Capacity, Constraints and Throughput Accounting

Introduction

Operations performance is governed not only by demand, technology and labour, but also by the capacity of the system through which work must flow. A plant may possess substantial installed equipment yet fail to meet customer requirements because one machine, activity or decision rule constrains the entire process. Conversely, an organisation may invest in capacity that remains unused while reporting apparently satisfactory unit costs. Operations Costing & Accounting therefore requires managers to distinguish between the capacity that exists, the capacity that can practically be used, and the capacity that is actually required.

This chapter connects capacity measurement with bottleneck analysis, the Theory of Constraints (TOC) and throughput accounting. The central managerial question is not simply, “What is the cost per unit?” It is: “How can scarce operational resources be used to generate the greatest sustainable contribution to organisational goals?”

Traditional cost systems often allocate fixed overhead across units and encourage local efficiency, large batches and high utilisation of every resource. Those behaviours can increase inventory and delay flow. Throughput accounting takes a system-wide perspective: in the short run, direct material is commonly treated as the principal truly variable cost, while operating expense and investment are managed in relation to the rate at which the system converts material into sales.

Learning objectives

By the end of this chapter, you should be able to:

1. Distinguish design, effective, practical, actual, idle and excess capacity.
2. Measure capacity utilisation and identify the causes of unused capacity.
3. Locate and diagnose bottlenecks using process-flow and capacity analysis.
4. Explain the Theory of Constraints and apply its five focusing steps.
5. Calculate throughput, throughput per constrained-resource minute and related decision measures.
6. Evaluate product mix, outsourcing and improvement decisions without confusing local cost efficiency with system optimisation.
7. Critically assess the strengths, limitations and governance implications of throughput accounting.

1. Capacity as an operational and accounting concept

Capacity is the maximum volume of output or activity that a resource or system can produce under specified conditions and within a stated period. Capacity is not a single universal number. It depends on the definition of output, product mix, operating hours, quality standards, maintenance policy, staffing, demand and technological conditions.

1.1 Capacity categories

Design capacity is often misleading for performance evaluation because it excludes setups, breaks, preventive maintenance, changeovers, quality losses and variability. Practical capacity is normally more useful for budgeting. For example, a machine available for 2,400 scheduled hours may have 240 hours of planned maintenance and 120 hours of unavoidable setup time. Its practical capacity is therefore 2,040 hours before considering demand or unplanned failure.

1.2 Capacity measures

For a single resource measured in output units:

For time-based resources, the same logic applies using productive hours in the numerator and available or practical hours in the denominator. The units must match: units with units, hours with hours, or standard minutes with standard minutes.

A resource may have low design-capacity utilisation but high effective utilisation. For instance, actual output of 1,800 units against design capacity of 2,400 units gives 75% design utilisation. If effective capacity is 2,000 units, effective utilisation is 90%. These measures tell different stories and should not be confused.

1.3 Idle, blocked, starved and excess capacity

A resource is idle when it is available but not processing work. It is starved when it cannot work because no input is available. It is blocked when it cannot release completed work because the downstream process or storage area is unavailable. These distinctions matter because the remedy differs:

• Starvation may require better scheduling, material availability or upstream reliability.
• Blocking may require downstream capacity, buffer management or quality release.
• Avoidable idle time may require improved demand management, staffing or maintenance planning.
• Structural excess capacity may require redeployment, product development, outsourcing or asset rationalisation.

Idle capacity is not automatically waste. Protective capacity at non-bottleneck resources can be valuable because it prevents disruption to the constraint. Similarly, a resource may appear idle because the system deliberately limits release to match the bottleneck.

2. Capacity economics and cost interpretation

Capacity decisions have both operational and accounting consequences. Fixed costs such as depreciation, salaried supervision and facility rent generally do not change immediately when output changes. If these costs are divided by actual units, a fall in volume increases reported unit cost even when the underlying resource has not become less efficient. This is the denominator effect.

A basic full-cost unit calculation is:

These formulas are useful for some external reporting and long-term pricing analyses, but their assumptions must be recognised. The allocation base may not reflect resource consumption, and the result may be inappropriate for short-run decisions when fixed costs are unavoidable.

