ACCA Applied Skills · Performance Management
Limiting Factors in ACCA Performance Management
A limiting factor is a scarce resource that stops a business making or selling as much as it wants. With one limiting factor, rank products by contribution per unit of the scarce resource and allocate the resource in that order. With two or more, use linear programming.
What this chapter covers
This chapter is about decision-making when something is in short supply. That can be machine hours, labour hours, materials or sales demand. Without a shortage, you would simply make every product with a positive contribution. With a shortage, you must choose which products to make and how much of each.
You start with the single limiting factor case. You calculate contribution per unit of the scarce resource, rank the products, and fill the available resource in rank order. You then extend this to make-or-buy, where you compare the extra cost of buying with the scarce resource saved by not making. Finally you handle two limiting factors by linear programming, using a graph or simultaneous equations, and read off shadow prices and slack.
The chapter links to several other parts of PM. It uses relevant costing and contribution from marginal costing. It feeds into pricing, product mix and budgeting questions. It also appears in the objective test sections as short calculations and in Section C as a longer, structured question.
Limiting factors are a reliable source of marks because the method is mechanical once you know it. Single-factor ranking and make-or-buy turn up as quick objective test questions, where answers are marked all or nothing and care with the ranking matters. Linear programming, shadow prices and slack can form part of a 20-mark constructed response question, where marks are given for layout, workings and interpretation. Students who practise the steps in order can collect most of these marks, and the chapter also strengthens your grasp of contribution, which you use throughout the paper.
Limiting factors: topics in the order to study them
- 1Limiting Factors and Key Factor AnalysisStart with the idea of a scarce resource and why contribution per unit of that resource, not per product, is the measure.
- 2Single Limiting Factor: Contribution per Unit of Scarce ResourceThis is the core method of ranking and allocating, and everything later builds on it.
- 3Limiting Factors with Make-or-Buy DecisionsIt reuses the ranking idea, applying it to extra buying cost per unit of scarce resource saved, so learn it right after the basic method.
- 4Multiple Limiting Factors and Linear ProgrammingMove to two scarce resources only when single-factor work is secure, since you need to define variables, constraints and an objective.
- 5Shadow Prices and SlackThese interpret the linear programming solution, so they come last, after you can find the optimal point.
How to prepare Limiting factors
Build the chapter in layers. Get the single-factor method automatic before you touch graphs, because it is the quickest source of marks.
- Read the scenario and identify the scarce resource. Check whether demand limits are also given, as these cap production too.
- Practise single-factor questions until you calculate contribution per unit, then contribution per scarce resource unit, then rank, without hesitation.
- Allocate the resource in rank order, respecting any maximum demand, and finish with a production plan and total contribution.
- For make-or-buy, work out the extra variable cost of buying per unit, divide by scarce resource saved per unit, and buy the lowest figure first.
- For linear programming, write the objective function and constraints, including non-negativity, then plot the lines on a graph and find the feasible region.
- Find the optimal point by testing the corner points or using the iso-contribution line, and solve the intersecting constraints with simultaneous equations.
- Calculate shadow prices by increasing a binding constraint by one unit and recalculating contribution. Identify slack by comparing resource used with resource available.
Common mistakes in Limiting factors
Ranking products by contribution per unit instead of per unit of scarce resource.
Fix: Always divide by the scarce resource used per unit before ranking, and write the resource unit in your working.
Ignoring maximum demand limits when allocating the resource.
Fix: Cap each product at its demand, then pass leftover resource to the next ranked product.
Including fixed overheads or sunk costs in make-or-buy comparisons.
Fix: Use only avoidable variable costs and the purchase price, unless the question says fixed costs change.
Plotting constraints inaccurately or choosing the wrong feasible region.
Fix: Calculate both intercepts for each line, label every line, and check the region with a test point such as the origin.
Treating a shadow price as the price you must pay to get extra resource.
Fix: Remember it is the extra contribution from one more unit, so it is the maximum premium worth paying above the normal cost of the resource.
Stating shadow prices or slack without checking that the constraint is binding.
Fix: Substitute the optimal solution into each constraint first. Spare resource means slack and a shadow price of zero.
Last-day revision: Limiting factors
- A limiting factor is the resource that restricts activity, so contribution per unit of that resource drives the decision.
- Single factor: rank by contribution per unit of scarce resource, not by contribution per product.
- Allocate the resource to the top-ranked product first, up to its maximum demand, then move down.
- Make-or-buy with a shortage: compare extra buying cost per unit of scarce resource saved, and buy the lowest first.
- Use relevant costs only: avoidable variable costs, not allocated fixed overheads.
- Linear programming needs an objective function, constraints and non-negativity conditions.
- The optimal solution lies at a corner of the feasible region, or along an edge if the objective line is parallel to a constraint.
- Solve intersecting constraint lines with simultaneous equations to get exact quantities.
- A shadow price is the increase in contribution from one extra unit of a scarce resource.
- A resource that is fully used (binding) has a positive shadow price, and a non-binding one has a shadow price of zero.
- Slack is the unused amount of a resource at the optimal solution.
- Always finish with a plan that states units to make and total contribution.
Limiting factors practice questions
- A company has a single limiting factor of skilled labour. Product M has contribution of $40 per unit and uses 5 hours. Product N has a selli…
- A company uses linear programming to plan production of two products. Which statement about the feasible region and the optimal solution is …
- In a linear programme, the shadow price of machine hours is $5 per hour and the constraint currently limits output to 100 hours. Which state…
- A company makes products X and Y. Machine hours are the only scarce resource. X has a contribution of $24 per unit and uses 3 machine hours;…
- Brenner Co needs 1,000 units each of components P and Q. Machine hours available are 3,000 and the machine time needed is 2 hours per unit o…
Limiting factors in other exams
The same ground in other exams, if you are preparing for more than one or want another angle on it.
Limiting factors: frequently asked questions
What is a limiting factor in ACCA PM?
It is a resource that restricts the output or sales of a business, such as labour hours, machine time, materials or demand. The business must decide how to use it to earn the highest contribution. The rest of the chapter is about making that choice.
How do I solve a single limiting factor question?
Calculate contribution per unit for each product. Divide by the scarce resource used per unit. Rank the products, then allocate the available resource in rank order, respecting any demand limits. Finish with the production plan and total contribution.
Do I need to draw graphs for linear programming in PM?
You should be able to understand and interpret a graph and use it to find the optimal point. In the computer-based exam you may be asked to read or complete the logic rather than draw by hand. You should still practise the underlying maths with intercepts and simultaneous equations.
What is the difference between shadow price and slack?
A shadow price is the extra contribution from one more unit of a fully used resource. Slack is the amount of a resource left unused at the optimal solution. A resource with slack has a shadow price of zero.
How does make-or-buy change when a resource is limited?
You cannot just compare the cost of making with the cost of buying. You calculate the extra cost of buying per unit of scarce resource saved and rank the components. The component with the lowest extra cost per unit saved is bought first, as it is cheapest to outsource.