The fastest plan, and the proof that none is faster.
After an attack the first need is a minimum operating strip (MOS) aircraft can use. On a simulated damage map this decides three things: where the strip goes, which unexploded ordnance (UXO) is cleared first, and how craters are shared between repair crews. Then it lays out, item by item, the evidence that this really is the fastest.
Simulated data
No real airfield
Task times, safety distances and machine sets are illustrative
Same seed, same result, for anyone
Excavators
Track loaders
Dump trucks
Rapid-set mixers
Sweepers
Survey drones
EOD teams
One repair set = 1 excavator + 1 compact track loader (saw / breaker) + 2 dump trucks + 1 rapid-set concrete mixer. The fleet forms 3 sets; the limit is excavators, track loaders, dump trucks, rapid-set mixers.
Everything below is computed live in your browser; change any setting and it recomputes. Seed 5
Recommended plan
Aircraft can operate in (assessment and sweep included)
2 h 23 min
= drone damage assessment 12 min + clearance and repairs 1 h 31 min + sweep 40 min
✓ Proven optimalOf 155 possible strip positions only 20 needed a full calculation; every other one is proven unable to be faster.550–2,050 m from the threshold, 7.5 m right of centre · 4 craters to repair, 2 UXO to clear first
Damage and strip
Crater to repair
Other crater
UXO and safety area
Recommended strip
Schematic: length compressed, width enlarged; craters are symbols sized by small / medium / large. Orange areas are UXO safety distances; craters inside one wait for clearance.
Each row is a drone, a team or a machine set. Drones map the damage first, then clearance and repairs (machines and people stay outside UXO safety radii), then the sweep; the strip opens at the line on the right.
An exact operations-research algorithm (branch and bound) computed this answer, and every step can be checked. Each of the five checks below can be re-run and challenged.
① Upper and lower bounds converge
While solving, two numbers are tracked: how long the best plan found so far takes (upper bound, only goes down) and how fast any plan could possibly be (lower bound, only goes up). When the two lines meet, that is a proof, not a guess.
Upper bound: best plan so far
Lower bound: nothing can be faster
Simulation · synthetic damage map · seed 5 · 3 repair crews, 1 EOD team · 3 excavators · 3 loaders · 6 trucks · 3 mixers · 1 sweeper · 2 survey drones · branch and bound: 20 of 155 strips solved in full
Data table
#
Upper bound: best plan so far
Lower bound: nothing can be faster
0
—
1 h 28 min
1
1 h 54 min
1 h 28 min
2
1 h 54 min
1 h 28 min
3
1 h 54 min
1 h 31 min
4
1 h 32 min
1 h 31 min
5
1 h 32 min
1 h 31 min
6
1 h 32 min
1 h 31 min
7
1 h 32 min
1 h 31 min
8
1 h 32 min
1 h 31 min
9
1 h 32 min
1 h 31 min
10
1 h 32 min
1 h 31 min
11
1 h 32 min
1 h 31 min
12
1 h 32 min
1 h 31 min
13
1 h 32 min
1 h 31 min
14
1 h 32 min
1 h 31 min
15
1 h 32 min
1 h 31 min
16
1 h 32 min
1 h 31 min
17
1 h 32 min
1 h 31 min
18
1 h 32 min
1 h 31 min
19
1 h 32 min
1 h 31 min
20
1 h 31 min
1 h 31 min
② Why each position cannot be faster
Every possible strip position has a lower bound no ordering can beat, with a one-line reason. Grey bars sit above the blue line and need no detailed calculation; the few below it were fully calculated and are also confirmed slower.
0–1,500 m from the threshold, 15 m right of centreBest 1 h 32 min, 1 min slower than the recommendation · Crater C8 lies inside the safety area of UXO U1: at least 24 min of clearance, then 67 min of repair, so no earlier than 1 h 31 min.5 neighbouring positions need the same repairs, same result
450–1,950 m from the threshold, 7.5 m right of centreBest 1 h 32 min, 1 min slower than the recommendation · Crater C8 lies inside the safety area of UXO U1: at least 24 min of clearance, then 67 min of repair, so no earlier than 1 h 31 min.3 neighbouring positions need the same repairs, same result
300–1,800 m from the threshold, 15 m right of centreBest 1 h 35 min, 4 min slower than the recommendation · Crater C8 lies inside the safety area of UXO U1: at least 24 min of clearance, then 67 min of repair, so no earlier than 1 h 31 min.2 neighbouring positions need the same repairs, same result
600–2,100 m from the threshold, 15 m right of centreBest 1 h 37 min, 6 min slower than the recommendation · Crater C8 lies inside the safety area of UXO U1: at least 24 min of clearance, then 67 min of repair, so no earlier than 1 h 31 min.
650–2,150 m from the threshold, 15 m right of centreBest 1 h 37 min, 6 min slower than the recommendation · Crater C8 lies inside the safety area of UXO U1: at least 24 min of clearance, then 67 min of repair, so no earlier than 1 h 31 min.1 neighbouring position need the same repairs, same result
1,000–2,500 m from the threshold, on the centre lineBest 1 h 38 min, 7 min slower than the recommendation · 3 UXO must be cleared first; 1 EOD team need at least 98 min: no earlier than 1 h 38 min.1 neighbouring position need the same repairs, same result
③ Against other ways of ordering
Same damage, same people, scheduled by common whiteboard rules. Then 10,000 random feasible plans: the optimum should sit at the far left with nothing beating it.
Optimum (proven)
1 h 31 min
Near to farStart at the shelter end and repair in order of distance
1 h 38 min7 min slower (+8%)
Biggest firstLeast-damaged strip, largest craters first
1 h 31 minAlso optimal here
Clear all UXO firstClear every UXO on the runway before any repair
3 h 15 min1 h 44 min slower (+114%)
Centre of the runwayThe strip at the runway centre, largest craters first
Besides the solver in this page, Google OR-Tools (CP-SAT) re-builds the model from the raw geometry and solves it independently. The answers must match exactly; the comparison is part of the automated tests, so any code change that breaks it is stopped.
100 random damage maps, 1–6 repair crews, 1–2 EOD teams: all 100 match
Small cases also checked by enumerating every ordering (brute force): match
Every position's lower bound is verified never to exceed its true fastest time
⑤ Does the answer hold when assumptions change?
"Optimal" holds only while the assumptions hold. Repair times, clearance times and crew numbers are assumptions, so change one at a time and see whether the recommendation moves.
Computing…
The sweet spot: how many crews actually help
Same damage, repair crews from 1 to 6 with one or two EOD teams; every point is a proven fastest time. Where the curve flattens is the sweet spot: more people barely change the time.
Computing…
Method and limits
Problem: pick a 1,500 × 15 m minimum operating strip (155 candidate positions), order UXO clearance, and assign craters to crews so the strip opens as early as possible.
Algorithm: branch and bound. Every candidate position gets a lower bound; positions are solved exactly in order of bound until the best plan is no slower than every remaining bound.
Not modelled: travel of people and vehicles, night and weather, equipment failure, curing time after repair, re-attack. Real use calibrates these parameters to unit doctrine.
Data: synthetic illustrative scenarios only; no real airfield, damage or unit data.