For capacity planning, managers should separately identify:

• committed capacity costs, which cannot readily be changed;
• discretionary capacity costs, which management can alter over a relevant horizon;
• step costs, which change when activity crosses a threshold; and
• truly variable costs, which change with each incremental unit or transaction.

The relevant cost of a decision is the future cost that differs between alternatives. An allocated fixed cost that remains unchanged is not relevant to a short-run make-or-buy decision, although avoidable supervision, tooling or transport costs may be relevant.

3. Process flow and bottleneck analysis

A constraint is anything that limits a system from achieving more of its goal. A bottleneck is a capacity-constrained resource whose available capacity is insufficient for the required flow under current conditions. The constraint may be a machine, labour skill, supplier, policy, approval rule, information system, market condition or managerial assumption.

3.1 Identifying the bottleneck

A disciplined analysis begins by mapping the process from order release to delivery. For each activity, record demand, processing time, available time, yield, changeovers, downtime and queue. A simple capacity calculation is:

If the load ratio exceeds 1, the resource lacks capacity for the stated demand. The resource with the highest sustained load ratio is a likely constraint, but managers should verify it through observed queues, missed due dates, work-in-process accumulation and schedule instability. A nominally overloaded activity may be relieved by yield improvement, alternate routing or product substitution.

For a resource with multiple products:

where the summation covers all products using the resource and all times are expressed in a common unit, such as minutes per week.

3.2 Flow, variability and protection

Little’s Law links work-in-process, throughput and flow time in a stable system:

Here, WIP is average work-in-process in units, throughput rate is average completed units per time period, and flow time is the average time a unit spends in the system. The relationship assumes a stable long-run system in which average input and output rates are equal and measurements use consistent time bases. It does not by itself identify a bottleneck or explain causation.

Variability reduces effective capacity through failures, uneven arrivals, rework, absenteeism and changing product mix. High utilisation near 100% can create disproportionate waiting time because there is little protective capacity to absorb variation. Thus, a lower utilisation target may improve delivery performance and total throughput.

Figure: A process constraint determines the maximum sustainable flow unless the constraint is relieved or bypassed.

4. The Theory of Constraints

The Theory of Constraints, associated particularly with Eliyahu M. Goldratt, views an organisation as a system whose performance is limited by a small number of constraints. Its purpose is not to maximise the efficiency of every department independently, but to increase the rate at which the system achieves its goal. In a commercial organisation, that goal is commonly expressed as making money now and in the future, subject to appropriate social, legal and ethical responsibilities.

4.1 The five focusing steps

1. Identify the constraint. Find the resource, rule or market condition preventing greater throughput. Use data and direct observation rather than departmental opinion.
2. Exploit the constraint. Obtain more output from existing capacity without major investment. Reduce downtime, improve quality, eliminate unnecessary setups, prioritise valuable work and ensure that the constraint never waits for material or information.
3. Subordinate everything else. Align non-constraints with the constraint’s requirements. Avoid releasing work faster than the constraint can process it, because excess release creates inventory and longer lead times.
4. Elevate the constraint. Add capacity through overtime, cross-training, additional equipment, alternate routing, supplier development, redesign or capital investment.
5. Repeat the process. Once one constraint is broken, another becomes dominant. Do not allow inertia, policies or performance measures to become the next constraint.

The third step is often the most culturally difficult. A non-bottleneck resource may be deliberately underutilised. That is not poor performance if it protects flow and reduces work-in-process. Local utilisation is subordinate to system throughput.

4.2 Drum-buffer-rope logic

The drum is the pace set by the constraint. The buffer is strategically positioned protection against disruption, often measured in time or work content rather than merely units. The rope is the release signal that prevents upstream processes from producing more work than the system can absorb. This mechanism coordinates release, protects the constraint and limits unnecessary inventory.

