Hong Life CalculatorsUnderstanding the product priority by contribution per constraint — concept and principle
When a factory, workshop or service team cannot make everything customers want, the scarce resource, often machine hours or skilled labour hours, decides what is worth producing first. This calculator compares two products by their contribution per hour of that limiting resource and tells you which one to make first. Managers, small manufacturers and accounting students use it for short-term product-mix decisions. It works with any currency; the default is US dollars.
How it is calculated
- Contribution per hour = contribution per unit ÷ constrained hours per unit
- Make first = the product with the higher contribution per hour (product A if they are equal)
Contribution per unit is the selling price minus variable costs per unit. Hours per unit is the time the product uses on the bottleneck resource, not total production time.
The principle
With a limited number of hours, the goal is to earn the most contribution from those hours, not from each unit. A product with a bigger contribution per unit can still be the worse choice if it uses much more of the scarce time. Ranking by contribution per unit of the constraint, also called the limiting factor approach, maximises total contribution while the constraint lasts. Fixed costs do not change with the choice, so they do not affect the ranking.
Worked example
- Inputs: product A earns $30 and needs 2 hours; product B earns $45 and needs 4 hours.
- A: 30 ÷ 2 = $15.00 per hour.
- B: 45 ÷ 4 = $11.25 per hour.
- Since 15 > 11.25, the result is Product A.
- With 100 hours available: A gives 50 units × $30 = $1,500; B gives 25 units × $45 = $1,125.
How to read the result
The higher figure tells you where each bottleneck hour earns most. Make that product up to its demand limit, then use the remaining hours on the next product. The gap between the two figures shows how costly a wrong choice would be. If the constraint is removed, for example by adding a shift, the ranking may no longer matter and per-unit contribution becomes relevant again.
Common mistakes
- Ranking by contribution per unit or by profit after fixed-cost allocation.
- Entering total hours instead of hours on the limiting resource.
- Ignoring demand limits, contractual commitments and product mix needs.
- Applying the rule when there is more than one binding constraint; that needs linear programming.
Frequently asked questions
What is a limiting factor?
Any resource that stops you meeting all demand, such as machine time, labour hours, materials or storage space.
What if there are two constraints?
The simple ranking may fail. Use linear programming, for example a spreadsheet solver, to find the best mix.
How is this related to the theory of constraints?
Throughput accounting, linked to Goldratt's theory of constraints, uses a similar idea: maximise throughput per unit of time on the bottleneck.
Sources: Charles T. Horngren, Srikant M. Datar and Madhav V. Rajan, Cost Accounting: A Managerial Emphasis, Pearson (product-mix decisions under capacity constraints) · Eliyahu M. Goldratt and Jeff Cox, The Goal, North River Press