Vose SoftwareModelRisk Optimizer example · Projects and construction
Schedule Acceleration Chosen by the Optimizer
Which activities should be accelerated, at least cost, for an 80% chance of opening the bridge within the contract?
From the model’s saved run
The Optimizer’s plan against the starting plan
The accelerations of the two plans, and how each performs on the same simulated projects.
S-curve (cumulative probability) of Starting plan, Optimizer’s plan, Contract duration from the saved simulation.
| Decision | Unit | Starting plan | Optimizer’s plan | Change |
|---|---|---|---|---|
| A Design: second design team | 1 = yes | – | – | – |
| C Demolition: extra possessions | 1 = yes | – | – | – |
| D North piling: second piling rig | 1 = yes | – | yes | added |
| E South piling: second piling rig | 1 = yes | – | yes | added |
| F River pier: pre-cast pier units | 1 = yes | – | yes | added |
| K Deck slab: pre-cast deck units | 1 = yes | – | – | – |
| Measure | Unit | Starting plan | Optimizer’s plan | Change | |
|---|---|---|---|---|---|
| Cost of the accelerations | US$k | 0 | 190 | 190 | |
| Chance of finishing within the contract | chance | 57.8% | 82.7% | 25.0% | ✔ better |
| Completion, P50 | weeks | 43.6 | 41.8 | −1.8 | ✔ better |
| Completion, P80 | weeks | 45.6 | 43.8 | −1.8 | ✔ better |
| Completion, mean | weeks | 43.6 | 41.9 | −1.7 | ✔ better |
| Programme with most likely durations | weeks | 40.0 | 38.6 | −1.4 | ✔ better |
| P80 completion date | date | 14 Jan 2028 | 1 Jan 2028 | ||
| Contract duration | weeks | 44 | 44 | ||
| On-time chance required (Inputs sheet) | chance | 80% | 80% |
Programme: most likely durations and no flood, the deterministic schedule (Network sheet, section 6).
The business question
A council's road bridge replacement takes 40 weeks with most likely durations, and the contract allows 44. But durations run long and parallel paths merge, so the chance of finishing on time is under 60% (PC-03). Six activities can be accelerated at a price: more designers, extra railway possessions, a second piling rig at either abutment, pre-cast pier units or pre-cast deck units.
Which are worth buying?
- Who it is for
- Planners, project managers and contractors who prepare, review or recover programmes.
- Main outputs
- The Optimizer's choice of accelerations against a starting plan with none (PC-03's programme) · for both plans: the cost of the accelerations, the chance of finishing within the contract, P50 and P80 completion and the programme with most likely durations · each activity's criticality index under both plans · the completion S-curves.
What the Optimizer decides
The Optimizer changes the blue cells: 1 accelerates the activity, 0 does it the normal way. The starting plan accelerates nothing: PC-03's programme.
| Decision | Starting plan | Optimizer’s plan |
|---|---|---|
| A Design: second design team | No | No |
| C Demolition: extra possessions | No | No |
| D North piling: second piling rig | No | Yes |
| E South piling: second piling rig | No | Yes |
| F River pier: pre-cast pier units | No | Yes |
| K Deck slab: pre-cast deck units | No | No |
- Goal
- Minimise the cost of the accelerations
- Limit
- Chance of finishing on time at least 80%
The Optimizer’s run: Vertex Detector, 64 plans tried, each on 10,000 samples, in 8.0 seconds.
How the model works
Four sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The start date, the contract duration and the chance of meeting it that is required. The flood risk to the river pier; and for each of six activities, the share of its duration that accelerating it saves and what that costs.
Decisions sheet
The six cells the Optimizer changes, one per activity that can be accelerated: 1 to accelerate it, 0 not to. The starting plan accelerates nothing. The goal is the least cost of the accelerations. The limit is the chance of finishing within the contract.
Network sheet
Each iteration draws every duration once. Both plans use the same draws, shortened by their own accelerations, and each is scheduled forwards and backwards: its completion, whether it meets the contract and which activities are critical are outputs. Both plans' programmes with most likely durations are calculated too.
Results sheet
Both plans on the same simulated projects: the cost, the chance of finishing within the contract, P50 and P80 completion, the S-curves, and how often each activity is critical under each plan.