TOC also uses conflict-resolution tools such as the current reality tree, evaporating cloud and future reality tree. These tools help managers move from symptoms—late deliveries, excess inventory or overtime—to underlying causes and assumptions. They are not substitutes for data; they structure disciplined inquiry.

5. Throughput accounting

Throughput accounting is a management accounting approach designed to support TOC decisions. Its central measures are throughput, investment and operating expense.

5.1 Core measures

Throughput (T) is the rate at which the system generates money through sales. In the short run, a common definition is:

Totally variable cost is the cost that changes directly with each additional unit sold; in many manufacturing applications it is primarily direct material. If a product sells for $120 and its direct material is $45, throughput per unit is $75, assuming no other cost varies directly with the unit.

Investment (I), sometimes called inventory, is money tied up in items intended for sale, including raw materials, work-in-process and finished goods, and sometimes other operating assets depending on the organisation’s measurement policy. It should be measured consistently and should avoid adding artificial profit through allocated conversion costs.

Operating expense (OE) is the money spent to turn investment into throughput. It includes labour, supervision, utilities, depreciation, rent, maintenance and other operating resources. The precise classification must be documented because some costs may be variable over a longer horizon.

Two useful system-level measures are:

If T and OE are measured per month, net profit is monthly; I is a stock measured at a point in time. ROI is dimensionless when both numerator and denominator are expressed in monetary units for the same reporting basis. These measures should not be confused with externally reported profit or conventional ROI unless definitions are reconciled.

For comparing products that consume a scarce resource:

The product with the higher result generates more throughput for each minute of the scarce resource, assuming demand exists, quality and cash constraints are satisfied, and other relevant constraints are unchanged.

5.2 Worked example: product-mix priority

A factory makes Products A and B. The data are:

Throughput per constraint minute is:

• A: $60 ÷ 3 = $20 per minute.
• B: $70 ÷ 5 = $14 per minute.

The constraint should first produce A, subject to its demand limit. Demand for A consumes 500 × 3 = 1,500 minutes. If the constraint has 2,400 minutes available, 900 minutes remain. These can produce 900 ÷ 5 = 180 units of B.

Weekly throughput is:

• A: 500 × $60 = $30,000.
• B: 180 × $70 = $12,600.
• Total: $42,600.

A conventional ranking based on selling price would incorrectly prioritise B; a ranking based on throughput per unit would also prioritise B because $70 exceeds $60. The constraint-minute measure gives the economically relevant ranking. This conclusion assumes that all produced units are sold, direct materials are the only totally variable cost, product quality is acceptable and no downstream constraint is tighter.

5.3 Exploit, subordinate and elevate in accounting decisions

A throughput-oriented decision process asks:

1. What resource limits additional sales?
2. How much throughput does each candidate product generate per unit of that resource?
3. Which costs change if the decision is implemented?
4. Will the decision increase total system throughput rather than merely departmental output?
5. What happens to investment, operating expense, quality, delivery and future capacity?

For example, paying overtime at a non-constraint may produce more units but no additional sales if the bottleneck remains unchanged. Conversely, paying premium freight to protect a bottleneck may be economically justified if the incremental throughput exceeds the incremental cost and risks are controlled.

6. Integrated capacity and throughput analysis

Capacity measurement and throughput accounting should be used together. Capacity analysis identifies where time is scarce; throughput accounting evaluates how scarce time should be allocated. Neither replaces strategic judgement.

A practical workflow is:

1. Define the planning horizon and output measure.
2. Map the end-to-end flow and establish demand assumptions.
3. Convert processing requirements into common time units.
4. Calculate practical capacity and load ratios for each resource.
5. Confirm the constraint using queue, downtime and delivery evidence.
6. Calculate throughput per constraint unit for alternative products or orders.
7. Exploit and subordinate before recommending capital expenditure.
8. Quantify the effects on throughput, investment, operating expense, quality and risk.
9. Monitor whether the constraint has moved.

Worked example: capacity relief

A bottleneck department has 2,000 practical minutes per week. Product X requires 4 minutes and generates $32 throughput per unit. Product Y requires 8 minutes and generates $56 throughput per unit. Confirmed demand is 300 units of X and 150 units of Y.

