Fixed-Capacity Service Models
Fixed-capacity service models are commercial and operating arrangements in which a client buys a set number of full-time equivalents (FTE) to handle its contacts, and the number does not move with demand. The pool is dedicated to that client and the fee is fixed. Demand moves with the seasons and with forecast error; because supply cannot follow it, service level in such a model is a consequence of how much capacity was bought, not a target that operations can be held to independently. This article sets out the arithmetic, why small pools are unusually sensitive to it, how to diagnose a missed month, and the remedies.
Definition and contrast
In a fixed-capacity model, often called a dedicated-cost or fixed-fee arrangement, the contract specifies FTE, hours of operation and usually a service-level objective, and the client pays for the pool whether demand is high or low. Two other arrangements explain most of the friction by contrast:
- Transactional pricing (per contact, per minute or per handled transaction). The provider is paid for volume and staffs to it. Seasonality is the provider's problem, priced into the rate.
- Shared pools. Several clients' work is pooled across a larger team. Peaks that do not coincide offset each other, and the larger pool is more efficient at any service level. This is the effect described in Pooling Architecture in Service Workforces.
The dedicated pool gives up both buffers: no volume-linked funding to flex with, and no other client's trough to borrow from. In exchange it gains control, exclusivity and a predictable cost — reasonable things to buy, provided both parties understand the service-level behaviour that comes with them.
Service level as a consequence of the purchase
Required FTE is a function of contact volume, handle time, shrinkage, the service-level target and the intraday arrival pattern. Every one of these moves month to month, so the requirement moves too. Purchased FTE does not.
In the synthetic worked example used throughout this article, a client buys 22 FTE for a pool handling phone calls and deferred work (email) on a 12-hour weekday operation, with a target of 80% of calls answered within 20 seconds. The forecast requirement averages 22.2 FTE across the year, so the purchase matches the average almost exactly. But the requirement ranges from 18.2 FTE in Dec to 25.5 in Feb. In 8 of the 12 months it exceeds the 22 FTE purchased. Projected service level falls below target in 5 months (fewer than the short months, because required FTE is sized in whole agents per interval, as plans do, while delivery assumes an ideal roster), as low as 67%, and rises well above it in the troughs.
Nobody has done anything wrong in this picture: the forecast is exact by construction, the pool is staffed exactly to its purchase, and the purchase equals the average requirement. The misses are simply what flat supply against seasonal demand produces.
Sized to the average
A pool sized to the mean requirement is often assumed to deliver the target "on average". The arithmetic is more specific than that, and the specific version is the one to state to a client.
Held flat at the mean requirement of 22.2 FTE, the worked example delivers an annual call-weighted service level of 82.3%, measured over all calls in the year. Yet 5 of the 12 months (Jan, Feb, Mar, Sep, Oct) fall below the monthly target. Surplus months cannot bank service for deficit months: a caller in a trough month who is answered in five seconds does nothing for a caller in a peak month waiting three minutes. Whether the annual figure lands above or below target depends on how deep the seasonality is; a monthly measure fails in the peak months by construction. This is a direct case of The Flaw of Averages: plans built on average conditions fail on the conditions that are not average.[1]
Meeting the target in every month needs about 24.6–25.5 FTE (the lower figure on an ideal roster, the higher in whole agents per interval), 11%–15% above the average, and idle in the troughs.
Small pools and the power of one
Dedicated pools are often small: 15 to 40 FTE, with only a handful of agents on the phones in any interval. At that scale the queueing curve is steep. Adding or removing one agent changes the probability of delay sharply, an effect the Power of One describes for real-time operations and Erlang Sensitivity and the Staffing Cliff describes for planning.[2][3]
The worked example quantifies it at the purchased 22 FTE:
| Change | Feb (peak) | Dec (trough) |
|---|---|---|
| Service level at 22 FTE | 67% | 98% |
| One FTE more | +5.6 pts | +0.8 pts |
| One FTE fewer | −6.6 pts | −1.3 pts |
| Phone and deferred volume +10% | −13.8 pts | −2.4 pts |
| Shrinkage +1 point | −1.9 pts | −0.4 pts |
In the peak month, one FTE (one person, less shrinkage, spread across the day) adds about 5.6 points of service level, and losing one costs about 6.6. The same FTE is worth far less in the trough, where the pool is already above target and the curve has flattened. The practical point: a single vacancy or a few points of unplanned absence in a peak month move the client's headline number as much as a typical single-driver forecast miss does, where a large shared pool would barely register either.
The shortage has to land somewhere
When required hours exceed purchased hours, the deficit is not optional. It shows up in one or more of three places:
- Phone service level, as longer waits and, where callers are impatient, abandonment
- Deferred work, as a backlog of email or cases beyond their turnaround objective
- Both, in some proportion set by how the pool is directed
Routing policy decides which. In the worked example's peak month at 22 FTE, protecting the phones holds service level at 80% and leaves about 2,096 deferred items unworked within the month. Protecting deferred work clears the backlog and drops phone service level to 49%. Sharing the deficit in proportion gives 67% with about 996 items unworked. Each is legitimate; none makes the deficit disappear, and a client who sees only phone service level sees only part of it.
