What the Estimator Does
A shipping schedule gives the day a vessel arrives. It does not say when the cargo reaches your door. The time from the end of vessel discharge to unloading at the door is port-to-door time, and it is made up of separate legs, each with its own average and its own unpredictability.
The Connect Lagos Traffic Port-to-Door Transit Time Estimator turns those legs into a delivery promise you can defend. It works in five steps:
- Split the journey into six legs and record the mean (average) and the standard deviation (σ, the typical spread around the average) of each.
- Add the means to get the expected total, and combine the spreads to get the total uncertainty.
- Choose a planning time that is met a stated share of the time (the service level), such as 90% or 95%.
- Test the promise against cost, against free time and against the leg most worth fixing.
- Compare where the time goes with where the uncertainty comes from. The two are often not the same.
All times are in elapsed hours, and one day means 24 hours, not working days.
The Formula
Step 1. Expected total time
T̄ = Σ mean of each leg
Step 2. Total spread
- Independent legs: σ = √(Σ σᵢ²)
- Linked legs: σ² = Σ σᵢ² + ρ × [(Σ σᵢ)² − Σ σᵢ²]
Here ρ (rho) is the correlation between legs, from 0 (independent) to 1 (they move together). A congestion event that slows several legs at once pushes ρ above zero.
Step 3. Planning time at a service level
Planning time = T̄ + z × σ
| Service level | z |
|---|---|
| 80% | 0.842 |
| 90% | 1.282 |
| 95% | 1.645 |
| 99% | 2.326 |
The buffer is the part of the planning time above the expected total: z × σ.
Step 4. Reliability of a promise
Probability of arriving within T = Φ((T − T̄) ÷ σ)
Φ is the standard normal cumulative distribution, available in any spreadsheet as NORM.S.DIST(z, TRUE).
Step 5. Where the time and the uncertainty sit
Leg share of time = Leg mean ÷ T̄
Leg share of uncertainty = Leg σ² ÷ Σ σᵢ²
The Estimator treats each leg's time as bell-shaped around its mean. Real delays have a longer upper tail, and the Limitations section explains the consequence.
Worked Example in Naira
The Scenario (Hypothetical)
Folake is a supply-chain manager at a food-packaging firm in Lagos. She imports packaging film and must give her production planner a delivery promise, measured from the end of vessel discharge. She is an illustrative character, and the shipment is not real. Every input below is assumed and is not current market data. They are not measured clearance times at any real terminal.
Assumed Inputs
| Leg | Mean (hours) | σ (hours) |
|---|---|---|
| A. Customs documentation and clearance | 60 | 24 |
| B. Examination, terminal charges and release | 30 | 15 |
| C. Truck call-up and gate queue | 10 | 5 |
| D. Loading and gate-out | 3 | 1 |
| E. Road transit, 40 km loaded | 3 | 1.5 |
| F. Delivery-site wait and unloading | 5 | 3 |
Calculation
Expected total
- T̄ = 60 + 30 + 10 + 3 + 3 + 5 = 111 hours (4.6 days)
Total spread (independent legs)
- Σ σ² = 576 + 225 + 25 + 1 + 2.25 + 9 = 838.25
- σ = √838.25 = 28.95 hours
Planning times
| Service level | z | Buffer (hours) | Planning time (hours) | Days |
|---|---|---|---|---|
| 50% | 0 | 0.0 | 111.0 | 4.6 |
| 80% | 0.842 | 24.4 | 135.4 | 5.6 |
| 90% | 1.282 | 37.1 | 148.1 | 6.2 |
| 95% | 1.645 | 47.6 | 158.6 | 6.6 |
| 99% | 2.326 | 67.3 | 178.3 | 7.4 |
Reliability of some natural promises
| Promise | Hours | Probability of meeting it |
|---|---|---|
| 5 days | 120 | 62.2% |
| 6 days | 144 | 87.3% |
| 7 days | 168 | 97.6% |
| 8 days | 192 | 99.7% |
Working for the 6-day promise: (144 − 111) ÷ 28.95 = 1.14, and Φ(1.14) = 0.873.