Required time is:

• X: 300 × 4 = 1,200 minutes.
• Y: 150 × 8 = 1,200 minutes.
• Total demand: 2,400 minutes.

The department is short by 400 minutes. Throughput per minute is $8 for X and $7 for Y. The feasible mix is therefore 300 X units and (800 ÷ 8) = 100 Y units if X demand is fully met. Throughput equals (300 × $32) + (100 × $56) = $15,200.

Suppose a temporary improvement reduces X processing time from 4 to 3 minutes without changing quality or material cost. Required time becomes 900 + 1,200 = 2,100 minutes, so demand still cannot be fully met. If instead a setup reduction saves 150 minutes, available time becomes 2,150 minutes. The additional 150 minutes should be allocated to X because its throughput per minute is higher, allowing 37.5 additional X units in a continuous model, or 37 whole units with 2 minutes unused in a discrete weekly schedule. The distinction between continuous and whole-unit calculations should be stated in operational plans.

7. Case study: Northstar Components

The following is an illustrative case, constructed for educational purposes.

Background

Northstar Components manufactures two precision assemblies for industrial customers. The plant has cutting, machining, finishing and inspection departments. Monthly sales have increased, but delivery performance has deteriorated. Finance reports rising product costs because fixed conversion costs are being allocated over fewer completed units. Production managers argue that every department must run at high utilisation to recover overhead.

Problem

The plant’s sales manager accepts a large order for Assembly B because its selling price is higher. However, customers are already experiencing delays. Work-in-process has accumulated before machining, while finishing staff frequently wait for released work. The chief operating officer asks whether the order should be accepted and which improvement should receive funding.

Analysis

The team maps the flow and measures practical monthly minutes:

Machining has a load ratio of 115% and is supported by the queue observed before it. It is the constraint. The team then calculates throughput per machining minute:

Although Assembly B has the higher unit throughput, Assembly A is more attractive when machining time is scarce. The team also identifies 900 minutes of avoidable machining downtime caused by delayed tooling, changeover sequencing and first-piece approval.

Approach and solution

Northstar first exploits the constraint. It introduces a tooling checklist, pre-stages materials, moves approval preparation upstream and sequences similar products together. It protects the machining centre with a time buffer and stops releasing work merely to keep cutting busy. Cutting utilisation falls, but the machining queue becomes more stable.

The company then subordinates the other departments. Finishing and inspection schedules are tied to machining output rather than to their own maximum capacity. The sales team uses the machining-minute contribution measure when evaluating new orders. Only after these actions does management consider elevation: a modest fixture investment and cross-training programme.

Outcome

The actions recover 600 of the 900 lost machining minutes. At $20 throughput per recovered minute, the theoretical additional throughput opportunity associated with prioritised Assembly A is $12,000 per month, subject to demand and downstream capacity. The plant also reduces work-in-process and improves due-date reliability. Reported cutting cost per unit initially increases because cutting is less fully loaded, but total throughput and customer performance improve. This is a useful warning against treating local absorption cost as the sole performance criterion.

Learning points

The case demonstrates that:

• the highest selling price is not necessarily the best use of scarce capacity;
• a non-bottleneck can be intentionally underutilised;
• exploiting existing capacity may be more effective than immediate capital investment;
• throughput analysis must include demand, quality and downstream feasibility; and
• accounting measures influence behaviour, so poorly designed metrics can damage flow.

8. Limitations, controls and contemporary practice

Throughput accounting is powerful but not a universal replacement for financial accounting. It is primarily an internal decision-support approach. External reporting normally requires recognised inventory valuation, expense recognition and disclosure rules. Organisations must reconcile internal throughput measures with statutory accounts and clearly label management measures.

