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Capacity and scheduling

The hours that can actually be sold divided by the time one unit takes, what is still free, how full the week is, and what to change when more has been promised than the week can hold.

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.

1. What you will learn

You will work out what a week can hold from the schedulable hours and the time one unit takes, say how much is still free and how full the week is, and name what sets the ceiling when it is not hours. You will also say which of the two numbers has to change when more has been promised than the week holds, and what each change costs.

2. What you already have

You can work out how many hours of work are inside one unit, and you know how many units the business needs to sell to break even. This lesson turns the first around: given the hours a week actually has, how many units fit? Put the two together and you have the range a business can operate in — above break-even, below its ceiling.

3. Words this lesson uses

4. Every business has a ceiling, and it is arithmetic

$$\text{capacity} = \frac{\text{hours that can actually be sold}}{\text{hours one unit takes}}$$

Two numbers, and nothing else. Effort is not in there; wanting it is not in there.

The top line is where the mistakes live: the hours that can be sold are not the hours in the week. Travel, setup, buying and the books come out first. A forty-hour week may hold thirty schedulable hours, and a ceiling built on the forty is a quarter too high.

The bottom line is simpler and still worth measuring: time one unit, start to finish.

A promise beyond the ceiling is not ambition but a promise that will be broken, and the honest response is to say which of the two numbers has to change — more schedulable hours, or less time per unit. Neither is trying harder.

5. The method, step by step, and how to check it

Log a normal week of hours. From the lesson on the owner's roles, you know where the hours go. Total them, and separate the ones a customer pays for from the ones they do not: travel, setup, cleaning down, buying, the books, quoting.

Time a unit, start to finish. Include the minutes attached to it — the setup for that job, the packing — but not the week's general admin, which has already come out of the top line. Time several and use a typical figure, not the best.

Divide, in the same unit. Minutes over sixty gives hours per unit; schedulable hours over hours per unit gives the ceiling. Mixing minutes and hours is the commonest slip in this lesson.

Subtract what is promised. The remainder is what the week can still take. Work out utilization — promised over ceiling — as well: it says how full the week is in a way that can be compared from week to week.

Keep a buffer. A week planned to exactly 100 percent has no room for a job that overruns, a late customer or a van that will not start. Many owners plan to 80 or 85 percent and treat the rest as the week's shock absorber.

Check the ceiling against real weeks. If the business regularly finishes more units than the ceiling says it can, the timing was too long; if it regularly falls short, the unsellable hours were underestimated. Adjust the two numbers to what the weeks actually show.

6. The ceiling is usually not the hours

Hours are the general case and often not the binding one. The real ceiling is whichever thing runs out first, and it is the only thing worth spending money to enlarge.

Buying a second bench when the ceiling is the kiln buys nothing, so ask what would have to change for one more unit to leave this week? And capacity says what fits, never what is worth fitting: contribution per hour of the bottleneck answers that half.

7. Moving the ceiling, and what each move costs

When demand is above the ceiling for weeks on end, one of the two numbers has to move, and each way of moving it has a price.

More schedulable hours. Cut the unsellable ones first: group jobs by area to cut travel, buy supplies once two weeks instead of every few days, move the books to a simpler system. Each hour recovered is an hour of capacity at no extra cost. After that, more hours mean longer weeks, which the owner's want may rule out, or help, which is a new fixed cost.

Less time per unit. Better tools, a jig, a template, doing jobs in batches, a checklist that removes rework. Each minute saved on a unit is a minute on every unit, so small savings add up fast: taking a 45-minute repair to 40 minutes raises a 30-hour week's ceiling from 40 repairs to 45.

Raise the price instead. When the week is full and customers are waiting, a price rise may lose a few jobs and raise the contribution of every job that remains. It moves neither number, and it changes which customers fill the ceiling — often the right move for an owner who wants shorter weeks rather than more work.

Change the mix. When the bottleneck is shared by several products, fill it with the ones that contribute most per hour of the bottleneck, and ration the rest. A kiln full of the highest-contribution pots earns more than a kiln full of whatever was ordered first, without a single extra firing.

Book ahead. Taking bookings rather than walk-ins smooths the week, so the same ceiling fills more evenly. A schedule that is full on Tuesdays and empty on Thursdays has capacity it cannot use; a booking system that offers Thursday first recovers some of it.

