Contribution Margin per Constraint Hour
Rank two products by contribution margin per minute of your bottleneck resource and find the value of an extra minute of capacity.
150 units of A and 20 units of B fit in the available constraint time. The constraint is fully used; one more minute is worth $2.
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How this works
When a bottleneck resource limits total output, ranking products by margin per unit or margin percentage gives the wrong answer, because it ignores how much of the scarce resource each product actually consumes. Theory of Constraints throughput accounting ranks products by contribution margin per unit of constraint time instead. This engine calculates that ranking for two products, allocates the available constraint minutes to the higher-ranked product first (up to its demand cap), then fills the remainder with the second product, and reports the value of one more minute of constraint capacity.
Assumptions
- Only one constraint (bottleneck) is modeled; no secondary or shifting constraints
- Product economics are constant regardless of volume produced
- Demand caps, when supplied, are firm ceilings for the period
Limitations
- Only compares two products; does not solve a general multi-product linear program
- Does not model changeover or setup time between products
- Does not model a downstream non-constraint resource that could itself become limiting after reallocation
Sources
Throughput-per-constraint-unit ranking follows Goldratt's Theory of Constraints and Corbett, Throughput Accounting, cross-checked against the standard contribution margin definition in Horngren, Datar, and Rajan, Cost Accounting: A Managerial Emphasis (16th edition).
Worked example
A machine has 2,000 minutes available this period. Product A earns $30 of margin per unit and takes 10 minutes, for $3 per constraint minute. Product B earns $50 per unit but takes 25 minutes, for only $2 per constraint minute. Even though B has the higher margin per unit, A is the better use of the constraint. If A's demand is 150 units, it uses 1,500 minutes, leaving 500 minutes, enough for 20 units of B. The combined plan earns $5,500, and since B is still minute-constrained at the end, one more minute of capacity is worth B's rate: $2.
Common use cases
- Deciding which order or product to prioritize on a bottleneck machine or work center
- Pricing decisions that account for scarce capacity, not just cost
- Justifying a capacity investment by the constraint value it would free up
- Job-shop or make-to-order prioritization when multiple orders compete for one resource