Important limitations include:

• Definition sensitivity: Classifying labour or energy as totally variable may be inaccurate over the relevant horizon.
• Multiple constraints: A system may contain interacting bottlenecks, supplier constraints and market limits. A single ranking can be inadequate.
• Demand uncertainty: A product with high throughput per minute is not valuable if it cannot be sold or if contractual commitments differ.
• Long-term effects: Persistently ignoring full costs can lead to underinvestment, poor pricing or strategic errors.
• Quality and risk: Maximising immediate throughput can encourage defects, unsafe work or expedited decisions that damage customers.
• Behavioural gaming: Managers may manipulate time standards, classifications or buffers to improve reported measures.
• Discrete operations: Whole-unit, batch, setup and sequence effects may make continuous formulas approximate rather than exact.

Governance requires transparent definitions, auditable data, separation of internal and external reporting, and balanced measures. A sound dashboard may include throughput, operating expense, investment, on-time delivery, first-pass yield, safety incidents, employee wellbeing and customer complaints. Throughput must never be pursued by bypassing regulatory, environmental, labour or product-safety obligations.

Digital manufacturing execution systems, process mining, sensors and advanced planning tools can improve constraint visibility. AI can forecast failures, identify patterns in queue formation, optimise sequencing and estimate remaining useful life. However, AI recommendations depend on data quality and objective design. A model trained only to maximise machine utilisation may worsen system flow by increasing work-in-process. Human oversight, explainability, cybersecurity, access control and validation of recommendations are therefore necessary.

Best practice is to combine TOC with lean methods, statistical process control, total productive maintenance and sound financial analysis. Lean tools can reduce waste and lead time; TOC identifies what deserves priority; maintenance protects availability; and accounting evaluates economic consequences. These approaches complement one another when the system goal is explicit and measures are aligned.

Chapter Summary

Capacity must be defined in relation to conditions, time and output. Design capacity is theoretical, while effective and practical capacity recognise planned operating realities. Actual output can be compared with different capacity bases, and idle, starved, blocked and excess capacity require different responses. Capacity analysis should use consistent units and realistic assumptions.

A bottleneck is a constraint that limits system flow. Required resource time, load ratios, process observation, queue evidence and delivery performance help identify it. The Theory of Constraints directs managers to identify, exploit, subordinate, elevate and then repeat. Drum-buffer-rope coordinates the system around the constraint and prevents excessive release of work.

Throughput accounting focuses on throughput, investment and operating expense. Throughput is commonly sales revenue less totally variable cost; net profit is throughput less operating expense. When a resource is scarce, throughput per constraint minute is generally more informative than selling price, unit throughput or allocated full cost alone. Decisions must nevertheless consider demand, quality, downstream capacity, long-term costs, ethics and governance.

The central managerial principle is system optimisation: improving the flow and economic performance of the whole operation rather than maximising local utilisation. Effective implementation requires reliable data, cross-functional discipline, transparent definitions and regular reassessment because constraints move.

Key Terms

Capacity: Maximum output or activity achievable under specified conditions and time.

Design capacity: Theoretical maximum capacity under ideal conditions.

Effective capacity: Capacity achievable under planned operating conditions.

Practical capacity: Effective capacity after normal unavoidable interruptions.

Utilisation: Actual output expressed as a proportion of a specified capacity base.

Idle capacity: Available capacity that is not being used.

Excess capacity: Capacity greater than expected or economically justified requirements.

Constraint: Any factor that limits achievement of the system goal.

Bottleneck: A capacity-constrained resource limiting process flow.

Throughput: Rate at which sales generate money, commonly sales less totally variable cost.

Investment: Money tied up in inventory and other assets according to the measurement policy.

Operating expense: Money spent to convert investment into throughput.

Throughput accounting: Internal management accounting approach supporting constraint-focused decisions.

Theory of Constraints: System-management philosophy focused on identifying and managing constraints.

Drum-buffer-rope: TOC scheduling logic that sets pace, protects flow and controls release.

Starvation: A condition in which a resource lacks input work.

Blocking: A condition in which a resource cannot release completed work.

Load ratio: Required resource time divided by available resource time.

Subordination: Aligning non-constraints with the requirements of the constraint.

Constraint minute: One unit of time on the scarce resource used for product prioritisation.

