Advanced Performance Management · Performance improvement models and techniques

Throughput Accounting and Theory of Constraints for APM

Updated 11 October 2026 · Fact-checked

Throughput accounting treats only sales revenue less totally variable costs, usually materials, as throughput. The Theory of Constraints says output is limited by one bottleneck. To solve a question, find the bottleneck, rank products by throughput per bottleneck hour, and fill capacity in that order. The throughput accounting ratio compares return per hour to cost per hour.

Understand Throughput Accounting and Theory of Constraints

Every business has a limit on what it can produce or sell. The Theory of Constraints (TOC) says that at any time one resource limits the output of the whole system. This is the bottleneck or binding constraint. It could be a machine, a skilled team, a material supply or even market demand.

If the bottleneck limits output, then extra effort elsewhere does not raise profit. A non-bottleneck machine that runs faster only builds up stock. An hour lost at the bottleneck is an hour lost for the whole business. So management attention should go to the bottleneck first.

Throughput accounting is the measurement side of TOC. Throughput is sales revenue less totally variable costs. In most exam questions the totally variable cost is direct material only. Direct labour is treated as a fixed cost in the short run, together with overheads. Together these are called total factory cost (or operating expenses). Throughput accounting does not build stock value from labour and overheads, so it does not reward producing for stock.

The key measure is throughput per bottleneck hour. You rank products by it and make the highest first, up to demand. The throughput accounting ratio (TPAR) is return per bottleneck hour divided by factory cost per bottleneck hour. A ratio above 1 means the product earns more than the cost of using the bottleneck hour. A ratio below 1 means it does not cover its share of factory cost.

TOC also gives a five-step cycle: identify the constraint, exploit it, subordinate everything else to it, elevate it (increase its capacity) and repeat because a new bottleneck will appear. APM questions often ask you to discuss these steps in the scenario, not only to calculate.

Key rules to remember

Throughput: Throughput = sales revenue − totally variable costs (usually direct materials); Labour is normally treated as fixed in the short run unless the question says it is truly variable.
Throughput per unit of bottleneck resource: Return per bottleneck hour = (selling price − material cost per unit) ÷ bottleneck hours per unit; Use this to rank products when the bottleneck is a physical resource.
Total factory cost per bottleneck hour: Cost per factory hour = total factory cost ÷ total bottleneck hours available; Total factory cost = labour + overheads (all costs except materials). It is the same for every product.
Throughput accounting ratio: TPAR = return per bottleneck hour ÷ cost per factory hour; Above 1 is worthwhile. Below 1 means the product does not cover factory cost for the bottleneck time it uses. Where there is a bottleneck, rank on return per hour, which gives the same order as TPAR.
Throughput profit: Profit = total throughput − total factory cost; Use the optimal production plan to find total throughput.
Bottleneck test: Resource hours needed at maximum demand ÷ hours available; the highest ratio above 1 is the bottleneck; Check every resource, not just the obvious one.

How to solve Throughput Accounting and Theory of Constraints questions

Use this order for any throughput accounting or TOC question. It keeps your working clear and earns the method marks.

1Identify the bottleneck. Compare hours needed to meet demand with hours available for each resource. The resource that is most short is the bottleneck.
2Calculate throughput per unit for each product: selling price less direct materials (and any other truly variable cost).
3Divide by the bottleneck hours per unit to get return per bottleneck hour. Rank the products from highest to lowest.
4Allocate bottleneck hours in rank order, producing up to maximum demand for each product until the hours run out. State units and hours used.
5Calculate total throughput and deduct total factory cost to find profit. Work out cost per factory hour and TPAR for each product if asked.
6Interpret the result. Say which products are worthwhile, what limits profit, and what could be done to raise the bottleneck's capacity or reduce time used.
7Apply the answer to the scenario. Comment on points such as the cost of overtime, outsourcing, pricing, quality and effects on staff behaviour, and link them to your numbers.

Quickest way: Rank by return per bottleneck hour, then fill capacity

When to use it: Use this when the question gives one clear scarce resource and asks for the best production plan or TPAR. It is the fastest route in the exam.

Write throughput per unit for each product (price − materials) in a small table.
Divide each by its bottleneck hours. That gives the ranking and the numerator of TPAR.
Divide total factory cost by total bottleneck hours once. That gives the TPAR denominator.
Fill hours in rank order against demand. Do not forget the last product may be made only in part.
Total throughput − factory cost = profit. Spend the last minutes on comments, not more arithmetic.

Common mistakes in Throughput Accounting and Theory of Constraints

Deducting labour and overhead per unit when calculating throughput.
Students are used to contribution and absorption costing, where labour is deducted.
Fix: In throughput accounting, deduct only totally variable costs, usually materials. Labour and overheads go into total factory cost, which is the same whatever the product mix.
Ranking products by throughput per unit instead of per bottleneck hour.
The per-unit figure is easy to see and looks like the answer.
Fix: Always divide by the hours used on the bottleneck. A product with a low throughput per unit may use very little bottleneck time and rank first.
Choosing the wrong bottleneck, or assuming it is the first machine in the process.
Students do not compare hours needed with hours available for every resource.
Fix: Calculate demand hours against capacity for each resource. The tightest one is the bottleneck. Demand can also be the constraint.
Calculating cost per factory hour with the wrong hours, such as total labour hours instead of bottleneck hours.
The question may give several sets of hours.
Fix: Use total factory cost divided by the hours available on the bottleneck resource. Label it clearly.
Stopping after calculating the TPAR with no interpretation.
Students treat it as a calculation topic.
Fix: State what the ratio means: above 1 means the product earns more than it costs per hour, below 1 means it does not cover the cost. Then say what management should do, such as raise price, cut bottleneck time or drop the product.
Treating throughput accounting as the right answer in every case with no criticism.
The technique is taught with clean numbers.
Fix: Mention limits: it is short-term, it treats labour as fixed, it ignores long-term product costing and the bottleneck can move. It suits environments such as JIT and lean.

