Seven process simulations, worked through
Seven worked example models show the same pattern: processing time is measured in minutes, lead time in days, and the gap consists of waiting in front of the step with the highest utilisation. In invoice approval the constraint sits in business approval, in the quotation process in costing, in complaints in the query, in onboarding in the appointment chain, in the service desk in second line, in permits on the peak day, and in recruitment in time to response. In five of the seven cases the most effective lever was not more staff but less variation.
Table of contents
Note: all figures come from example models, not from client engagements. They are chosen to match typical orders of magnitude. Insert your own. The pattern holds.
Seven processes, each in the same form: situation, utilisation per step, result, most effective lever.
1. Invoice approval
1,200 invoices a month, five steps, approval spread across 14 people as a side task.
| Step | Processing | Utilisation |
|---|---|---|
| Scan | 2–4 min | 41 % |
| ERP entry | 6–14 min | 79 % |
| Business approval | 3–6 min | high, very variable |
| Coding | 4–8 min | 62 % |
| Payment run | 2×/week | — |
Result: processing time 20–30 min, lead time 8–12 working days. Five to eight days are spent waiting for business approval.
Most effective lever: not document capture. OCR shortens entry, after which approval takes the full volume. The constraint moves and lead time barely falls. A value threshold and a cover arrangement act more strongly and cost almost nothing. In detail.
2. Quotation process
60 enquiries a month, four steps, technical costing by two specialists.
| Step | Processing | Capacity |
|---|---|---|
| Log the enquiry | 10–20 min | Sales support |
| Technical costing | 2–8 h | 2 people, also on projects |
| Commercial review | 30–60 min | 1 person |
| Approval and dispatch | 15 min | Sales management |
Result: lead time P50 = 6 days, P90 = 19 days. The spread in costing (a factor of four between simple and complex) produces most of the waiting.
Most effective lever: separate enquiries by complexity. Simple quotations bypass costing via a price list. P90 falls to 8 days with no added capacity. The reason: waiting grows with the square of variation. Two queues beat one mixed queue.
Why this is worth more than cost savings: for quotations, lead time acts on win rate, not on cost. Answering second loses you deals you already costed.
3. Complaint handling
400 cases a month, of which 35 % involve a query to the customer or supplier.
Result: cases without a query: lead time P50 = 1.4 days. Cases with a query: P50 = 9 days. Mixed, that yields an average of 4.1 days that no single case ever experiences.
The finding: the constraint is not the handling but the double waiting of query cases: once for the handler, once for the answer.
Most effective lever: avoid queries rather than accelerate them. A mandatory field in the intake form covering the three most common query reasons cuts the query rate from 35 % to 12 %. P50 falls to 2.2 days.
The lesson: an average across two case groups with entirely different behaviour is not a metric but a disguise.
4. Employee onboarding
12 starters a month, seven participants (HR, IT, department, facilities, data protection).
The difference from every other example: volume is tiny, utilisation is below 20 % everywhere. Lead time is still three weeks.
Why: capacity is not scarce, appointments are. Each step waits not for free processing time but for a day on which the responsible person thinks of it. Seven participants with two days of response time each add up to two weeks without anyone being busy.
Most effective lever: parallelise rather than accelerate. IT account, access card and workstation run simultaneously rather than in sequence, triggered by one event. Lead time 21 → 9 days.
5. IT service desk
900 tickets a month, two lines, 20 % escalation.
| Step | Processing | Utilisation |
|---|---|---|
| First line | 5–15 min | 74 % |
| Second line | 30–180 min | 91 % |
Result: 80 % of tickets close the same day. The escalated 20 % take P50 = 4 days, P90 = 13 days. They generate practically every complaint.
Most effective lever: not adding second-line capacity but reducing the escalation rate. Every percentage point fewer escalations relieves the 91 % step disproportionately, because waiting there falls with ρ/(1−ρ): from 91 % to 85 %, waiting halves.
6. Permits in public administration
2,400 applications a year, very unevenly distributed: 40 % within two months.
On the annual average: utilisation 71 %. Looks healthy.
In the peak week: utilisation 148 %. The queue then grows every day and takes months to clear, because only the difference to capacity is available for clearing it, not the full capacity.
Result: lead time 9 days in a quiet quarter, 46 days after the peak. Same authority, same people.
Most effective lever: pull work forward rather than add staff. If 20 % of applications can be handled in the quiet period (appointment slots, pre-checks, deadline management), peak utilisation drops below 100 %, and the 46 days disappear.
The lesson: for seasonal processes, an annual average is the most misleading metric available.
7. Recruitment
80 applications a month for 6 positions, five steps with scheduling.
Result: time to first response P50 = 8 days, P90 = 21 days. Candidate drop-out rises measurably from day 10.
The finding: the constraint is not screening but scheduling the first interview: three calendars, two weeks of lead time, no fixed rule.
Most effective lever: fixed slots. Two hours a week reserved in every participant's calendar, candidates choose. P50 falls to 3 days. Nobody spends more time, only differently distributed time.
The pattern across all seven
| Example | Processing time | Lead time | Most effective lever |
|---|---|---|---|
| Invoice approval | 25 min | 8–12 days | Value threshold, cover |
| Quotation | 3–9 h | 6–19 days | Split by complexity |
| Complaints | 20–40 min | 1.4 / 9 days | Avoid queries |
| Onboarding | 4 h | 21 days | Parallelise |
| Service desk | 15–180 min | 0 / 4 days | Cut escalation rate |
| Permits | 45 min | 9 / 46 days | Level the peak |
| Recruitment | 2 h | 8 days | Fixed slots |
Three observations:
- Processing time and lead time differ by two to three orders of magnitude. Any measure aimed only at processing time attacks the smaller number.
- In five of seven cases the best lever was free. Reduce variation, parallelise, level the peak, avoid queries. No investment, and all of them hard to sell as a project.
- The obvious lever was almost never the best one. More staff, faster software, more automation: useful, but rarely where the time actually goes.
Frequently asked
Why is lead time so much longer than processing time?
Because of the waiting in between. A case spends most of its life not being processed but sitting in a tray until somebody has capacity. In administrative processes, 90 to 99 percent of lead time is waiting. That is why any measure which only accelerates processing attacks the smaller of the two numbers.
Are these figures real?
They are example models, not client data, and they are labelled as such. The orders of magnitude match what is typical in administrative and service processes. The value lies in the pattern rather than the absolute values: insert your own volumes and capacities and the structure of the finding usually survives.
Why does reducing variation often beat adding capacity?
Because waiting grows with the square of the coefficients of variation. Halve the variation and you quarter its contribution to the queue. Capacity acts through the factor ρ/(1−ρ), which only responds strongly near the limit. In practice: separate cases by type, level the inflow, abolish queries. That is usually cheaper than another position.
How do I recognise the onboarding pattern in my process?
By low utilisation everywhere and long lead time nonetheless. Then capacity is not scarce, attention is: each step waits for a day on which somebody thinks of it. The lever there is parallelisation and event-driven triggering, not more staff.
How many steps should these models have?
Five to ten, as in all seven examples. Modelling more finely does not move the constraint: it sits where utilisation is highest, and that is just as visible coarsely. Extra steps cost input time and create an impression of precision the input data cannot support.
Run the numbers on your own process
FlowVisual turns the figures in this article into a model that runs, with your volumes, your capacities, your range.
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