Where the time and the uncertainty sit
| Leg | Mean | Share of time | σ² | Share of uncertainty |
|---|---|---|---|---|
| A. Clearance | 60 h | 54.1% | 576.00 | 68.7% |
| B. Release | 30 h | 27.0% | 225.00 | 26.8% |
| C. Gate queue | 10 h | 9.0% | 25.00 | 3.0% |
| D. Loading and gate-out | 3 h | 2.7% | 1.00 | 0.1% |
| E. Road transit | 3 h | 2.7% | 2.25 | 0.3% |
| F. Delivery site | 5 h | 4.5% | 9.00 | 1.1% |
| Total | 111 h | 100.0% | 838.25 | 100.0% |
Result
A promise of 5 days looks close to the average of 4.6 days, but it is met only 62% of the time. A promise of 6.6 days is met 95% of the time. The gap between the average and a reliable promise is 47.6 hours, or two full days.
In these assumed inputs, the road journey is 2.7% of the time and 0.3% of the uncertainty. The two clearance legs, A and B, are 81.1% of the time and 95.6% of the uncertainty. A planner who focuses on the drive is working on the part of the journey that matters least.
What Linked Delays Do to the Answer
The independent calculation assumes a slow day at the terminal does not also slow the next leg. In practice, a congestion event often hits clearance, release and the gate queue together. Hold the means constant and change only ρ.
| Correlation (ρ) | Total σ | 95% planning time | Days | Probability of meeting a 6-day promise |
|---|---|---|---|---|
| 0 (independent) | 28.95 h | 158.6 h | 6.6 | 87.3% |
| 0.5 | 40.55 h | 177.7 h | 7.4 | 79.2% |
| 1.0 (move together) | 49.50 h | 192.4 h | 8.0 | 74.8% |
Working for ρ = 0.5: σ² = 838.25 + 0.5 × (49.5² − 838.25) = 838.25 + 806 = 1,644.25, so σ = 40.55. The 95% planning time grows by nearly a day and a half between the independent and fully linked cases.
Break-Even Tests
All three tests use Folake's example. Test 1 uses a separate set of assumed cost figures.
Test 1: The Cost-Balanced Promise
A promise that is too tight risks a late delivery, and one that is too loose ties up capital, space and planning time.
Formula: Optimal service level = Cost per day late ÷ (Cost per day late + Cost per day early)
Assume a late delivery stops the production line at ₦1,500,000 per day, and early arrival costs about ₦150,000 per day in extra storage and financing.
- Optimal service level: ₦1,500,000 ÷ (₦1,500,000 + ₦150,000) = 90.9%
- The matching z is about 1.335
- Promise: 111 + 1.335 × 28.95 = 149.6 hours, which is 6.2 days
The costs set the promise, and a different ratio of costs gives a different answer:
| Cost per day late | Cost per day early | Service level | Promise (hours) | Days |
|---|---|---|---|---|
| ₦750,000 | ₦150,000 | 83.3% | 139.0 | 5.8 |
| ₦1,500,000 | ₦150,000 | 90.9% | 149.6 | 6.2 |
| ₦3,000,000 | ₦150,000 | 95.2% | 159.3 | 6.6 |
A firm that loses more from a stopped line should promise a longer, safer date. That follows from the arithmetic and is not a matter of caution.
Test 2: Free-Time Exposure
Demurrage starts when containers stay past the free time. Use legs A to D, which run from discharge to gate-out. Their mean is 103 hours and their σ is √827 = 28.76 hours. Assume 5 days (120 hours) of free time and 4 containers at ₦60,000 per container per day (₦240,000 a day), the same inputs as the Connect Lagos Traffic Port Demurrage Calculator.
- Probability of leaving within free time: Φ((120 − 103) ÷ 28.76) = Φ(0.59) = 72.3%
- Probability of paying demurrage: 27.7%
- Expected hours beyond free time: 4.9 hours, or 0.21 days
| Case | Probability of exceeding free time | Expected demurrage, pro rata | Expected demurrage, whole days billed |
|---|---|---|---|
| Base | 27.7% | ₦49,200 | ₦88,100 |
| Clearance cut by 12 hours (leg A mean 48 h) | 15.7% | ₦23,600 | ₦46,300 |
The "pro rata" column charges only for the hours beyond free time. The "whole days" column charges any part of a day as a full day. Your shipping line's terms decide which applies. The shipment faces a better than one-in-four chance of paying, even though the average journey fits inside free time.
