Back to the on-screen lesson ·
The output each resource allows, the smallest of them as the binding constraint, the demand it leaves unserved, where the limit moves when the constraint is relieved, and what that relief is worth.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will turn each resource a business uses into the output it could support on its own, name the one that runs out first as the binding constraint, count the demand it turns away, and find where the limit moves when that resource is relieved. You will also value the relief by the units it adds up to the next ceiling.
You can rank products by what they earn for an hour of a full resource. That assumed you knew which resource was full. A business has several — time, space, stock, equipment — and usually only one of them is holding it back at any moment. This lesson finds that one by a single division for each resource, and then prices what it would be worth to relieve it, which is always less than it first appears, because relief only helps until the next resource runs out.
| Term | What it means |
|---|---|
| Capacity | How much of a resource there is in a period. |
| Binding constraint | The resource that runs out first: the one that prevents one more sale. |
| Slack | Capacity left unused on the resources that are not binding. |
| Next ceiling | The output the next-tightest resource allows, where the limit moves once the constraint is relieved. |
| Relieving the constraint | Adding capacity to the binding resource, or taking work off it. |
| Bottleneck | An everyday name for the binding constraint. |
Corner Bean wants to serve 200 lunches a day. Every lunch needs three things: 4 minutes of kitchen time, a seat for one sitting, and a portion prepped the day before. The kitchen has 720 minutes a day, there are 120 seat-sittings, and Alexa preps 160 portions.
$$\text{units a resource allows} = \frac{\text{available}}{\text{used by one unit}}$$
The kitchen allows 180 lunches, the seats 120, the prep 160. The café serves 120, because the 121st lunch has no seat. The seats are the binding constraint; the kitchen has 60 lunches of slack and the prep 40.
Everything useful follows from naming the right one. Another hour of kitchen time adds nothing today. Prepping 200 portions adds nothing but waste. A table for four on the sidewalk adds four lunches a sitting straight away. An hour lost at the constraint is an hour lost to the whole business; an hour saved anywhere else is a mirage.
Another way: steps
Another way: table
Corner Bean's lunch, resource by resource.
| Resource | Available | Used by one lunch | Lunches it allows |
|---|---|---|---|
| Kitchen time | 720 minutes | 4 | 180 |
| Seats over three sittings | 120 | 1 | 120 |
| Portions prepped | 160 | 1 | 160 |
The smallest figure in the last column is what the café can do.
List what one unit needs. Every resource a lunch, a repair or a veg box passes through: people's time, equipment time, space, stock, even the counter time to take the order.
Measure what is available. In the same period and the same units: minutes a day, seats a day, portions prepped for the day. Use realistic figures — the hours staff actually work, not the hours the shop is open.
Divide, then take the smallest. Each resource's available amount over what one unit uses is the most it allows on its own. The smallest is the binding constraint; the others have slack.
Compare with demand. Demand less the smallest ceiling is the business turned away.
Check the answer by watching the business at its busiest. The binding constraint should be where work piles up and where nobody is ever idle. If the arithmetic says the seats bind but the line is at the grill, one of the figures is wrong — often the minutes a unit takes, measured on a quiet day rather than in the rush.
Suppose Alexa doubles the seats with a sidewalk license: 240 seat-sittings. The café does not jump to 240 lunches. It jumps to 160, where the prepped portions run out, and the prep becomes the constraint. Prep another 40 and the kitchen stops it at 180.
So a plan to grow is a sequence: find the constraint, relieve it as cheaply as possible, find the next one. The payoff from each step is only as big as the gap to the next ceiling, which is why the cost of relieving a constraint should be set against that gap, not against the demand.
Slack is not waste to be cut in a hurry, either. The kitchen's spare 60 lunches are what let the café grow once the seats are fixed; sell off the second oven to save money and the kitchen may become the constraint before the sidewalk tables have paid for themselves. Know which resources have slack and how much, and treat that slack as the room the next step needs.
Buying more of the binding resource is the obvious fix and often the most expensive. Cheaper ones come first.
Take work off the constraint. Anything the constraint does that another resource could do should move. If the grill cook also plates and garnishes, someone with slack can plate while the cook grills.
Prepare ahead. Work done before the rush, on a resource that has slack then, saves the constraint's minutes during it: sandwiches assembled at ten, repair kits laid out the night before.
Never let the constraint wait. An idle minute at the constraint is a sale lost for good; an idle minute anywhere else costs nothing. So the constraint gets the first break cover, the first delivery of stock and the first repair when something breaks.
