Is the extra crew cheaper than the damages?
Crews are committed weeks before anybody knows what the weather will do, and the damages for being late are convex while the cost of an extra crew is not. The optimizer searches every crew count against a season of simulated weather and beats the plan everybody signs.
Construction Advanced Optimization under Uncertainty Pro engine
After you install, this is the model to open.
How Many Crews, When the Weather Is a Guess
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
This one runs on a Pro engine, and every free install includes five full-quality runs on your own numbers, shared across all five Pro engines rather than five for each. After that, Pro is $199/year.
The answer
- Crews to commit
- 7 the plan weather says six
- Expected cost, 7 crews
- $447,713 against $451,206 for six
- Late with 6 crews
- 82% of simulated weathers
- Late with 7
- 33% and 9% with an eighth crew
Two hundred and sixty crew days of exterior work, fifty working days before the deadline, crews at $1,450 a day plus $9,800 each to mobilize, and liquidated damages of $12,000 for every day you are late. At the most likely weather, 18% of days lost, the cheapest plan is six crews at $443,500, and that is the plan that gets signed. Switch the mode to Optimize decisions and click Run with the weather drawn from a PERT running from 5% to 55% of days lost.
The answer is seven crews, at about $448,000 of expected cost against about $451,800 for six. Read those two numbers next to the deterministic ones, because they disagree: on the plan weather the seventh crew looks like $2,100 of waste, and once the weather is a range it is a saving of about $3,800. The reason is not the average weather at all.
Six crews finish late in 82% of weathers. Seven crews finish late in 33%. Eight finish late in 9%. Damages are convex, so a week of rain in a tight programme costs far more than a week of sunshine saves, and a plan built on the most likely weather is a plan that is late four times in five. Now the second run, because when you are minimizing a cost the cautious statistic is the high percentile rather than the low one.
Change Statistic from Mean to P95 and run again: the answer moves to eight crews. That is worth pricing rather than accepting. Eight crews cost about $455,500 on average against about $448,000 for seven, so the eighth crew costs about $7,500 of expected money, and it takes the bad case from about $457,100 down to about $456,000, which is about $1,100.
At $12,000 a day of damages the eighth crew is expensive insurance and the honest answer is seven. Change the damages figure to $25,000 a day, which is a different contract rather than a different opinion, and rerun: eight crews now wins at about $458,200 against about $462,600 for seven. The crew count is set by the damages clause, not by the weather, and this is the sheet that shows it.
What the model cannot see: it spreads the lost weather evenly across the window, so it cannot know that losing ten days in a row in March is worse than losing ten days scattered, and it assumes crews are interchangeable and available at three days notice, which is the assumption most likely to break in a busy summer. To make it yours, put your own measured crew days in, take the weather share from a local climate table for the actual months of the programme rather than an annual average, and copy the damages figure straight out of the contract.
The model
It arrives on a tab called Template: How Many Crews:
| Work to complete (crew days) | 260 |
| Crews committed (count) | 5 |
| Calendar days to the deadline | 70 |
| Working days in that window | 50 |
| Share of working days lost to weather | 0.18 |
| Workable days | 41 |
| Crew days available | 205 |
| Crew days short | 55 |
| Days late | 11 |
| Crew day rate ($) | 1450 |
| Mobilization and standby per crew ($) | 9800 |
| Cost of the work actually done ($) | 297,250 |
| Cost of committing the crews ($) | 49,000 |
| Liquidated damages per day late ($) | 12000 |
plus 2 more rows on the sheet.
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
Next question
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- Which matters more, your markup or your prep time?What Makes Us Win a Bid?
- What is one more person on the gang worth?What Explains How Much a Crew Gets Done?
- Are you paying for machine days you never use?Which Plant Do We Hire and Which Do We Own?
- Which tenders should you not price at all?Score the Sites Before You Bid
- Do rain days really cost you money?What Moves With Cost on This Job?
Every model like this one, and the method behind them: Optimization under uncertainty.