6.4 Limiting Factor Analysis and Make-or-Buy Decisions

In short-term operational planning, organizations often face resource constraints—such as shortages of direct labor hours, machine capacity, raw materials, or floor space. When availability of a key resource is insufficient to meet maximum market demand, that resource is termed a Limiting Factor (or bottleneck). Management accountants perform Limiting Factor Analysis to determine the production plan that maximizes total contribution and profit.

Q2022 syllabus scope note: AAT removed limiting-factor optimisation and make-or-buy calculations from the MATS assessment when Q2022 replaced AQ2016 — the assessable short-term decision techniques are contribution analysis, relevant costs, CVP analysis, and changing-activity calculations (sections 6.1–6.3). This section is retained as extension context: constraint-based thinking aids interpretation of capacity questions, and these techniques are assessed at Level 4 in Applied Management Accounting.

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Single Limiting Factor Optimization Methodology

To maximize profit when a single resource is scarce, companies must NOT rank products by contribution per unit or profit margin per unit. Instead, products must be ranked by Contribution per Unit of Limiting Factor.

Standard 5-Step Solution Procedure:

1. Identify the Limiting Factor: Calculate the total resource required to meet full market demand for all products and compare it against total available capacity to confirm a shortfall.
2. Calculate Contribution per Unit for each product: Selling Price per Unit - Variable Costs per Unit.
3. Calculate Contribution per Unit of Limiting Factor: $\text{Contribution per Unit of Limiting Factor} = \frac{\text{Unit Contribution}}{\text{Resource Quantity Required per Unit}}$
4. Rank Products: Assign Rank 1 to the product with the highest contribution per unit of scarce resource, Rank 2 to the next, etc.
5. Construct Optimal Production Plan: Allocate available scarce resource units to Rank 1 product up to maximum market demand, then allocate remaining resource to Rank 2, and so forth.

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Step-by-Step Worked Example

Operational Constraints:

• Available Machine Hours = 4,000 hours.
• Fixed Overhead = £30,000.

Step 1: Confirm Limiting Factor

• Total machine hours required = (1,000 × 2 hrs) + (1,200 × 3 hrs) + (800 × 2 hrs) = 2,000 + 3,600 + 1,600 = 7,200 hours.
• Since 7,200 hours required > 4,000 hours available, Machine Hours are the Limiting Factor (shortfall of 3,200 hours).

Step 2 & 3: Contribution per Unit & per Machine Hour

Step 4 & 5: Optimal Production Schedule

1. Produce Product Z (Rank 1): 800 units × 2 hrs = 1,600 hours used. Contribution = 800 × £30 = £24,000. (Remaining hours: 4,000 - 1,600 = 2,400 hrs).
2. Produce Product X / Y (Rank 2): Suppose management prioritizes Product X: 1,000 units × 2 hrs = 2,000 hours used. Contribution = 1,000 × £24 = £24,000. (Remaining hours: 2,400 - 2,000 = 400 hrs).
3. Produce Product Y (Balance): 400 hrs / 3 hrs per unit = 133.3 units. Contribution = 133.3 × £36 = £4,800.

$\text{Total Maximized Contribution} = £24,000 + £24,000 + £4,800 = £52,800$ $\text{Net Operating Profit} = £52,800 \text{ Total Contribution} - £30,000 \text{ Fixed Costs} = \mathbf{£22,800}$

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Make-or-Buy (Outsourcing) Decisions

Make-or-buy decisions involve choosing whether to manufacture a component internally or purchase it from an external supplier.

1. Simple Make-or-Buy (Without Limiting Factors)

• Compare internal variable production cost per unit against external purchase price per unit.
• If avoidable fixed costs exist, compare total internal avoidable cost vs external purchase cost.
• Decision Rule: Buy externally if External Purchase Price < Internal Avoidable Variable + Fixed Cost per Unit.

2. Make-or-Buy WITH a Limiting Factor

When internal capacity is constrained, the firm may manufacture some components internally and sub-contract (buy) the remainder.

• Formula for Extra Cost of Buying per Unit of Scarce Resource: $\text{Extra Cost per Unit of Scarce Resource Saved} = \frac{\text{External Purchase Price} - \text{Internal Variable Cost}}{\text{Quantity of Limiting Factor per Unit}}$
• Ranking Rule: Rank components by Extra Cost Saved per Unit of Limiting Factor. Produce highest extra cost components internally first (because making them in-house saves the largest amount of external expenditure per scarce hour/kg) and buy the lowest extra cost components externally!

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Qualitative and Strategic Factors in Make-or-Buy Decisions

Financial cost calculations provide only part of the answer. Management must weigh non-financial risks before outsourcing:

1. Quality Control: External suppliers may deliver inferior components, damaging brand reputation.
2. Supplier Reliability and Lead Times: Delivery delays could halt internal assembly lines.
3. Loss of Core Technical Expertise: Outsourcing key operations risks leaking proprietary technology to competitors.
4. Price Inflation Risk: Suppliers may offer low initial prices but raise prices dramatically once the buyer has shut internal manufacturing capacity.
5. Impact on Staff & Employee Morale: Internal manufacturing shutdowns can lead to redundancies and industrial action.