Line-of-Support Capacity Model¶

Capacity model — instantiates Sustainment-Reach Alignment

Computes what a support line actually delivers to the front at a given reach, after subtracting what the line spends feeding, guarding, and running itself.

The central deceit of overreach is counting what you dispatch instead of what arrives. Line-of-Support Capacity Model is the accounting that corrects it: it defines the operating front and its support requirement, maps the line that sustains it, and computes net delivered support as a function of reach — gross dispatched minus everything the line itself consumes to cover the distance (transport, relays, guards, coordination, repair, attrition, management overhead). Its distinguishing output is the shape of the curve as reach grows: because the line's self-consumption climbs with distance while its throughput does not, net delivery bends over and eventually falls, and the model pinpoints the reach where the next increment of extension costs more support than it frees. It is deterministic capacity accounting — the steady-state picture — as distinct from a stochastic stress test of the same line.

Example¶

A wildfire incident-management team must decide how far up a canyon to push hand crews from the base camp at the trailhead. The dispatch numbers look ample: plenty of water, fuel, food, medical, and comms leaving camp each morning. The capacity model tells a different story. It defines the front (the number of crews and their daily support requirement), maps the line up-canyon (vehicle turnaround, the pump relays lifting water, the comms repeaters, the road crews keeping the track open), and then charges each mile of advance its true cost: longer hauls tie up more vehicles carrying support for the haul itself, more relays to power and guard, more road to maintain. Netting it out, the model shows that beyond ≈8 miles up-canyon each additional mile of crew advance consumes more support capacity than it delivers to the fireline — the crews could go farther, but the line can't feed them there. That crossover, not the dispatch total, is what sets the sustainable depth of the push.

How it works¶

Net, not gross. The core quantity is delivered-minus-self-consumed; dispatched totals are explicitly discounted by what the line eats en route.
Cost is a function of reach. Transport, relay, guarding, coordination, and repair loads are modeled as rising with distance, capturing the self-consuming geometry rather than a flat overhead.^[1]
The curve, not a point. Output is net delivery across a range of reaches, exposing the crossover where marginal net support turns negative — the model's decision-relevant feature.

Tuning parameters¶

Cost-growth curve — how support cost scales with reach (linear, super-linear); the steeper the assumed growth, the nearer the crossover.
Protected margin — how far net support must exceed the front's requirement before advance is allowed; a larger margin pulls the sustainable reach in.
Scope of "the line" — which support functions are counted (just transport, or also coordination, repair, security, management); a narrow scope flatters reach.
Granularity — one aggregate line, or a segment-by-segment model that shows where self-consumption concentrates.
Static vs. loaded inputs — nominal costs versus costs under current utilization; running the model at real load exposes strain a nominal run hides.

When it helps, and when it misleads¶

Its strength is dismantling the gross-dispatch illusion and giving every downstream mechanism a common currency: net delivered support at a given reach. It turns "we're sending plenty" into "this much actually lands there, and here is the distance past which sending more is self-defeating."

Its failure modes are the modeler's. Leave a support function out of "the line" and the model overstates sustainable reach; assume a gentle cost curve and the crossover drifts optimistically far out; and a clean number invites false precision over costs (coordination, attrition, morale) that resist being counted. The classic misuse is scoping the line narrowly to justify a reach already chosen. It is also only the steady-state picture — it says nothing about variance — which is why it is paired with a Lead-Time Stress Simulation. The discipline is to count the whole line, test the cost curve rather than assume it, and carry the uncertainty forward.

How it implements the components¶

Line-of-Support Capacity Model is the archetype's measurement and modeling core — it produces the picture the intervening mechanisms act on:

operating_front_definition — it specifies the front and the support required to keep it viable, the anchor everything else is measured against.
sustainment_line_map — it maps the line base-to-front: handoffs, relays, repair, authority, and replenishment paths.
net_delivery_metric — it defines and computes net delivered support, the gross-minus-self-consumption quantity at the model's heart (a live gauge of it is a Net-Supply Ratio Dashboard).
reach_cost_model — it models how support cost, delay, and fragility grow with reach, producing the crossover-bearing curve.

It does not act on its own findings — pacing (front_pace_gate — Advance Pause and Consolidation Window), buffering (staging_and_buffer_layer — Forward Staging Cache), localizing (local_substitution_option — Local Sourcing or Repair Protocol), and rescoping (retraction_or_rescope_rule — Front Rescope Playbook) are the interventions — nor model variability (reach_scenario_library — Lead-Time Stress Simulation).

Instantiates: Sustainment-Reach Alignment — the model that measures net delivered support against reach.
Sibling mechanisms: Lead-Time Stress Simulation · Net-Supply Ratio Dashboard · Reach-Limit Gate · Advance Pause and Consolidation Window · Forward Staging Cache · Front Rescope Playbook · Priority Supply Ladder · Local Sourcing or Repair Protocol · Relay-Hub Network · Support Burn-Rate Review · Support-Line Postmortem

Notes¶

This model is an input, not a decision: it says how much support reaches the front at each reach, not what to do about it. The interventions — pace, gate, buffer, localize, reprioritize, rescope — consume its net-delivery curve. Keeping the model separate from the actions is what lets a team improve the estimate (count another support function, load real utilization) without re-arguing every expansion decision at once.

References¶

[1] Militaries track this as the tooth-to-tail ratio — the proportion of a force devoted to support ("tail") versus combat power ("tooth"). As reach grows the tail grows to sustain it, and the model exists to keep the tail's rising self-consumption explicit rather than buried inside a gross dispatch figure. ↩