A factory manager says a line is only 75% utilised, yet the business cannot fill its orders. Your first move should be to inspect the denominator. Seventy-five per cent of what: nameplate speed, staffed hours, actual output or good units ready to ship?
A capacity case becomes much easier once demand and usable output are expressed in the same units, for the same product mix and period. Then you can locate the shortfall and compare ways to close it.
The calculation is the beginning of the decision. You still need to know whether the extra output can move through the rest of the business and reach a paying customer.
Fix the unit and the service requirement
Suppose a packaging line is rated at 100 packs an hour. It is scheduled for an eight-hour shift, and customers need 600 good packs per shift.
Management divides 600 by 800 and describes the line as 75% utilised. That calculation compares required good output with theoretical output at rated speed. It says nothing about setup, downtime, speed losses or defects.
Confirm which packs are being produced. If one product takes twice as long as another, a single “packs per hour” rate may be wrong for the current mix. Also check when the output is due. Capacity available tomorrow does not satisfy an order promised today.
Use a consistent definition throughout the case: good packs of the required mix, available for dispatch per shift.
Convert rated capacity into usable output
Assume setup and downtime consume two hours. During the remaining six hours, the line runs at its rated speed. Its first-pass yield is 90%, and defective packs cannot be recovered within the shift.
| Step | Calculation | Output |
|---|---|---|
| Theoretical output | 8 hours × 100 packs/hour | 800 packs |
| Output after lost time | 6 hours × 100 packs/hour | 600 packs |
| Good output | 600 × 90% yield | 540 good packs |
The line is short of the 600-pack requirement by 60 good packs. Demand is about 111% of usable capacity: 600 divided by 540.
That does not mean equipment physically operates at 111% utilisation. It means the required output exceeds what the stated operating conditions can deliver. Label the ratio so the interviewer knows what you are comparing.
The Lean Enterprise Institute's definition of overall equipment effectiveness separates availability, operating performance and quality. You do not need to recite the acronym, but the distinction helps you avoid treating every loss as missing machine hours.
Quick Case Math Drill
A solar panel assembler has committed to ship 340 good panels per shift to a developer, and the plant manager says the line can cope.
- Rated speed
- 40 panels per hour
- Shift time
- 12 hours, with 3 lost to setup and maintenance
- Flash test pass rate
- 85%, failed panels scrapped
By how many good panels per shift will the line fall short?
Count each loss once
You can calculate the example from eight scheduled hours with a 75% availability factor, or from six available hours directly. Both give the same answer when multiplied by speed and yield.
Do not start with six hours and multiply by 75% availability again. You would deduct the same two lost hours twice.
Check the speed measure too. If “90 good packs per operating hour” already includes defects, do not apply another 90% yield. If observed output per scheduled hour already includes downtime, do not separately remove that downtime without rebuilding the rate.
A useful interview habit is to explain what each number includes before multiplying. That is more valuable than memorising a formula whose inputs you have not defined.
Find the constraint across the whole process
Suppose a setup improvement increases packaging output, but final inspection can approve only 570 good packs per shift. The business still cannot ship 600.
Map the other required steps: material supply, preparation, packaging, inspection and dispatch. Compare each stage in a common finished-output unit, allowing for product routes and losses. A machine with spare capacity is irrelevant if the missing output must pass through a different constrained stage.
Shared resources deserve attention. Two lines may both depend on one technician for setup or one inspection team for release. Adding their standalone capacities can overstate what they can produce at the same time.
Use the operations framework when the problem involves queues and handoffs as well as the amount of capacity available.
Compare different ways to recover the 60-pack gap
The current line produces 540 good packs. Consider two changes before buying another machine.
Reducing setup and downtime by one hour creates seven productive hours. At the same speed and yield, output rises to 630 good packs. That clears the 600 requirement by 30.
Improving yield from 90% to 95% while keeping six productive hours gives 570 good packs. It helps, but leaves half of the original shortfall unresolved.
Combining both changes gives 7 × 100 × 95% = 665 good packs, provided the changes are compatible and the downstream process can handle them.
Now compare feasibility, cost and timing. A setup reduction may require preparation work before the shift rather than faster work during it. A quality improvement may need maintenance or an input change. Overtime may be quick but expensive; outsourcing may introduce qualification, transport and lead-time constraints.
Do not assume a free improvement just because the arithmetic is attractive. Identify what must change operationally to achieve the new input.
Test the economics of added capacity
Suppose recovering the missing 60 packs allows the company to make 60 additional sales per shift, each contributing £8 after normal variable costs. The extra contribution is £480 per shift.
An overtime option costs £300 per shift beyond those normal variable costs. It adds £180 per shift before any other change. Over 20 shifts, that is £3,600.
The comparison depends on the 60 packs being incremental sales. If the company merely brings forward orders that would otherwise ship tomorrow without penalty or lost business, the benefit is different. If the overtime wage is already in the £8 contribution calculation, subtracting it again would double-count the cost.
For a permanent machine purchase, compare its investment and running costs with a credible demand forecast over its useful period. A temporary peak does not automatically justify permanent capacity.
Quick Exhibit Drill
A coffee roaster turns away wholesale orders every shift. Its operations lead has costed three ways to pack more bags.
