Performance improvement models and techniques: formula sheet

Key formulas

Definition of BPR

BPR = fundamental rethinking + radical redesign of processes → dramatic improvement in cost, quality, service and speed

Use the four key words fundamental, radical, dramatic and processes when defining it.

BPR versus kaizen

BPR: radical, top-down, one-off, high risk, big gain. Kaizen: incremental, bottom-up, continuous, low risk, small gains

A comparison format works best in answers. Compare on scale, who drives it, timing, risk and cost.

Lean waste test

Value-adding activity = one the customer would pay for. Everything else = waste to remove or reduce

Used to identify non-value-adding steps before redesign or improvement.

Lean: five principles

Specify value → Map value stream → Create flow → Establish pull → Pursue perfection

Use as a checklist when asked how to apply lean to a process or service.

Six Sigma: DMAIC

Define → Measure → Analyse → Improve → Control

Use for improving an existing process. Always name the stage and link it to the scenario.

Defects per million opportunities

DPMO = (number of defects ÷ (units × opportunities per unit)) × 1,000,000

Measures process quality. Six Sigma performance is commonly quoted as 3.4 DPMO, which allows for a long-term 1.5 sigma shift in the process mean.

Costs of quality

Total cost of quality = prevention + appraisal + internal failure + external failure

TQM aims to raise prevention spend to reduce failure costs. Do not treat appraisal spend as a substitute for prevention.

Process cycle efficiency

Value-adding time ÷ total lead time

A common lean measure. A low result shows much of the time is waiting or other waste.

Performance gap

Gap = Benchmark performance − Own performance

For measures where lower is better, such as cost or defect rate, reverse it: Gap = Own − Benchmark. State the direction clearly.

Percentage gap

Gap % = (Benchmark − Own) ÷ Benchmark × 100

This form is for measures where higher is better. For lower-is-better measures, such as time, cost or defect rate, use Gap % = (Own − Benchmark) ÷ Benchmark × 100. Use the same base throughout. Dividing by your own figure gives a different percentage, so say which base you use.

Benchmarking cycle

Plan → Collect data → Analyse gap → Set targets → Implement → Monitor and repeat

A memory aid for the process, not a fixed ACCA model. Use it to structure answers.

Margin in the value chain

Margin = Total value to customers − Total cost of value activities

Use it to show that improving value or cutting activity cost raises margin.

Cost driver rate

Cost driver rate = Activity cost pool ÷ Total volume of the cost driver

Used to trace activity cost to products or customers, for example cost per set-up or per purchase order.

Activity cost of a product

Activity cost = Cost driver rate × Number of driver units the product uses

Add the cost of each activity to get the product's total overhead.

Non-value-added cost share

NVA share = Cost of non-value-added activities ÷ Total activity cost × 100%

A rough guide to the scope for savings. Only classify an activity as NVA if customers would not pay for it.

Porter's activity groups

Primary: inbound logistics, operations, outbound logistics, marketing and sales, service. Support: procurement, technology development, HRM, firm infrastructure

Know these names and apply them to the scenario's business.

Target cost

Target cost = Target selling price − Target profit

If profit is a margin on price, profit = price × margin %. If it is a mark-up on cost, divide the price by (1 + mark-up) to get cost.

Cost gap

Cost gap = Current estimated cost − Target cost

A positive figure means cost must fall. It is the amount the team must find through redesign or process change.

Kaizen reduction target

Target cost in period = Previous cost × (1 − reduction %)

Applied period by period, so the reduction compounds on the new, lower base.

Life cycle cost per unit

Total life cycle cost ÷ Total units over the life

Total life cycle cost includes pre-production, production, marketing, service and end-of-life costs. Use the same units for the whole life.

Discounted life cycle cost

Σ cash cost in year t ÷ (1 + r)^t

Use if the question gives a cost of capital and asks for present value of life cycle costs.

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.