Worked examples

Example 1

A company makes three products using one machine, which is the bottleneck. Machine hours available are 1,000. Total factory cost is $12,000. Data per unit and maximum demand: X: price $50, materials $20, 2 machine hours, demand 200 units. Y: price $42, materials $12, 1.5 machine hours, demand 300 units. Z: price $36, materials $18, 0.5 machine hours, demand 400 units. (a) Find the optimal production plan and the profit. (b) Calculate the TPAR for each product.

Show the solution

Check the bottleneck: hours needed at full demand = X 200 × 2 = 400, Y 300 × 1.5 = 450, Z 400 × 0.5 = 200. Total = 1,050 hours against 1,000 available, so the machine is short.
Throughput per unit: X = 50 − 20 = $30. Y = 42 − 12 = $30. Z = 36 − 18 = $18.
Return per machine hour: X = 30 ÷ 2 = $15. Y = 30 ÷ 1.5 = $20. Z = 18 ÷ 0.5 = $36.
Ranking: Z first, Y second, X third.
Allocate hours: Z 400 units use 200 hours. Y 300 units use 450 hours (650 used in total). That leaves 350 hours for X, which gives 350 ÷ 2 = 175 units.
Total throughput: Z 400 × 18 = $7,200. Y 300 × 30 = $9,000. X 175 × 30 = $5,250. Total = $21,450.
Profit = 21,450 − 12,000 = $9,450.
Cost per factory hour = 12,000 ÷ 1,000 = $12.
TPAR: X = 15 ÷ 12 = 1.25. Y = 20 ÷ 12 = 1.67. Z = 36 ÷ 12 = 3.00.

Answer: Make 400 Z, 300 Y and 175 X for a profit of $9,450. TPARs are X 1.25, Y 1.67 and Z 3.00. All are above 1, so every product is worthwhile, but X is the first to be cut back because demand cannot be fully met.

Example 2

A firm has 20,000 bottleneck hours and total factory cost of $240,000. Product A sells for $80 with materials of $30 and uses 4 bottleneck hours. Product B sells for $60 with materials of $24 and uses 3 bottleneck hours. (a) Calculate the TPAR for each product. (b) Engineers can cut Product A's bottleneck time to 3.2 hours. Find the new TPAR for A. (c) What price for B would give a TPAR of 1.2?

Show the solution

Cost per factory hour = 240,000 ÷ 20,000 = $12.
(a) A: return per hour = (80 − 30) ÷ 4 = 50 ÷ 4 = $12.50. TPAR = 12.50 ÷ 12 = 1.04.
B: return per hour = (60 − 24) ÷ 3 = 36 ÷ 3 = $12. TPAR = 12 ÷ 12 = 1.00.
(b) New return per hour for A = 50 ÷ 3.2 = $15.625. TPAR = 15.625 ÷ 12 = 1.30.
(c) A TPAR of 1.2 needs a return per hour of 1.2 × 12 = $14.40. Throughput per unit = 14.40 × 3 = $43.20. Price = 43.20 + 24 = $67.20.

Answer: (a) A 1.04 and B 1.00, so both only just cover factory cost, and B breaks even on it. (b) A rises to 1.30 after the time saving, which shows that releasing bottleneck time raises returns. (c) B needs a price of $67.20 to reach a TPAR of 1.2.

Exam tips

Read the scenario for the bottleneck before calculating. Say clearly which resource is the constraint and show the hours check.
Show a small table: throughput per unit, bottleneck hours, return per hour, rank. Markers can then follow your logic even if you slip on one number.
Use the professional skills marks. After the numbers, give a short recommendation to the board, for example overtime, outsourcing or a price change, and weigh the cost and risk.
In discussion parts, link TOC to the scenario: how to exploit, subordinate and elevate the constraint, and note that the bottleneck may move once it is relaxed.
Write the TPAR rule in words: above 1 the product earns more than its factory cost for the hour used, below 1 it does not. Do not leave a ratio unexplained.

Practice questions from Performance improvement models and techniques

Throughput Accounting and Theory of Constraints in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Throughput Accounting and Theory of Constraints: frequently asked questions

How do you calculate the throughput accounting ratio?

Divide the return per bottleneck hour by the cost per factory hour. Return per hour is (selling price − materials) ÷ bottleneck hours per unit. Cost per factory hour is total factory cost ÷ bottleneck hours available.

What does a TPAR above 1 mean?

It means the product earns more throughput per bottleneck hour than the factory cost of that hour. The product adds to profit. A ratio below 1 means it does not cover its factory cost for the time it uses.

What is the difference between throughput and contribution?

Throughput deducts only totally variable costs, usually direct materials. Contribution normally also deducts variable labour and variable overheads. In throughput accounting labour is treated as a fixed factory cost in the short run.

How is throughput accounting examined in APM?

It usually appears as a short calculation of return per hour, ranking and TPAR, followed by discussion. You may need to explain TOC, the five steps and how to relieve the bottleneck. Expect to apply it to the scenario in a way that supports a recommendation.