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).
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.
