Use when an ops leader (Director of CX, Head of Support, VP Ops, Head of BizOps, Head of IT ops, Head of Finance ops) is sizing ops capacity, building a headcount plan, modeling utilization risk, planning Q3 capacity or annual support capacity, or designing CS coverage — and needs Erlang-C queueing math, P90 demand sizing, shrinkage-adjusted FTE, manager-trigger thresholds, and a quarterly hiring sequence with ramp + attrition. Apply when sustained team utilization is above 80% or when the team is growing >50% in 12 months. Run before committing the headcount budget. This is NOT engineering capacity (see vpe-advisor for DORA + cycle time) and NOT strategic 3-year workforce planning (see chro-advisor).
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name
capacity-planner
description
Use when an ops leader (Director of CX, Head of Support, VP Ops, Head of BizOps, Head of IT ops, Head of Finance ops) is sizing ops capacity, building a headcount plan, modeling utilization risk, planning Q3 capacity or annual support capacity, or designing CS coverage — and needs Erlang-C queueing math, P90 demand sizing, shrinkage-adjusted FTE, manager-trigger thresholds, and a quarterly hiring sequence with ramp + attrition. Apply when sustained team utilization is above 80% or when the team is growing >50% in 12 months. Run before committing the headcount budget. This is NOT engineering capacity (see vpe-advisor for DORA + cycle time) and NOT strategic 3-year workforce planning (see chro-advisor).
Sizing tool for ops teams that handle queued work — Support, CX,
Customer Success, BizOps, IT ops, Finance ops. Built on Erlang-C
queueing theory, Little's Law, and the operational-leadership canon
(Fournier, Larson, Cleveland, Reinertsen). Deterministic, stdlib-only,
no LLM calls.
Purpose
You are an ops leader sized 15 → 35 with no idea how the 35-person org
will actually behave at peak load. Or you are at 88% utilization and
SLA is starting to slip. Or you have a hiring budget approved and need
to sequence it across four quarters without burning out the existing
team. This skill answers those questions with arithmetic, not vibes.
It produces three artifacts:
Capacity sizing at 70/80/90% utilization against P50/P90/P99
demand, with P(SLA breach) at each point and a SAFE/WATCH/AT_RISK/CRITICAL
risk band.
Utilization health at the per-member traffic-light level plus a
team verdict (HEALTHY/SQUEEZED/OVERLOADED/UNBALANCED).
12-month quarterly hiring plan accounting for ramp curves,
attrition, QoQ demand growth, and span-of-control manager triggers.
When to use
Annual ops capacity planning (October-November for the following
fiscal year).
Quarterly re-sizing if demand changed >15% or attrition spiked.
Pre-budget defense — the math that justifies the headcount ask
to your CFO.
Diagnostic when an ops team is missing SLA and you need to know
whether it's a sizing problem, a process problem, or a bottleneck
problem.
M&A / new-segment launch modeling — sizing a new team or
combined org.
Workflow
Intake demand. Pull P50/P90/P99 daily ticket/case volume from
your work system (Zendesk, Intercom, JSM, ServiceNow, Salesforce).
If you only have averages, stop and pull the distribution. Single-
point demand estimates are the most expensive anti-pattern in ops.
Model throughput. Run capacity_modeler.py with your demand,
AHT, SLA target, current FTE, and shrinkage. Use --profile for
your function (support / cx / bizops / finance-ops / it-ops). Read
the 80%-utilization row — that's your sizing point.
Flag utilization risk. Run utilization_analyzer.py against
your current team's actual utilization data. Anyone >85% sustained
is a throughput-collapse risk per Reinertsen. Spread >30 percentage
points across team means UNBALANCED — fix that before hiring.
Sequence hiring. Run with current FTE,
target EOY, ramp time, attrition, and growth. It will front-load
hires (Q1 35%, Q4 15%), apply ramp curves, and trigger a manager
hire when span of control crosses 7 ICs/manager.
hiring_sequencer.py
Walk the Forcing-question library (see below). One question at
a time. Do not skip ahead. Answers must be written down before
you commit the plan.
Scripts
scripts/capacity_modeler.py — Erlang-C sizing with shrinkage
adjustment and P50/P90/P99 breach probabilities. --profile
for industry defaults.
scripts/utilization_analyzer.py — per-member traffic-light +
team-level health verdict with variance detection.
scripts/hiring_sequencer.py — 12-month quarterly plan with ramp,
attrition, growth, max-hires-per-quarter constraint, and
manager-trigger logic.
All three accept --input <path> (JSON), --output {markdown,json},
--sample (built-in example), and --help. Stdlib only.
Quick example
# Emits an Erlang-C capacity model (required headcount + P50/P90/P99 breach probabilities) for the built-in examplecd business-operations/skills/capacity-planner && python3 scripts/capacity_modeler.py --sample
References
references/queueing_theory_canon.md — Erlang, Little, Hopp &
Spearman, Reinertsen, Kingman, Cleveland, ITIL, Armony et al. (8
sources). The math.
references/ops_workforce_planning_canon.md — Fournier, Larson,
Google SRE Workbook, Frei, Lawler, Bersin, Gartner, Grove (8
sources). The people factors.
references/capacity_anti_patterns.md — 11 named anti-patterns
with cited sources, tool guards, and the meta-discipline that
Lencioni + Goldratt + Christensen impose. (8+ named sources.)
