Capacity and bottlenecks: the slowest step sets output
When each step has several machines or people, work out each step's capacity, find the slowest one, value an hour there, and see where the limit moves next. A worked example from a dairy plant in India.
Key takeaways
- A process can never make more than its slowest step. So an hour lost at that step is an hour lost for the whole business, and an hour saved anywhere else is worth almost nothing.
- Common mistakes: Fixing the step that looks busiest or most broken instead of the one with the lowest capacity.
- What is the capacity of each step?
- Is demand higher than the slowest step?
Key idea
A process can never make more than its slowest step. So an hour lost at that step is an hour lost for the whole business, and an hour saved anywhere else is worth almost nothing.
Capacity is the most a step can handle in a given time, such as bottles per hour or patients per day. The bottleneck is the step with the lowest capacity. The case type "Operations and process improvement" shows the basic rule on a sandwich line where each step is one person. Real processes are messier: a step often has several machines or several people doing the same job. Then the capacity of the step is the number of machines (or people) times what each one can do. Work that out for every step first, then compare the steps with each other and with demand (how much customers want).
Four questions for any process
- 1What is the capacity of each step? Machines or people at the step x what each one handles per hour.
- 2Which step is slowest? That step sets output, as long as demand is higher.
- 3Is demand higher than the slowest step? If not, the limit is demand, and buying capacity will not help.
- 4If we fix the slowest step, which step becomes the limit next, and how much do we really gain?
Worked case
A dairy plant in Gujarat that cannot keep up in summer
The prompt
A dairy in Gujarat, India bottles flavoured milk. In summer, shops want 5,500 bottles an hour, and the plant runs 16 hours a day. Each bottle earns INR 6 of contribution (price minus the costs that move with each bottle). The steps, machines and rates are in the table with this case. The plant manager wants to buy a faster filling machine. What should the dairy do? (The dairy is fictional and the figures are illustrative.)
The structure
- Output = the lower of demand and the slowest step; the value of a fix = extra bottles x contribution
- Capacity of each step = machines x rate
- Key: Output today and the shortfall against demand
- What the shortfall costs a day
- Options: fix the slowest step, then check the next one
The exhibit
| Step | Machines or packing stations | Bottles per hour, each | Step capacity per hour |
|---|---|---|---|
| Fill | 2 | 3,000 | 6,000 |
| Cap | 1 | 7,000 | 7,000 |
| Label | 1 | 4,500 | 4,500 |
| Pack into crates | 3 | 1,800 | 5,400 |
Working it through
1. Filling capacity
Two fillers at 3,000 bottles an hour each.
Fill capacity (bottles per hour):2 × 3,000 = 6,0002. Packing capacity
Three packing stations at 1,800 bottles an hour each.
Pack capacity (bottles per hour):3 × 1,800 = 5,4003. Output today
Output is the lowest of demand and the four step capacities. Labelling is the bottleneck.
Output (bottles per hour):min(5,500; 6,000; 7,000; 4,500; 5,400) = 4,5004. Shortfall
Shops want 5,500 an hour and the line makes 4,500.
Bottles short each hour:5,500 - 4,500 = 1,0005. What the shortfall costs
1,000 bottles an hour, for 16 hours, at INR 6 each.
Contribution lost a day (INR):1,000 × 16 × 6 = 96,0006. The faster filler
Even if filling doubled to 12,000 an hour, labelling still allows only 4,500. The filler adds nothing.
Output with a faster filler (bottles per hour):min(5,500; 12,000; 7,000; 4,500; 5,400) = 4,5007. A second labeller
Labelling doubles to 9,000. Now packing, at 5,400, is the slowest step.
Output with two labellers (bottles per hour):min(5,500; 6,000; 7,000; 9,000; 5,400) = 5,4008. The real gain
The gain is 900 bottles an hour, not 1,000, because packing becomes the limit.
Extra contribution a day (INR):(5,400 - 4,500) × 16 × 6 = 86,4009. Payback
A second labeller costs INR 25 lakh (2,500,000). Divide by the daily gain.
Payback (summer days):2,500,000 ÷ 86,400 = 28.9410. Then fix packing cheaply
A fourth packing station takes packing to 7,200 an hour, so output reaches demand.
Output with four packing stations (bottles per hour):min(5,500; 6,000; 7,000; 9,000; 4 × 1,800) = 5,500
What the exhibit shows
Labelling, at 4,500 bottles an hour, is the slowest step, so the whole line makes 4,500 an hour however fast the fillers run.
The recommendation
Do not buy the faster filler: labelling is the bottleneck, so a faster filler adds no output at all. Buy a second labeller instead. It lifts output from 4,500 to 5,400 bottles an hour and earns about INR 86,400 a day, so its INR 25 lakh cost pays back in about 29 summer days. Then add a fourth packing station for the peak season, which closes the last 100 bottles an hour of the gap. The risk is that summer demand is shorter or weaker than planned; check how many days a year demand stays above 4,500 an hour before buying.
Risks: Demand above 4,500 an hour may last only a few weeks; A second labeller needs floor space and an operator on every shift.
A bank in Manila, the Philippines, handles home loan applications in three steps. Document check: 4 staff, each handles 30 a day. Credit review: 3 staff, each handles 25 a day. Approval: 1 manager who signs 90 a day. 100 applications arrive each day. How many applications a day does the office finish?
Fixing the step that looks busiest or most broken instead of the one with the lowest capacity. Counting one machine when a step has several. Valuing a fix at the full shortfall when the next step will cap the gain. Forgetting demand: if customers want less than the slowest step can make, extra capacity earns nothing. Letting the bottleneck stand idle at lunch or shift change, which loses output for the whole plant.
A plant's three steps can make 900, 600 and 750 units an hour. Customers want 700 an hour. How many units an hour does the plant sell?
Which hour of lost production costs the business most?
Customers want 400 units an hour. The slowest step can make 500. The client wants a faster machine at that step. What do you say?
Factories, hospitals, ports and airports all live by their bottleneck. The industrial manufacturing brief shows how factories measure and raise output before they build anything new.
Read the industrial manufacturing briefSources for this lesson (1)
- Recognized public explanations of case-interview concepts and terms
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