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Microlesson · 5-min read

Limiting Factor / Key Factor Decisions

# Limiting Factor / Key Factor

## Concept

A limiting factor (also called key factor) is any factor of production — material, labour hours, machine hours, or even demand — that is in short supply and therefore restricts total output.

When capacity is constrained, the firm cannot make as much of every product as it would like. The objective then shifts: maximise contribution per unit of the limiting factor, not per unit of product.

## Four Standard Decision Cases

### Case A — Choose any one or both products

1. Calculate contribution per unit of each product.

2. Divide by the key factor consumed per unit (e.g., kg of material, labour hours).

3. Result: contribution per unit of key factor.

4. Produce the product with the highest contribution per unit of key factor.

### Case B — Optimum Product Mix

1–3. Same as Case A.

4. Rank products by contribution per key factor.

5. Allocate the limited resource first to Rank 1, then Rank 2, etc., until the resource is exhausted.

6. Exception: If the question stipulates that a minimum quantity of another product must be made first (e.g., to honour a contract), satisfy that constraint first, then optimise the remaining capacity.

### Case C — Special Order Decision

1. Compute total profit before accepting the special order.

2. Compute total profit after accepting it (consider any displacement of existing production).

3. Accept the order only if it increases total profit.

### Case D — Make or Buy

1. Calculate total variable cost of making in-house (only relevant — avoidable costs).

2. Calculate total cost of buying from outside (purchase price + any handling).

3. Choose the cheaper option, considering also qualitative factors (quality, reliability, capacity freed up).

## Key Insight

With a binding constraint, ranking by contribution per unit can mislead. A product with a high contribution per unit may consume a lot of the scarce resource per unit — and a lower-contribution product may actually generate more total contribution from the same resource pool.

Worked example

### Example 1

Case A/B Example: Material is limited to 1,000 kg.

  • Product X: Contribution ₹40/unit, uses 4 kg/unit → ₹10 per kg
  • Product Y: Contribution ₹30/unit, uses 2 kg/unit → ₹15 per kg

Ranking by contribution per unit suggests X; by contribution per kg, Y wins.

  • All-Y: 1,000/2 = 500 units × ₹30 = ₹15,000 contribution
  • All-X: 1,000/4 = 250 units × ₹40 = ₹10,000 contribution

Produce Product Y.

### Example 2

Case D (Make or Buy): Variable cost to make = ₹120/unit; outside purchase price = ₹100/unit; fixed costs are unavoidable either way.

Buy at ₹100 — saves ₹20/unit. (If making in-house frees no fixed cost, only variable cost is the basis of comparison.)

Caveat: If freed capacity can produce another contribution-earning product, add that opportunity benefit to the 'Make' side.

⚠️ Common exam mistakes

  • Ranking by contribution per unit instead of contribution per unit of the limiting factor — the most common error.
  • Ignoring minimum production constraints (contractual or strategic) when constructing the optimum mix.
  • In special-order problems, including fixed costs in the incremental analysis when they don't change.
  • In Make-or-Buy, comparing total cost (including unavoidable fixed cost) instead of avoidable / variable cost.
  • Forgetting that multiple resources may be constrained simultaneously — in that case, simple ranking fails and linear programming is required.
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