 8 hours * 60 minutes / hour * $0.50 cents * 26.3 extra products per minute = $12,624.00 per day in additional revenue

Over six months it generates $2,203,880.00

there’s the issue of what is called sensation transference. This is a concept coined by one of the great figures in twentieth-century marketing, a man called Louis Cheskin, who was born in Ukraine at the turn of the century and immigrated to the United States as a child. Cheskin was convinced that when people give an assessment of something they might buy in a supermarket or a department store, without realizing it, they transfer sensations or impressions that they have about the packaging of the product to the product itself. To put it another way, Cheskin believed that most of us don’t make a distinction — on an unconscious level — between the package and the product. The product is the package and the product combined.

Liquor containers tend to be extreme

There has always been a fun battle between the marketing and production side of packaging. The Marketing Department comes up with a beautifullly unique, oddly shaped, off center bottle that enhances and improves the sensation transference while the Production Department has to produce the product efficiently enough so that the price point can be optimized. There are many things that can affect a bottle’s ability to be efficiently produced, such as the center of gravity, material type, side contour, contact surfaces, etc. My experience is solidly on the production side of packaging, and that’s why posts like this on the amazing packaging design blog, TheDieline, give me nightmares.

50 Favorite Liquor Package Designs

It also keep us in business.