Assets
assets/capacity_brief_template.md — 20-minute fill-out template
with JSON skeletons for all three tools and an output checklist.
Assumptions
This skill assumes:
Work is queued (tickets, cases, work items) — not project-style.
If your team's work isn't queued, this is the wrong skill.
Demand has a stationary-enough distribution within a quarter.
Step-changes (new product launch, M&A, regulatory shift) require
re-running mid-quarter.
You have at least 90 days of historical demand data to compute
P50/P90/P99. If not, generate the distribution from your sales /
user-base forecast first.
Service is single-class within a queue. If you have hard
priority tiers (P1/P2/P3 with class-specific SLAs), model each as
a separate queue and sum.
Channels are modeled coherently. Multi-channel teams use the
appropriate --profile with built-in shrinkage premium.
Anti-patterns
See references/capacity_anti_patterns.md for the full taxonomy with
sources. Top eight:
c-level-advisor/vpe-advisor measures engineering throughput
via DORA 4 metrics, story points, deployment frequency, and cycle
time bottlenecks. It is for engineering teams shipping code. This
skill is for ops teams handling tickets/cases. Different unit of
work, different math (Erlang-C vs. DORA), different bottleneck
(queueing-blind staffing vs. WIP + lead time).
c-level-advisor/chro-advisor does strategic workforce
planning (1-5 year capability portfolios, talent supply, leadership
succession). This skill does operational 0-12 month capacity
sizing against demand. Per Lawler: conflating them gets you hired
into the wrong jobs.
project-management/* tracks delivery throughput on projects
(Jira velocity, sprint capacity). This skill sizes around steady-
state queued work.
Sibling process-mapperfinds the bottleneck. This skill
sizes the team around a known bottleneck. Order of operations:
process-mapper first → capacity-planner second. Hiring around the
wrong constraint wastes the hires.
business-growth/cs-coverage (if it exists) sizes Customer
Success coverage by ARR/CSM ratio and segment. This skill sizes by
queued work volume (tickets, cases, escalations). For a CS team
that handles both relationship work AND a ticket queue, run both.
Discipline: walk these one at a time. Do not skip ahead. Answers must
be written down. If you can't answer one, that is your next investigation.
Q1 — "What is your bottleneck, and have you confirmed it empirically?"
Recommended answer: a named, measured stage in the workflow with
queue-time data showing where work waits. Not a vibe. Not "escalations
take too long". An actual measured queue.
Why it's the first question: Goldratt (The Goal, 1984) — every
system has exactly one binding constraint at a time. Sizing around the
wrong constraint wastes hires entirely. If you do not know your
bottleneck, run process-mapper BEFORE this skill.
Canon: Eli Goldratt, The Goal (1984); Reinertsen, Principles of
Product Development Flow (2009).
Q2 — "What service trade-off are you accepting?"
Recommended answer: a written, explicit choice — fast vs. empathetic,
broad vs. deep, low-cost vs. high-quality. Frances Frei is unambiguous:
you cannot win all four. The team that tries wins zero.
Why it matters: AHT, SLA, and shrinkage inputs are the operational
expression of this trade-off. If they don't agree (e.g., you set AHT for
"empathy" but SLA for "speed"), the plan is internally inconsistent.
Canon: Frances Frei & Anne Morriss, Uncommon Service (HBR Press,
2012).
Q3 — "What's your demand P90, and what's the gap to your P99?"
Recommended answer: two specific numbers from the last 90 days of
data, with the calendar context of each (e.g., "P90 was 480 tickets/day
on normal Tuesdays; P99 was 720 on the day after the November release").
A team sized to P50 misses SLA half the time. A team sized to P99
overstaffs by 30-50%. P90 is the right operating sizing point per
Cleveland.
Canon: Brad Cleveland, Call Center Management on Fast Forward (4th
ed., 2019); A.K. Erlang, The Theory of Probabilities and Telephone
Conversations (1909).
Q4 — "At your planned utilization, what is P(SLA breach) at P90 and at P99?"
Recommended answer: two probabilities, computed (not guessed) from
Erlang-C with your specific N, AHT, and SLA target. If P(breach at P90)
10% you are understaffed at the sizing point. If P(breach at P99) >
50% you have no surge plan and the next peak event will be visible to
the CEO.
Q5 — "Have you budgeted replacement hires for the attrition you'll see this year?"
Recommended answer: yes, with a specific number. At 30% annual
attrition (Bersin BPO midpoint), a 20-FTE team loses ~6 people this year.
If your "add 5 net" plan is actually a "hire 11" plan, the recruiting
volume changes drastically. Anti-pattern #3.
Q6 — "When does span of control trigger a manager hire, and who is the candidate?"
Recommended answer: a specific quarter (from hiring_sequencer.py)
and at least one identified candidate (internal lead or external hire).
Past 7 ICs/manager, 1:1s degrade, feedback cycles slip, attrition
climbs. Past 10 you have a coverage crisis. Hire the manager BEFORE
crossing 10, not after.
Canon: Camille Fournier, The Manager's Path (O'Reilly, 2017),
ch. 5; Andy Grove, High Output Management (1983).
Q7 — "What is your surge plan for the P99 day?"
Recommended answer: an explicit, documented plan — overflow tier,
BPO contracted capacity, on-call rotation, executive escalation tree,
OR a written degradation contract that says "on P99 days we extend SLA
to X minutes and notify customers proactively". If the answer is "we'll
figure it out", the P99 day is a fire visible to the board.