- Unfilled orders
- 100 bags per shift, lost if unmet
- Contribution per bag
- £6 after normal variable costs
| Option | Extra bags per shift | Added cost per shift (£) |
|---|---|---|
| Overtime packing | 60 | 150 |
| Temporary packer | 100 | 330 |
| Leased packing machine | 200 | 500 |
Which option adds the most profit per shift, and by how much?
Protect the ability to meet the promise
The setup improvement leaves 30 good packs of nominal spare capacity, only 5% above the 600-pack requirement. Whether that is enough depends on demand variation, breakdowns, job mix and the delivery target.
At the improved rate of 90 good packs per operating hour, losing another half-hour reduces 630 to 585. The apparently comfortable solution would miss the target again.
Test a plausible bad shift, instead of planning only around the average. A highly loaded operation has little spare capacity to recover when work takes longer or equipment stops.
A recommendation could therefore combine setup reduction with a limited overflow option while the company observes actual reliability. If demand is growing steadily and that option becomes expensive, the case for permanent investment strengthens.
Present the capacity decision clearly
For the original prompt, the answer is straightforward: the supposed spare quarter is not available under current conditions. The line can produce 540 good packs, against demand of 600. Removing one hour of lost time could raise output to 630, but the company must validate that change and check inspection, dispatch and variability before accepting more orders.
That explanation connects the denominator, the proposed fix and the remaining constraint. It gives management something concrete to test.
Practise the opening with Manufacturing Capacity Bottleneck. State the output unit, explain how you would calculate usable capacity and identify the first comparison needed to locate the system's limit.
Structure drill
Would your case structure convince an MBB interviewer?
Manufacturing Capacity Bottleneck
Compare usable capacity with demand before choosing a new line or outsourcing. Present your approach to Casey, Case Room’s AI interviewer, then review feedback on your structure and starting point.
Frequently asked questions
Measuring usable capacity
A line is only 75% utilised, so why can the business not fill its orders?
The 75% figure may use the wrong denominator. In the example, management divides 600 required good packs by 800 packs of theoretical output at rated speed. That ignores setup, downtime, speed losses and defects, so the apparent spare quarter of capacity may not exist at all.
What should I check first in a capacity case?
Ask what the utilisation figure is a percentage of: nameplate speed, staffed hours, actual output or good units ready to ship. Then express demand and usable output in the same units, for the same product mix and period. Only then can you locate the shortfall reliably.
How do I turn rated capacity into usable output?
Deduct each loss step by step. A line rated at 100 packs an hour over an eight-hour shift has 800 packs of theoretical output. Losing two hours to setup and downtime leaves 600 packs at rated speed. With 90% first-pass yield, and no recovery of defects within the shift, usable output is 540 good packs.
How do I avoid double-counting downtime or yield?
Apply each loss once. You can use eight scheduled hours with 75% availability, or six available hours directly. Do not take six hours and multiply by 75% again. Check speed measures too. If a figure such as 90 good packs per operating hour already reflects yield, applying yield again would understate output.
Can defective units count towards capacity?
Only if they can be turned into good units within the relevant period. In the example, defective packs cannot be recovered within the shift, so only good packs count against the 600 requirement. If rework were possible, you would need to clarify where it happens and whether it uses capacity elsewhere.
Finding the constraint and closing the gap
Why might fixing one machine fail to solve the shortfall?
Another stage may be the real constraint. If a setup improvement lifts packaging output but final inspection can approve only 570 good packs per shift, the business still cannot ship 600. Spare capacity at one machine is irrelevant if the missing output must pass through a slower step.
How do I compare capacity across different stages of a process?
Convert every stage into a common finished-output unit. Map each required step, such as material supply, preparation, packaging, inspection and dispatch, and allow for product routes and losses along the way. This shows which stage limits finished output, rather than which machine looks busiest.
Is it better to reduce downtime or improve yield?
It depends on the numbers, so calculate both. In the example, removing one hour of lost time gives seven productive hours and 630 good packs, clearing the requirement by 30. Raising yield from 90% to 95% over six hours gives 570, which still leaves half the gap. Test options like these before buying another machine.
Economics, resilience and the final answer
How do I work out whether overtime is worth paying for?
Compare the extra contribution with the extra cost. If recovering 60 packs enables 60 additional sales at £8 contribution each, that is £480 per shift. Overtime costing £300 beyond normal variable costs leaves £180 per shift, or £3,600 over 20 shifts. This only holds if the recovered packs genuinely become additional sales.
Is 30 packs of spare capacity enough headroom?
Not automatically. Thirty packs is only 5% above the 600 requirement, and whether that is enough depends on demand variation, breakdowns, job mix and the delivery target. At 90 good packs per operating hour, losing another half-hour cuts 630 to 585, which misses the target again. Test a plausible bad shift, not just an average one.
How should I present my conclusion in a capacity case?
Start by stating that the supposed spare quarter is not available, because the line makes 540 good packs against demand of 600. Then give the fix and its conditions. Removing one hour of lost time could raise output to 630, but the company must validate this and check inspection, dispatch and variability before accepting more orders.