ModelRisk techniques
Find similar models
- Product
- Type
- Application
- Uses
The results in detail
Which activities are critical
Criticality index: how often the activity is on the critical path in the simulation, under each plan.
Chart: Starting plan, Optimizer’s plan.
| Activity | Programme critical | Starting plan criticality | Optimizer’s plan criticality | Accelerated in the plan |
|---|---|---|---|---|
| A Design and approvals | yes | 100% | 100% | no |
| B Site set-up and traffic management | yes | 99% | 96% | – |
| C Demolish the old bridge | yes | 99% | 96% | no |
| D North abutment piling | yes | 38% | 40% | yes |
| E South abutment piling | yes | 43% | 45% | yes |
| F River pier | 19% | 10% | yes | |
| G Fabricate steel girders (off site) | 1% | 4% | – | |
| H North abutment walls | yes | 38% | 40% | – |
| I South abutment walls | yes | 43% | 45% | – |
| J Deliver and erect girders | yes | 100% | 100% | – |
| K Deck slab | yes | 100% | 100% | no |
| L Waterproofing and surfacing | yes | 92% | 92% | – |
| M Parapets and finishes | 8% | 8% | – | |
| N Approach road tie-ins | 0% | 0% | – | |
| O Testing and opening | yes | 100% | 100% | – |
Programme: critical in the starting plan's programme. Accelerated: in the Optimizer’s plan (– = not an option).
How to read these results
- The starting plan — PC-03's programme, with nothing accelerated — finishes within the 44-week contract in under 60% of the simulated projects, well short of the 80% required.
- The Optimizer buys a second piling rig at each abutment and pre-cast units for the river pier, for about US$190k. The chance of finishing on time rises to a little over 80%, and P80 completion falls by about two weeks, to within the contract.
The pier is not on the 40-week critical path, and on paper its pre-cast units save nothing: the programme is the same with or without them. Accelerate only the pilings and the chance stalls at about three in four, because the pier, with its flood risk, then sets the pace in over a third of the projects.
With all three accelerated, it does so in about one in ten.
- Design, demolition and the deck lie on every path, so time saved there counts in full. But each saves only about a week, for US$140k–160k, and no plan that uses them reaches 80% for less.
- Try a 90% requirement on the Inputs sheet and run the Optimizer again: it adds the pre-cast deck units as well, and the cost rises by about three-quarters.
Run the Optimizer yourself. Open the workbook, open the Optimizer from the ModelRisk ribbon (the saved task opens with it) and press Start; then simulate to compare the plans.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Programme and target 3 inputs
When the work starts, what the contract allows, and how sure the council wants to be.
| Assumption | Unit | Value |
|---|---|---|
| Start dateNotice to proceed (1 March 2027). | date | 1 Mar 2027 |
| Contract durationCompletion date in the contract: 44 weeks after the start. | weeks | 44 |
| On-time chance requiredThe chance of finishing within the contract that the Optimizer must reach: the council wants P80 or better. | chance | 80% |
Risk event 2 inputs
A flood stops work in the river until the water level drops.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Chance of a flood during the pier worksGauge records: one flood in four winters over the cofferdam's design level. | chance | Fixed | 25% | ||
| Delay to the river pier from a floodPumping out, inspection and repair of the cofferdam. | weeks | Risk event · PERT | 2.0 | 3.0 | 6.0 |
Acceleration: time saved 6 inputs
The share of the activity's duration saved if it is accelerated, whatever the duration turns out to be.
| Assumption | Unit | Value |
|---|---|---|
| Design: a second design teamMore designers, and fortnightly reviews with the highway authority instead of one at the end. | of its duration | 10% |
| Demolition: extra railway possessionsTwo more night possessions a week; the railway charges for each one. | of its duration | 25% |
| North abutment piling: a second piling rigTwo rigs share the piles; mobilisation and pile testing take as long as before. | of its duration | 20% |
| South abutment piling: a second piling rigA heavier second rig for the softer ground near the river bank. | of its duration | 20% |
| River pier: pre-cast pier unitsPier shafts cast off site and lifted into the cofferdam. A flood delays the work as much as before. | of its duration | 25% |
| Deck slab: pre-cast deck unitsPre-cast planks as permanent formwork: less concrete poured and cured on site. | of its duration | 20% |
Acceleration: cost 6 inputs
The extra cost of each acceleration, paid if it is chosen.