Whichever move is chosen, cost it with the contribution arithmetic from the pricing unit: extra capacity is worth only the contribution of the units that will actually fill it.

The opposite problem deserves the same care. A week that is regularly only half full does not have a capacity problem; it has a demand problem, and the lessons on customers, offers and channels are where the answer lies. Adding capacity to a half-empty week adds fixed cost and nothing else. Utilization, tracked week by week, tells the owner which of the two problems the business has — and it is common for a business to swing between them with the seasons, full in the busy months and half empty in the quiet ones. The response then is not a bigger ceiling but a better spread of work across the year: bookings taken ahead for the busy season, and offers aimed at the quiet one. Plot utilization for each week of a year and the pattern is usually obvious at a glance, which makes the next year's plan much easier to draw up.

8. In the world: a bakery's oven

A small bakery sells bread, pastries and celebration cakes. The owner believes her limit is her own hours: she works about 50 a week. When she measures, she finds the oven is the bottleneck. It is free for about 32 hours a week once cleaning and heating are out; bread takes 40 minutes of oven time a batch of 12 loaves, and a celebration cake 90 minutes on its own.

Her regular bread takes 15 batches a week: 10 oven hours. Pastries take another 12. That leaves 10 oven hours, or about 6 cakes a week — and she has been taking orders for 9, working late to fit them in by baking at night, which also meant the next morning's bread was late. Adding hours of her own did nothing for the oven.

She compares contribution per oven hour: bread earns about 18, pastries 22, cakes 35. So she cuts two batches of the lowest-selling bread, freeing about 1.3 oven hours, raises cake prices by a tenth to cool demand slightly, and caps cake orders at seven a week, with a waiting list. The week now fits the oven, the bread is on time, and the contribution from the oven's hours is higher than when she was trying to do everything.

9. In the world: theory of constraints

Operations managers speak of the theory of constraints: every system has one bottleneck, the output of the whole system is the output of that bottleneck, and improving anything else produces only lines. Small businesses rediscover it every time a second bench is bought for a shop limited by its kiln.

10. Where this goes wrong

Dividing by the hours in the week. Travel, setup, buying and the books come out first, and they are rarely small.

Treating the ceiling as a target to beat. It is a division. A week that goes past it did so because one of the two numbers was wrong, and finding out which is more useful than celebrating.

Planning to exactly 100 percent. One overrun and every later job is late; leave a buffer.

Assuming the owner's extra hours are free. They come out of a person who has to be there next week too. If they are the plan, they belong in the schedulable hours, counted rather than borrowed quietly.

Believing a promise creates capacity. Saying yes changes neither line of the division. It changes only who finds out, and when.

Enlarging the wrong thing. Spend on the bottleneck or spend nothing; capacity anywhere else produces work that lines.

11. A week at Bright Home Cleaning

1. Find the schedulable hours from a forty-hour week with ten of travel and restocking.

   $40 - 10 = 30$

   Only these can be sold.

2. Turn a ninety-minute clean into hours.

   $90 \div 60 = 1.5$

   Time it; do not estimate it.

3. Divide for the ceiling.

   $30 \div 1.5 = 20$

   Two numbers, one division.

4. Find the utilization with 22 booked.

   $22 \div 20 = 110\%$

   Over-promised by two cleans.

5. Say which number moves.

   $\text{move 2 cleans, or cut travel by 3 hours}$

   Twenty-two booked is not a busy week; it is two disappointed customers.

12. Lunch at Neighborhood Kitchen

1. Find the hours that matter.

   $\text{twelve to two} = 2 \text{ hours}$

   Almost every box sells in the rush.

2. Turn six minutes a box at the counter into hours.

   $6 \div 60 = 0.1$

   The counter's time per box.

3. Find the counter's ceiling.

   $2 \div 0.1 = 20 \text{ an hour} \times 2 = 40$

   The counter is the bottleneck, not the cooking.

4. Compare with the cooking's ceiling of 120 boxes.

   $40 < 120$

   Cooking more makes food that is still there at three.

5. Move the bottleneck's number: boxes pre-packed, a card reader by the register.

   $6 \to 3 \text{ minutes a box}$

   Spend on the bottleneck.

6. Find the new ceiling.

   $2 \div 0.05 = 40 \text{ an hour} \times 2 = 80$

   Doubled, without a second cook.