Value for money (3Es)

Economy = inputs bought at lowest cost for the right quality; Efficiency = outputs ÷ inputs; Effectiveness = outcomes achieved against objectives

Add a fourth E, equity, where fair access to the service matters. Always link each E to a measure from the scenario.

Efficiency measure

Efficiency = output achieved ÷ resources used

Example: cases handled per staff member, or cost per patient. Compare with a target or a peer.

Cost per unit of service

Cost per service unit = total cost of service ÷ number of service units delivered

Define the unit carefully (patient day, case, student). Different case mixes make comparisons unfair.

Suitability check

Context features → technique that fits → benefits → limits and risks → recommendation

This is a method, not a calculation. Use it to structure every evaluation answer.

Quick revision

• BPR is radical redesign of processes to get large gains; it carries high risk and disruption.
• Lean aims to remove waste and focus on what the customer values.
• Six Sigma uses data to cut defects and variation, often through the DMAIC approach.
• TQM is a culture of continuous quality improvement involving all staff, covering prevention, appraisal and failure costs.
• Benchmarking compares performance or practice with others; types include internal, competitor, functional and generic.
• Value chain analysis separates primary and support activities to find where value is created or lost.
• ABM uses activity cost information to manage cost drivers, not just to allocate overheads.
• Target cost = target selling price − target profit margin; compare it with the current cost to find the gap.
• Kaizen costing seeks small, continual cost reductions during production.
• Life cycle costing includes costs before, during and after production, so early design decisions matter.
• Throughput = sales revenue − direct material cost; the aim is to maximise throughput through the bottleneck.
• In every answer, apply the tool to the scenario and state at least one limitation.

Common mistakes

• Treating BPR as simply cost cutting or redundancies. Fix: Say BPR redesigns processes for dramatic gains in cost, quality, service and speed. Job losses may follow but are not the definition.
• Describing BPR and kaizen as the same thing. Fix: Always contrast them: radical and one-off versus incremental and continuous. Mention who drives each.
• Treating lean and Six Sigma as the same thing. Fix: State the difference: lean removes waste and delay; Six Sigma reduces defects and variation. Then say how they complement each other.
• Listing DMAIC stages without applying them. Fix: Give one specific action per stage using scenario facts, such as what to measure and which root causes to test.
• Listing the four types with textbook definitions and nothing else. Fix: Apply each type to the scenario. Say which suits the organisation and why, using its data and industry.
• Confusing functional with competitor benchmarking. Fix: Competitor means direct rivals in the same market. Functional means the best performer of a process in any industry, often a non-rival.
• Listing Porter's nine activities with no link to the scenario. Fix: Use the model as a checklist only. Write about the activities the scenario describes and use its facts.
• Calling an activity non-value-added just because it costs money. Fix: Apply the customer test. If customers would pay for it or it is needed to meet their requirements, it adds value. Inspection may be needed by law, so say so.
• Treating profit as a mark-up on cost when it is a margin on price, or the reverse. Fix: Read whether the percentage is of selling price or of cost. Margin: price × (1 − margin). Mark-up: price ÷ (1 + mark-up).
• Calculating the cost gap the wrong way round or ignoring its sign. Fix: Always do current cost minus target cost. Positive means savings are needed.

Exam tips

• Always compare BPR with an incremental alternative. Examiners often reward a reasoned choice, not a description of one method.
• Use scenario facts in every paragraph. Generic lists of advantages and disadvantages earn few marks.
• Include change management. Resistance, communication and leadership are standard points for evaluation questions.
• Write in the requested format, such as a report or briefing note, and keep a clear recommendation to earn professional skills marks.
• Link BPR to performance measurement: say how you would check success, for example using cycle time, cost per transaction and customer satisfaction.
• Always link the approach to scenario facts. A generic definition earns few marks. Name the specific wastes, defects or cultural issues you can see.
• Use DMAIC as your structure for Six Sigma answers, with one scenario-based action at each stage.
• Show professional skills by giving a balanced view: benefits, costs, risks and a clear recommendation.