| Assumption | Unit | Value |
|---|---|---|
| Design: a second design teamTwo more designers through the design period, and the extra reviews. | US$ thousand | 160 |
| Demolition: extra railway possessionsPossession fees and night-time rates. | US$ thousand | 150 |
| North abutment piling: a second piling rigSecond rig and crew: mobilisation, hire and operators. | US$ thousand | 65 |
| South abutment piling: a second piling rigA heavier rig: higher mobilisation and hire. | US$ thousand | 70 |
| River pier: pre-cast pier unitsCasting yard, transport and a larger crane, less the work saved in the river. | US$ thousand | 55 |
| Deck slab: pre-cast deck unitsPlanks, transport and a larger crane, less the formwork saved. | US$ thousand | 140 |
Units and conventions
- Time
- Weeks from the start of the project; dates are the start date plus whole weeks.
- Money
- US$ thousand (US$k): the extra cost of each acceleration over the normal method.
- Accelerate
- 1 = the activity is accelerated, 0 = it is done the normal way. Accelerating saves a fixed share of the activity's duration, whatever that duration turns out to be.
- Critical
- An activity is critical in an iteration if it has no float. Its criticality index is the share of iterations in which it is critical.
- Programme
- The schedule with most likely durations and no flood: the deterministic programme a planner would draw.
Key assumptions and limitations
- Logic
- Finish-to-start links only, no lags; resources are not limited; accelerating one activity does not slow another.
- Acceleration
- Each saves a fixed share of its activity's duration for a fixed cost, paid whether or not it turns out to be needed. It does not shorten the flood delay.
- Independence
- Durations are independent of each other; in practice common causes (productivity, weather) can link them.
- Optimizer
- Each plan the Optimizer tries is judged on the same 10,000 simulated projects (common random numbers, seed 1) as the simulation on the Results sheet, so plans are compared fairly and the limit the Optimizer met holds on the Results sheet too.
- Data
- The project, the durations and the acceleration options are invented for this example.
How to use it
- Enter your durations on the Network sheet, and your contract, the chance required, the flood risk and your acceleration options on the Inputs sheet.
- On the ModelRisk ribbon, open the Optimizer: the task is saved in this workbook. Press Start. When it finishes, apply the best solution: the 1s and 0s on the Decisions sheet change.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set) to compare the new plan with the starting plan on the Results sheet.
- To watch the search from the beginning, copy the starting plan onto the Optimizer’s plan first. To see why the 40-week critical path misleads, accelerate only the two pilings and simulate.
ModelRisk functions used
- ModelRisk Optimizer
- Chooses which activities to accelerate: least cost of the accelerations, with the chance of finishing within the contract at least the chance required.
- VosePERT
- Each activity's duration from its low, most likely and high estimates.
- VoseRiskEvent, VosePERTObject
- The flood: no delay, or a PERT number of weeks.
- VoseInput, VoseOutput
- Name the durations and the outputs of both plans, including whether each activity is critical.
- VoseSimProbability, VoseSimPercentile
- The chance of finishing on time and the completion percentiles of both plans.
- VoseSimMean
- The mean completion and each activity's criticality index under both plans.
Further reading
- Monte Carlo simulation explained (Vose guide)
- Hulett, D. T. (2009). Practical Schedule Risk Analysis. Gower.
- Kelley, J. E. (1961). Critical-path planning and scheduling: mathematical basis. Operations Research 9(3), 296–320.
- PC-03 Schedule risk on a project network: the same bridge and network, with the criticality index and merge bias explained.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
Related example models
- ModelRisk★★★★★Integrated Cost and Schedule RiskBudget and completion date together: how confident can the sponsor be of both, for the treatment works upgrade?Schedule, time-dependent costs and shared risk events simulated together, with the joint chance of meeting budget and date.
- ModelRisk★★★★★Risk Register: Threats and OpportunitiesHow much risk contingency does the hospital extension need?A risk register turned into a simulation: risk events with linked cost and schedule impacts.
- ModelRisk★★★★★Construction Cash Flow and Peak FundingIs a US$40 million facility enough?A 48-month cash flow with S-curve spend, off-plan sales and a revolving facility with monthly interest.
An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.