The Faster I Go the Behinder I Get – back when I was a project engineer at Kraft Foods (as it was known then), our objective for every packaging line was to increase output. And the obvious way to do that was to run the line faster. Unfortunately, at some point, as you increase operating speed, production actually decreases, because you lose more product to problems than you gain from the increased speed.

I agree that this case exists and when a line performing very poorly, slowing things down to get control of the situation is the first and easiest thing you can do. There is, however, a reason management wants to increase production: It’s incredibly profitable to do so and worth the time (and money) to figure out how. Slowing down is not the only way to increase throughput on a consistent basis.

if the new filler you bought can run 300 bottles/min, but the labeler can only consistently run 280, you will encounter problems.

Jack’s slowdown approach would have us run the filler at a consistent rate of 280/min to match the labeler. Let’s assume that “running consistently” equates to an efficiency of 98% and this can be achieved at both the filler and the labeler. At a line speed of 280/min, the overall throughput of our simple line is 0.98 * 0.98 * 280 = 268.9 products per minute (ppm).

Higher efficiency doesn't always mean more throughput

If you raise the line to the rated filler speed (300/min) and raise the labeler to 320/min, you’re going to take a hit in efficiency on the labeler, right? If we add a buffer with a capacity of 900 products between the filler and labeler, we can withstand efficiencies on the labeler as low as 84% before dropping the line speed below 268.9ppm. For reference ow how bad 84% is, that is equal to one hour, sixteen minutes, and forty-eight seconds of downtime in an eight hour shift. If we can consistently hold an efficiency of 92% (38 minutes of downtime per shift) at the higher speed, our line will run at 294ppm. This is a 9.3% increase over slowing the line down.

Slow Down:
0.98 * 0.98 * 280 = 268.9ppm

Buffered:
0.98 * 300 = 294ppm
0.92 * 320 = 294.4ppm

294 – 268.9 = 25.1
25.1/268.9 = 0.093 = 9.3%

Jack ends with three steps:

• Slow the line incrementally until your long-term (daily? weekly?) throughput peaks and begins to decrease.
• Continue to slow the line for a short period to make sure that you have really maximized throughput and that the throughput is stabilized across all shifts.
• Slowly increase speed until output starts to fall off. Then, go back to the sustainable speed.

In many cases this may work to improve results, but it will not maximize throughput or get management off your back. If the line described above runs two eight hour shifts per day, five days per week, fifty weeks out of the year, and has a profit margin of $0.50 per product, a 9.3% improvement translates to $3,012,000 in yearly positive cash flow.

To maximize throughput:

• Identify the constraint
• Protect the constraint from all interruptions
• Increase the speed of the constraint if possible

More examples and formulas:
Packaging Throughput Example
How Big Should my Buffer Be?
Non-linear line analysis
Accumulation in a Puck Line

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.

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