13. A repair bench that is always behind

1. Find the schedulable hours: 45 worked, 12 on diagnosis calls, buying and the books.

   $45 - 12 = 33$

   The top line.

2. Time a repair: 45 minutes.

   $45 \div 60 = 0.75$

   The bottom line.

3. Find the ceiling.

   $33 \div 0.75 = 44$

   Repairs a week.

4. Compare with a typical week's bookings of 50.

   $50 - 44 = 6$

   Six repairs late every week.

5. Cut the unsellable hours: buy parts weekly and use a booking form.

   $12 \to 8; \quad 37 \div 0.75 \approx 49$

   Five more repairs from recovered hours.

6. Trim the repair with a jig: 45 to 42 minutes.

   $37 \div 0.7 \approx 52$

   Every repair a little faster.

7. Check the new utilization.

   $50 \div 52 \approx 96\%$

   Now within the ceiling, with a thin buffer; a small price rise could widen it.

14. Your turn: 30 schedulable hours, a repair takes 45 minutes, 32 already promised

1. Find how many hours one repair takes.

   $45 \div 60 = 0.75$

   Minutes over sixty.

2. Find what the week holds.

   $30 \div 0.75 = 40$

   Schedulable hours over hours per repair.

3. Your turn: work this step out. Its working is at the end of the packet.

   Find what is still free.

15. Guided practice

Four businesses. Match each one to the thing that actually sets its ceiling.

16. Guided practice

Complete the worked solution: an owner works $27$ hours a week, of which $7$ go on travel, setup, buying and the books. One job takes $60$ minutes, and $12$ jobs are already promised. What can the week still take?

1. Take the unsellable hours out of the week.

   $27 - 7 =$ _h

   Only schedulable hours can be sold.

2. Turn one job's minutes into hours.

   $60 \div 60 = 1$

   Hours divide by hours.

3. Divide for the ceiling.

   $(\text{schedulable}) \div 1 =$ _c

   Schedulable hours over hours per job.

4. Take off the jobs promised.

   $(\text{ceiling}) - 12 =$ _f

   What is still free this week.

5. Compare with the ceiling from all the hours.

   $27 \div 1 > (\text{ceiling})$

   Dividing the whole week would promise jobs the week cannot hold.

17. Guided practice

Monica's Market Stall has taken $16$ orders this week, each one a bulk order packed for a cafe that takes $12$ minutes. How much of the week do they take? Answer in hours.

Answer: unit: h / min

18. Practice

A week at Maya's Ceramics has $30$ schedulable hours, and one mug takes $15$ minutes — so the week holds $120$. The owner has promised $164$. What follows?

• One of the two numbers has to change — more schedulable hours, or less time per mug — and until one does, $44$ of the promise will be late
• Push through it: $120$ is a target, and a good week goes past its target
• Stay late and clear the extra $44$ — the owner is not paid by the hour, so those hours cost nothing
• Nothing: the work has been promised, so the week now has to hold $164$

19. Practice

Bright Home Cleaning's owner works $30$ hours a week, but $6$ of them go on driving between houses, restocking and the books. A clean takes $90$ minutes. How many cleans can the week hold?

Answer:

20. Practice

Neighborhood Kitchen's week holds $240$ lunch boxs and $156$ are promised. What percentage of the week's capacity is already promised?

Answer:

21. Somewhere new

A bicycle-repair round has $12$ schedulable hours a week and takes half an hour over a job. Each job contributes $14$ dollars, and the round's fixed costs are $112$ dollars a week. For how many jobs a week does the round more than cover its fixed costs and still fit inside the hours?

This task has no paper form; do it on a device.

22. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

23. Test question

Neighborhood Kitchen has $24$ schedulable hours in the week — what is left after travel, setup, buying and the books. One lunch box takes $6$ minutes, and $199$ are already promised. Work out what the week holds and what is still free.

24. What you can do now

You can turn schedulable hours and minutes per unit into a ceiling, work out utilization, and say what is still free this week. Tell someone why the hours in the week are the wrong top line, and what you would say to an owner who has promised more than the week can hold. Next: stock and what it costs to hold it.

Working for the steps left to you

14. Your turn: 30 schedulable hours, a repair takes 45 minutes, 32 already promised, step 3