Limiting Factor Analysis: Choosing the Best Product Mix
How to make the most profit when one resource is in short supply.
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The method in four steps
- Identify the limiting factor (the resource that restricts output).
- Calculate the contribution per unit of each product.
- Divide by the amount of scarce resource each unit uses to get contribution per unit of limiting factor.
- Rank the products, then allocate the scarce resource in rank order, up to each product’s maximum demand.
Fixed costs are ignored when ranking, because they do not change with the product mix.
Worked example
A company makes three products from a scarce material. Only 6,000 kg are available.
| Product X | Product Y | Product Z | |
|---|---|---|---|
| Contribution per unit | 20 | 18 | 10 |
| Material per unit | 5 kg | 3 kg | 2 kg |
| Maximum demand (units) | 800 | 1,000 | 1,200 |
| Contribution per kg | 4.00 | 6.00 | 5.00 |
| Rank | 3rd | 1st | 2nd |
Allocate the 6,000 kg in rank order:
| Product | Units | Material used | Material left | Contribution |
|---|---|---|---|---|
| Y (1st) | 1,000 (full demand) | 3,000 kg | 3,000 kg | 18,000 |
| Z (2nd) | 1,200 (full demand) | 2,400 kg | 600 kg | 12,000 |
| X (3rd) | 120 (600 ÷ 5) | 600 kg | 0 | 2,400 |
| Total | 6,000 kg | 32,400 |
Why ranking by contribution per unit misleads
Product X has the highest contribution per unit (20), but it uses the most scarce material. If you made X first: 800 units use 4,000 kg and earn 16,000. The remaining 2,000 kg make 666.7 units of Y, earning 12,000. Total contribution = 28,000, which is 4,400 less than the correct plan. Ranking per kg of scarce resource gives the better answer.
What if there is more than one limiting factor?
With two or more scarce resources the simple ranking no longer works, and the problem is solved with linear programming, which finds the combination of products that maximises contribution within all the limits. The principle is the same: use scarce resources where they earn the most.
Common mistakes
- Ranking by contribution per unit instead of per unit of the scarce resource.
- Ignoring demand limits. Do not plan more units than customers will buy.
- Including fixed costs in the ranking. They are the same under any mix.
Quick check
1. Product A earns 24 per unit and uses 6 machine hours. Product B earns 14 per unit and uses 2 machine hours. Which ranks first?
A: 24 ÷ 6 = 4 per hour. B: 14 ÷ 2 = 7 per hour. B ranks first, even though A has the higher contribution per unit.
2. Why are fixed costs ignored when ranking products?
Fixed costs are the same whichever products are made, so they cannot make one product better than another.
Practise with Problem 6 (limiting factor).
Frequently asked questions
What is a limiting factor?
A resource in short supply that restricts the output a business can achieve, such as materials, labour hours, machine hours or demand.
How do you rank products when a resource is scarce?
By contribution per unit of the scarce resource. Make the highest-ranked product first, up to its demand, then the next.
Is the limiting factor always a physical resource?
No. It can be sales demand, cash or any other constraint.
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