Test 3: Which Leg Is Worth Fixing?
Compare four changes by how much each cuts the 95% planning time of 158.6 hours.
| Change | New 95% planning time | Saving |
|---|---|---|
| Cut leg A's mean by 12 hours (60 to 48) | 146.6 h | −12.0 h |
| Halve leg A's spread (σ from 24 to 12) | 144.2 h | −14.5 h |
| Halve the spread of both clearance legs A and B | 136.4 h | −22.3 h |
| Halve the road leg's time and its spread (mean 1.5 h, σ 0.75 h) | 157.1 h | −1.5 h |
Working for the second change: Σ σ² falls to 838.25 − 576 + 144 = 406.25, so σ = 20.16, and 111 + 1.645 × 20.16 = 144.2.
Making clearance more predictable saves more than making it faster by 12 hours. A road leg twice as fast saves 1.5 hours.
Worked Example in Dollars
The Scenario (Hypothetical)
Ethan is a purchasing manager in Dallas who receives containers from a US Gulf Coast port to an inland warehouse 250 miles away. He is an illustrative character, and these numbers are separate from the naira example. All are assumed. Customs entry and terminal procedures in the United States differ from Nigeria's, so use your own broker's records.
Assumed Inputs
| Leg | Mean (hours) | σ (hours) |
|---|---|---|
| A. Customs and documentation | 18 | 6 |
| B. Terminal examination and release | 12 | 6 |
| C. Truck appointment and gate | 4 | 2 |
| D. Loading and gate-out | 1.5 | 0.5 |
| E. Road transit, 250 miles loaded | 5.5 | 1 |
| F. Warehouse wait and unloading | 3 | 1.5 |
Calculation
- Expected total: 18 + 12 + 4 + 1.5 + 5.5 + 3 = 44 hours (1.8 days)
- Σ σ² = 36 + 36 + 4 + 0.25 + 1 + 2.25 = 79.5, so σ = 8.92 hours
| Service level | Buffer (hours) | Planning time (hours) | Days |
|---|---|---|---|
| 50% | 0.0 | 44.0 | 1.8 |
| 80% | 7.5 | 51.5 | 2.1 |
| 90% | 11.4 | 55.4 | 2.3 |
| 95% | 14.7 | 58.7 | 2.4 |
| 99% | 20.7 | 64.7 | 2.7 |
| Promise | Hours | Probability of meeting it |
|---|---|---|
| 2 days | 48 | 67.3% |
| 2.25 days | 54 | 86.9% |
| 2.5 days | 60 | 96.4% |
| 3 days | 72 | 99.9% |
Where the time and the uncertainty sit: legs A and B are 68.2% of the time and 90.6% of the uncertainty. The road leg is 12.5% of the time and 1.3% of the uncertainty.
Comparing the Two Examples
| Measure | Lagos (assumed) | US (assumed) |
|---|---|---|
| Expected total | 111 h (4.6 days) | 44 h (1.8 days) |
| Total σ | 28.95 h | 8.92 h |
| Spread as share of expected total (σ ÷ T̄) | 26.1% | 20.3% |
| 95% planning time | 158.6 h (6.6 days) | 58.7 h (2.4 days) |
| 95% buffer as share of expected total | 42.9% | 33.3% |
| Clearance legs, share of time | 81.1% | 68.2% |
| Clearance legs, share of uncertainty | 95.6% | 90.6% |
| Road leg, share of time | 2.7% | 12.5% |
In both examples, almost all the uncertainty sits in clearance and release, so the right lever is similar. The road leg matters more in the US example because the distance is longer and clearance is quicker in the assumed inputs. These are illustrative inputs, so neither column says anything about real operations in either market.