Steer the mix toward what uses it least. The last lesson's ranking by contribution an hour applies at exactly this point.
Only when those are done does it make sense to pay for more of the constraint — and then the question is the one this lesson answers: how many extra units will it really add before the next ceiling, and what are they worth?
A business rarely has one constraint all the time. Corner Bean's seats bind at lunch; at seven in the morning, when everyone wants a takeout coffee, the espresso machine binds and the seats sit empty; in the afternoon nothing binds at all. Long Row Gardens is held by its van in summer, by its picking hours in the spring rush, and by its land in winter. A repair shop is held by parts one week and by the bench the next.
So the arithmetic should be done for each part of the day, or each season, that matters: the breakfast rush, the lunch rush, the quiet afternoon; the spring, the summer, the winter. Each has its own table of ceilings, and its own smallest figure.
This changes what is worth doing. A second espresso machine earns only in the breakfast rush, so its value is the extra coffees in that hour or two, not across the day. Sidewalk tables earn only at lunch and only in the months when people will sit outside. A fix whose value is counted across the whole day, or the whole year, when it only helps in one part of it, will always look better than it is.
It also changes where slack can be used. The afternoon's idle kitchen is exactly the resource that can prepare the next day's lunches, taking work off the lunchtime constraint. Seeing each part of the day's constraint separately is what shows which resource is free, and when, to help the one that is full.
A bicycle repair shop is overwhelmed every spring. Customers wait two weeks for a service, and the owner is about to hire a second mechanic at 3,200 dollars a month. Before signing, she works through the constraint.
Each service needs 60 minutes of a mechanic, 15 minutes on the one workstand with a wheel-truing jig, and a parts kit. Her mechanic works 150 hours a month: 150 services. The workstand is free about 200 hours a month, 15 minutes a service: 800 services. Her supplier can deliver 180 kits a month. Demand in spring is about 260 services.
The mechanic binds at 150. A second mechanic doubles that to 300 — but the kits stop the shop at 180. So the second mechanic would add 30 services a month, not 110, until she finds a second supplier. At 45 dollars of contribution a service, that is 1,350 a month against 3,200 of wages.
She does two things instead. She asks the supplier for a bigger standing order and finds a second wholesaler for common parts, lifting the kits to 300. Then she hires the mechanic. The new limit is now 300 services, the shop does 260, and the extra 110 services contribute 4,950 a month against the 3,200 wage. The order of the two steps made the difference between losing 1,850 a month and gaining 1,750.
Manufacturing consultants popularized the idea that every system has one constraint and that improving anything else is wasted effort. Their five-step routine — find the constraint, get the most out of it, arrange everything else around it, add to it, and look for the next one — is the method of this lesson, and it has been applied to hospitals, software teams and airports as well as factories.
The largest expense is the constraint. Rent can be the biggest bill while the grill is what runs out.
The busiest-looking person is the constraint. Look for work piling up in front of a resource and no idle time at it.
More of anything means more sales. Only more of the binding resource does, and only up to the next ceiling.
The constraint never changes. It moves with the menu, the season and every fix.
Relieving the constraint is worth all the demand it turns away. Only the units up to the next ceiling.
One constraint all day. The breakfast rush, the lunch rush and the quiet afternoon can each have a different one; work each part of the day on its own.
A fix helps all day. A second espresso machine earns only while the machine binds; count its value in those hours alone, and set its cost against that, not against a whole day of coffees it will never make. A fix that pays in its own hours is worth having; one that pays only across the whole day is not.
Divide the bench time: 2,400 minutes at 40 a repair.
$2400 \div 40 = 60$
Repairs the bench allows.
Divide the technician's time: 4,200 minutes at 50.
$4200 \div 50 = 84$
Repairs the technician allows.
Read the screens in stock.
$45$
One screen a repair.
Take the smallest.
$\min(60, 84, 45) = 45$
The screens bind, with 90 repairs wanted.
Order 45 more screens and find the new limit.
$\min(60, 84, 90) = 60$
The bench binds next; the week reaches 60, not 90.
Find each ceiling: kitchen 180, seats 120, prep 160.
$\min(180, 120, 160) = 120$
The seats bind.
Find the lunches turned away with 200 wanted.
$200 - 120 = 80$
Demand beyond the seats.
Add 60 sidewalk seat-sittings.