Review Questions

Short Answer Questions

1. Distinguish design capacity, effective capacity and practical capacity.
2. What is the difference between a starved resource and a blocked resource?
3. State the five focusing steps of the Theory of Constraints.
4. Define throughput in the conventional throughput-accounting sense.
5. Why can a lower utilisation rate improve operational performance?

Long Answer Questions

1. Explain how capacity definitions influence budgeting, performance measurement and investment decisions.
2. Discuss why local efficiency and high utilisation at every department may reduce total system performance.
3. Explain drum-buffer-rope scheduling and its relationship to bottleneck protection.
4. Critically evaluate the use of throughput per constraint minute for product-mix decisions.
5. Compare throughput accounting with conventional full-cost allocation for short-run operational decisions.

Analytical / Application Questions

1. A resource has 3,600 practical minutes per week. Product A requires 6 minutes and generates $48 throughput per unit; Product B requires 9 minutes and generates $63. Demand is 400 units of A and 300 units of B. Determine the priority order and a feasible weekly mix that maximises throughput, assuming no other constraint.
2. A plant reports 95% utilisation at a non-bottleneck while orders are late because another department operates at 120% of practical capacity. Analyse why management should not automatically expand the 95%-utilised department, and recommend two actions.
3. A proposed automation project costs $80,000, increases constraint capacity by 1,000 minutes per month and raises monthly operating expense by $2,500. If the additional minutes generate $9 throughput per minute and can be sold, assess the monthly economic effect and identify non-financial checks required before approval.

Multiple Choice Questions with Answers

Question 1

Which capacity measure most directly reflects planned maintenance, normal setups and other expected operating interruptions?

A. Design capacity

B. Practical capacity

C. Theoretical demand

D. Maximum market capacity

Correct Answer: B. Practical capacity

Question 2

A product generates $72 of throughput and uses 6 minutes of the bottleneck. What is its throughput per constraint minute?

A. $12

B. $18

C. $66

D. $432

Correct Answer: A. $12

Question 3

Which action is the third focusing step in the Theory of Constraints?

A. Identify the constraint

B. Exploit the constraint

C. Subordinate everything else

D. Eliminate all inventory

Correct Answer: C. Subordinate everything else

Question 4

A resource requires 9,000 minutes for demand and has 7,500 available minutes. What is its capacity load ratio?

A. 83.3%

B. 100%

C. 120%

D. 150%

Correct Answer: C. 120%

Question 5

Under the common short-run definition, throughput equals:

A. Sales revenue plus fixed cost

B. Sales revenue minus totally variable cost

C. Operating expense minus investment

D. Allocated overhead divided by units

Correct Answer: B. Sales revenue minus totally variable cost

Question 6

In drum-buffer-rope logic, the drum represents:

A. The pace set by the constraint

B. The total inventory value

C. The accounting close date

D. The fastest non-bottleneck process

Correct Answer: A. The pace set by the constraint

Question 7

If throughput is $50,000 and operating expense is $37,000 for a period, what is net profit under throughput accounting?

A. $13,000

B. $37,000

C. $50,000

D. $87,000

Correct Answer: A. $13,000

Question 8

Which situation describes a blocked resource?

A. It has no input material available

B. It cannot release completed work because downstream capacity is unavailable

C. It is processing the highest-throughput product

D. It is operating below design capacity by choice

Correct Answer: B. It cannot release completed work because downstream capacity is unavailable

Question 9

Why is selling price alone inadequate for prioritising products at a bottleneck?

A. Selling price never affects revenue

B. It ignores the scarce-resource time and variable cost associated with the product

C. Selling price is always equal to direct material cost

D. Bottlenecks affect only quality, not capacity

Correct Answer: B. It ignores the scarce-resource time and variable cost associated with the product

Question 10

A valid governance practice for throughput accounting is to:

A. Use internal measures as an undisclosed substitute for statutory accounts

B. Maximise bottleneck utilisation regardless of safety

C. Document definitions and reconcile internal measures with external reporting

D. Exclude quality and customer measures from performance evaluation

Correct Answer: C. Document definitions and reconcile internal measures with external reporting