Capacity Model · Northwind Financial (synthetic demo)

What this page answers: how many reps does this floor need, half hour by half hour, and where is the real shortfall?

111 reps

Peak shortfall

at 9:00 ET

2,296

Attempts lost to shortfall

attempts/day the gap can't place

1,396

Attempts idle in surplus

attempts/day parked in overstaffed slots

Split shift: 14 Core reps to 8:00-11:00 + 17:00-21:00

Best single move

recovers ~231 attempts/day, re-simulated

losing reachrunning hotbalancedidle risktoo thin to judge

Balance board · verdict by tier × half hour
Tier	8:00	8:30	9:00	9:30	10:00	10:30	11:00	11:30	12:00	12:30	13:00	13:30	14:00	14:30	15:00	15:30	16:00	16:30	17:00	17:30	18:00	18:30	19:00	19:30	20:00	20:30
Tier 1	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0
Tier 2	+3	+0	+31	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+36	+33	+9	+8	+8	+12
Tier 3	+37	+20	+54	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+0	+2	+9	+39	+38	+25	+24	+24	+25
Tier 4	+17	+15	+26	+20	+22	+22	+20	+11	+9	-19	-49	-47	-76	-70	-71	-73	-42	+18	+19	+18	+18	+18	+12	+11	+11	+12

Cell value = reps short (+) or spare (−) for that tier and half hour, with supply allocated top-tier-first. Color is the verdict; the number carries the same information for color-blind readers and print.

Worst half hours, ranked
Slot (ET)	Needed	Present	Gap	Driver
9:00	179	68	+111	backlog release at open
18:00	129	36	+94	late-window arrivals
18:30	126	37	+89	late-window arrivals
8:00	121	64	+57	backlog release at open
20:30	81	33	+48	late-window arrivals
19:00	81	36	+45	late-window arrivals

Coverage moves, ranked by attempts recovered
Move	Attempts recovered / day	Cost
Split shift: 14 Core reps to 8:00-11:00 + 17:00-21:00	+231	hardest to staff; biggest edge coverage
Move 18 reps Early to Late	+15	no headcount change; evening differential likely
Start Core 60 min earlier (9:30 to 8:30)	-99	no headcount change; shift-bid window required

Each move is re-simulated through the same supply model, not hand-estimated. A negative number means the move sounds sensible and makes the day worse.

Assumptions · every constant is visible, none live only in code
Assumption	Value	Note
Roster	180 reps	synthetic shift templates below
Fresh leads / day	2,600	poisson arrivals, mid-morning peak
Aged follow-up pool	3,900	worked when fresh demand allows
Handle time	7.5 min / attempt	sensitivity: ±20% below
Occupancy target	78%	productive share of a staffed half hour; sensitivity: ±10%
Attempts earned	2.2 fresh · 1.1 follow-up	per lead on the model day
Calling window	8:00 am local (TCPA)	demand is held until the lead's local window opens

Demand · Eastern leadsDemand · Central leadsDemand · Mountain leadsDemand · Pacific leadsReps present

What it found: demand does not spike once at 9 am; it climbs a staircase, one step per timezone's legal open, then re-peaks in the evening when working leads answer. The shift mix is built for a single morning peak.

Shortfall (needed > present)Surplus (present > needed)

Sensitivity · peak shortfall (reps) under assumption shifts
	Occ ×0.9	Occ ×1.0	Occ ×1.1
AHT ×0.8	91	75	62
AHT ×1.0	131	111	95
AHT ×1.2	171	147	127

The headline gap moves by double digits under modest assumption changes. That fragility is the finding: treat the gap as a scenario, not a measurement.

What this does and does not prove

It proves: under the stated assumptions, demand and supply are misaligned in a specific, repeatable shape: a surge at each timezone's legal open that the current shift mix does not follow, and a surplus in the early afternoon.

It does not prove a service failure. The gap is a scenario under an occupancy and handle-time contract. Before anyone reads it as "we are failing customers," it must survive three falsification checks:

Measured first-response delay on leads arriving inside the gap windows (from dialer logs, not from this model).
Front-line confirmation: do team leads actually observe queue pressure at the flagged half hours?
Abandoned-contact rate moving with the gap, slot by slot.

If any check fails, revise the assumptions before revising the schedule. An alarming number that cannot survive its own falsification checks is not a finding; it is a liability.

Measurement contract · how each slice is handled
Slice	Supply side	Demand side	Status
Fresh vs aged leads	aged pool worked only in surplus slots	both demand terms stated in assumptions	modeled
Timezone	supply is timezone-blind (one floor)	demand held to the lead's local open (TCPA)	modeled
Lunches / breaks	staggered lunch dip 12:00-14:00	n/a	modeled
Shrinkage (meetings, absence)	inside the occupancy constant	n/a	assumption
Skill routing by tier	top-tier-first allocation	tier demand weighted by priority	simplified
Redials / callbacks	not separated from attempts	inside attempts-per-lead	simplified
Weekend / holiday shape	out of scope	out of scope	out of scope

Why a contract table exists: every capacity fight is really a fight about a hidden assumption. Writing down how each slice is handled on both sides of the model is what turns an argument into a review.

Full method notes: docs/METHODOLOGY.md. Regenerate everything with python3 build.py (seeded).