$120 + 60 = 180$
The seats now allow 180.
Find the new limit.
$\min(180, 180, 160) = 160$
The prep binds next.
Find the lunches the license really adds.
$160 - 120 = 40$
Not 60: the prep stops it at 160.
Value them at 5 contribution, less the license of 90 a day.
$40 \times 5 - 90 = 110$
The license adds 110 a day, until the prep is increased too.
Divide the packing time: 900 minutes at 6 a box.
$900 \div 6 = 150$
Boxes packing allows.
Read the van drops.
$120$
One drop a box.
Divide the harvest: 1,050 kg at 7 a box.
$1050 \div 7 = 150$
Boxes the harvest allows.
Take the smallest.
$\min(150, 120, 150) = 120$
The van binds.
Find the slack elsewhere.
$150 - 120 = 30$
Thirty boxes of packing and of harvest unused.
Add a third round of 40 drops and find the new limit.
$\min(150, 160, 150) = 150$
Packing and harvest both bind at 150.
Find what the third round really adds.
$150 - 120 = 30$
Thirty boxes, not forty: ten drops of the new round would go unused.
Find the boxes packing allows.
$900 \div 6 = 150$
Available over used by one.
Take the smallest of the three.
$\min(150, 120, 150) = 120$
The van binds.
Find the slack.
Corner Bean is planning its coffees in the morning rush. It has $240$ shots of shots the machine can pull, and each one uses $2$; $120$ minutes of barista time, each using $1$; and $100$ cups of clean cups on the shelf, each using $1$. For each resource, fill in the most coffees in the morning rush it could support on its own.
| Most it could support | |
|---|---|
| shots the machine can pull | |
| barista time | |
| clean cups on the shelf |
Complete the worked solution: a caterer has $286$ minutes of kitchen time a week, and each meal uses $2$; $505$ minutes of packing time, each meal using $5$; and $122$ containers. Customers want $157$ meals. Find the constraint and the meals it turns away.
Divide the kitchen time.
$286 \div 2 =$ x
Meals the kitchen allows on its own.
Divide the packing time.
$505 \div 5 =$ y
Meals packing allows on its own.
Read the containers.
$\text{one container a meal: } 122$
Meals the containers allow.
Take the smallest of the three.
$\min(\text{kitchen}, \text{packing}, 122) =$ m
The caterer stops at the first resource to run out.
Take it from the demand.
$157 - (\text{most it can make}) =$ d
The meals turned away until the constraint grows.
Fixit Mobile is planning its repairs a week. It has $2400$ minutes of bench time, and each one uses $40$; $4200$ minutes of technician time, each using $50$; and $45$ screens of screens in stock, each using $1$. Customers want $90$. Which resource prevents one more sale?
At Fixit Mobile, bench time could support $60$ repairs a week, technician time $84$, and screens in stock $45$. Customers want $90$. Mark the most repairs a week the business can actually serve.
0 |——————————| 90
Mark the position with a cross, then write the value:
Alexa kept notes through a busy Saturday lunch at Corner Bean, trying to find out what stopped her serving more people. Mark every note that shows the grill is the constraint.
This task has no paper form; do it on a device.
A café's seats allow $136$ lunches a day, and its kitchen, the next-tightest resource, allows $151$. A sidewalk license would add $47$ seats' worth of lunches a day and cost $70$ dollars a day. Each lunch contributes $10$ dollars, and customers would fill every seat. How many dollars a day does the license add?
Answer:
At Fixit Mobile, bench time could support $60$ repairs a week, technician time $84$, and screens in stock $45$. Customers want $90$. The owner doubles the resource that runs out first and changes nothing else. Mark the most repairs a week the business can now serve.
0 |——————————| 90
Mark the position with a cross, then write the value:
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Corner Bean is planning its coffees in the morning rush. It has $240$ shots of shots the machine can pull, and each one uses $2$; $120$ minutes of barista time, each using $1$; and $100$ cups of clean cups on the shelf, each using $1$. Customers want $150$. How many of the coffees in the morning rush customers want will go unserved?
Answer:
You can find the resource that prevents one more sale and say what relieving it would really add. Tell someone why an extra hour anywhere else is worth nothing today. Next: ranking jobs by what they earn for each hour of that resource.
15. Your turn: 900 packing minutes at 6 a box, 120 van drops, 150 boxes of veg, step 3
$150 - 120 = 30$
Packing and the veg have 30 boxes each to spare.