Which Measure to Trust
| Measure | What it ignores | Best used for |
|---|---|---|
| Vessel arrival date | Everything after discharge | Starting the clock only |
| Expected total (T̄) | How likely the average is to be met | Rough planning |
| Planning time at 90% or 95% | Fat tails and the linking between legs | Making a delivery promise |
| Reliability of a given promise | Whether the promise is costly to miss | Judging how risky a date is |
| Share of uncertainty by leg | Whether the leg can actually be changed | Choosing where to spend effort |
| Cost-balanced service level | Costs that are hard to estimate | Setting the promise by economics |
When the Estimator Matters and When It Does Not
It matters most when:
- A production line, retail launch or contract deadline depends on a delivery date.
- Free time is short compared with the realistic clearance time.
- You are deciding whether to spend money on a faster haulier or on better clearance.
It matters less when:
- The cargo is not time-sensitive and you hold ample stock.
- Your own records show little variation from shipment to shipment.
- The container leaves the port within hours, so one leg dominates.
Run It With Your Own Numbers
Use this checklist and template to build the Estimator from your own shipments.
Checklist
- Define the clock: start at the end of vessel discharge and stop when unloading at the door finishes.
- For each shipment, record the timestamp of every leg: documents lodged, duty paid, examination finished, release, truck called, gate-in, gate-out, arrival at the door and unloading finished.
- Take the timestamps from your clearing agent, the terminal operator and your haulier's records, and note which source each came from.
- Use at least 20 shipments if you can. With fewer than about 10, treat every spread as rough and widen the buffer.
- Calculate the mean and the standard deviation of each leg from your own records.
- Check whether delays cluster on the same days, which signals ρ above zero, and run the linked case.
- Choose a service level from your own cost of lateness and cost of earliness, using Test 1.
- Compare the dwell time with your free time under Test 2, using the terms in your shipping line's contract.
- Use the share-of-uncertainty column to pick which leg to work on, then re-run Test 3 on that leg.
- Confirm current clearance and gate procedures with your clearing agent, the terminal operator, the Nigerian Ports Authority (NPA) and the Nigeria Customs Service, since processes change.
- Re-measure every quarter and compare each leg with the last period.
Template
| Leg | Mean (h) | σ (h) | σ² | Share of time | Share of uncertainty |
|---|---|---|---|---|---|
| A. Customs documentation and clearance | % | % | |||
| B. Examination, charges and release | % | % | |||
| C. Truck call-up and gate queue | % | % | |||
| D. Loading and gate-out | % | % | |||
| E. Road transit | % | % | |||
| F. Delivery-site wait and unloading | % | % | |||
| Total | 100% | 100% |
| Result line | Your figure |
|---|---|
| Expected total T̄ | hours |
| Total σ (independent) | hours |
| Total σ (with your ρ) | hours |
| T̄ + z × σ = Planning time at your service level | hours / days |
| Cost per day late ÷ (late + early) = Cost-balanced service level | % |
| P(dwell within free time) | % |
| Leg with the largest share of uncertainty |
Limitations
- The Estimator assumes each leg's time follows a bell-shaped curve. Real delays are skewed, with occasional very long ones, so the normal model understates the risk in the tail. A shipment that sits at the port for 11 days, as in the Port Demurrage Calculator's example, would be about 5.6 standard deviations above the assumed mean. A normal model calls that almost impossible, so treat it as a warning about the model and not about the case.
- Means and spreads come from your own past shipments, so they describe the conditions of that period. A strike, a policy change or a new terminal procedure can make them obsolete.
- The calculation uses one correlation figure for all legs. Real links differ by pair, and the same event may slow some legs and speed others.
- The Estimator does not include time spent waiting for a vessel to berth, since the clock starts at discharge, and it excludes storage or detention charges.
- It measures time, not cost. Use the Connect Lagos Traffic Haulage Cost-per-Tonne Estimator for truck cost and the Connect Lagos Traffic Fleet Utilisation Tracker for waiting time across a fleet.
- Every input above is an assumption chosen to show the method. Replace each with verified figures from your own records before relying on the output.
This resource is educational and is not personalised financial, legal or logistics advice. Consult a licensed professional, such as a clearing agent or freight lawyer, before making decisions on a shipment.
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