Industry: Defense Product: ModelRisk Application: Optimizing Naval Operations Under Uncertainty
A standing maritime commitment requires keeping at least two surface combatants effectively on station, continuously, for a year. The arithmetic looks reassuring: each ship cycles through roughly 45 days on station, a week of transit each way, and about five weeks of in-port maintenance, so a ship spends a little under half its time on task — and five ships should therefore deliver about two on station at any moment. Size the task group to that average and you commit five ships. The simulation says that a five-ship group meets the two-ship presence requirement in only 53% of campaign-years — barely better than a coin flip — because maintenance overruns, unplanned breakdowns and a shared sea-state state pull ships off station in clusters the average never shows.
A fleet operations staff rebuilt its force-generation case in ModelRisk after a rotation in which scheduled upkeep slipped and a breakdown coincided, briefly dropping the station below its mandated presence. The mandate was to size the task group against the distribution of delivered presence — with the assurance probability and the cost of a presence gap attached — not against the steady-state duty-cycle number.
The three task-group sizes produce three distinct presence distributions. The four-ship group centres at 1.6 ships and sits entirely left of the requirement; the five-ship group straddles the line, with nearly half its mass below two; only the six-ship group clears the requirement with margin. The width of each distribution — set by how the cycle phases line up across ships in a given year — is the planning signal the duty-cycle average discards.
This is a sortie-generation and on-station-availability model, not an inventory or deployment-lift problem: each ship rotates through a maintenance-transit-station cycle, and presence is what the rotation delivers, not what a duty factor promises. The simulation runs 8,000 campaign-years, advancing every ship through its cycle day by day:
The deterministic duty-cycle calculation uses mean phase lengths and a mean weather factor; it never sees the year when two maintenance overruns and a rough-weather stretch coincide — the conjunction that opens a presence gap.
The duty-cycle math is not wrong about the average — five ships really do deliver about 2.01 on station on average. It is wrong about the thing the commitment actually demands: reliability. Presence is driven by how the cycles phase against each other and against the shared weather state, and those align badly often enough that:
A force sized to "average equals requirement" is a force that fails the requirement nearly half the time. Only the distribution exposes that the mean sitting exactly on the target is the worst place to be.
Sweeping the rotation from 3 to 10 ships traces the trade-off. Fleet sustainment cost rises linearly at $14M per ship; the presence-shortfall penalty — the cost of buying alternative coverage when the station falls short, here $0.3M per ship-presence-day below requirement — falls steeply as ships are added. Total cost bottoms out at a five-ship group ($77M), the cost optimum. But that optimum holds the station only 53% of the time. The six-ship group is the first to reach 90%+ assurance (98%), for about $7M more — and from six ships up, the shortfall penalty has effectively vanished, so every further ship is pure cost with no readiness return. The cost-optimal force and the assured force differ by a single hull, and only the simulation shows that the cheaper option buys a coin flip.
Around the five-ship group — baseline of 2.01 ships on station — the tornado ranks the levers. On-station endurance dominates: a ±25% change in how long a ship can hold station before cycling home moves mean presence by about 0.56 ships, more than any other factor. Maintenance/upkeep duration is second (~0.42 ships) — every day of upkeep overrun is a day off station. The shared weather/sea-state factor is third (~0.32 ships); unplanned breakdowns and transit time follow well behind. The reading: extending on-station endurance (longer logistics legs, at-sea replenishment) and tightening upkeep schedules buy presence more cheaply than adding a hull — exactly where a duty-cycle spreadsheet offers no guidance.
The cumulative view makes the assurance gap explicit. The five-ship group falls below the two-ship requirement in 47% of campaign-years; the six-ship group, in just 3%. Reading the curves the other way, the six-ship group delivers a P10 presence of 2.15 ships — even a bad year clears the requirement — which is the property a standing commitment actually needs and a single mean-presence figure can never demonstrate.
A presence plan written against a mean duty cycle is a plan for an average year that the rotation rarely delivers; the task group sized to that average is the one that opens a gap in the campaign that matters. ModelRisk turns "how many ships hold the station?" into "what is the distribution of presence delivered, and what is the smallest force that holds the line even in a bad year?"