Caller patience changes where the phone share of the damage appears. Erlang C assumes no caller ever hangs up, so every shortage becomes waiting. Erlang-A lets callers abandon after a random patience.[4] Rerun with a mean patience of 150 seconds, the worked example's peak month reports 83% answered within 20 seconds instead of 67%, with 10.2% of callers abandoning. Service level looks healthier because callers who give up shorten the queue for those behind them, although the abandoned calls themselves still count as misses, so a pool reported on service level alone looks best relative to reality in exactly the months it is shortest. Report abandonment alongside it, and treat patience as an estimate until it is fitted to the pool's own abandonment.
The shrinkage convention
Required FTE converts required productive hours into paid people, and there are two ways plans do it:
- Net: a productive FTE-month is paid hours × (1 − shrinkage). This is the definition of shrinkage as a share of paid time.
- Gross-up: a productive FTE-month is paid hours ÷ (1 + shrinkage).
They agree at low shrinkage and diverge as it rises. At 35% shrinkage the net form needs 1.538 paid hours per productive hour and the gross-up 1.35, so the gross-up books about 12% less requirement. A pool sized by gross-up is shorter than its plan shows, most of all in high-shrinkage months. Establish which convention produced a requirement before diagnosing against it.
Diagnosing a missed month
When a client asks why service fell short, the gap between FTE held and FTE required at actual conditions can be split into three parts that add up exactly:
- Supply delivery: FTE actually held against FTE purchased. Vacancies, attrition and delayed hiring are the provider's to own.
- Structural shortfall: FTE purchased against the forecast requirement. This part was known in advance and follows from the purchase.
- Forecast misses: the forecast requirement against the requirement at actual volume, handle time, deferred volume and shrinkage.
The third part is split across drivers with Shapley values, which average each driver's contribution over every order of adding the others, so the attribution does not depend on which driver is examined first.[5] In the months with actuals, the worked example's FTE held ran below its contract. In its weakest actual month, Mar, the pool held −7.3 FTE against the actual requirement. Of that, −1.0 was supply delivery and −2.8 structural. The forecast misses split as volume −1.4, handle time −1.1, deferred volume −0.2 and shrinkage −0.8. The decomposition puts the provider's own miss beside the client's, and separates what was a surprise from what was bought.
Remedies
None is free, and the choice is commercial as much as operational.
- A seasonal flex band or banked hours. The pool varies within an agreed band, or hours unused in troughs are banked against peaks.
- Seasonal or annual measurement. A lower target in known peak months, or service level measured over the year rather than month by month, aligns the objective with the capacity bought.
- Overflow to a shared pool. Peaks spill to a larger team at a transactional rate, recovering some of the pooling benefit the dedicated model gives up.
- Blending deferred work into phone idle time. In a small pool held to a fast answer time, phone occupancy is low and idle minutes are plentiful. Working deferred items in them recovers real capacity, at some cost to answer-time consistency.
- Hours of operation and channel shift. Narrower hours or moving demand to self-service or asynchronous channels reduce the requirement rather than the pool.
- Accepting the delivered level. A client may prefer the fixed cost and accept the service level that capacity yields in each month — paying for a pool and receiving what it can do. Legitimate, when chosen knowingly.
Whatever the commercial answer, the practice is the same: a monthly capacity review setting forecast against actual for every driver, FTE held against FTE required, and projected service level for the months ahead.
Worked example
The synthetic pool from the figure, at 22 FTE purchased in every month: target 80% in 20 seconds, Erlang A at a mean patience of 150 seconds.
| Month | Required FTE | Purchased FTE | Gap (purchased − required) | Service level (Erlang C) | Service level (Erlang A) | Abandonment (Erlang A) |
|---|---|---|---|---|---|---|
| Jan | 24.8 | 22 | −2.8 | 71% | 84% | 9.1% |
| Feb | 25.5 | 22 | −3.5 | 67% | 83% | 10.2% |
| Mar | 24.8 | 22 | −2.8 | 71% | 84% | 9.1% |
| Apr | 22.4 | 22 | −0.4 | 85% | 91% | 5.4% |
| May | 22.7 | 22 | −0.7 | 83% | 90% | 5.8% |
| Jun | 20.7 | 22 | +1.3 | 92% | 95% | 2.9% |
| Jul | 18.5 | 22 | +3.5 | 98% | 98% | 1.0% |
| Aug | 18.8 | 22 | +3.2 | 97% | 98% | 1.3% |
| Sep | 23.2 | 22 | −1.2 | 78% | 88% | 7.2% |
| Oct | 24.4 | 22 | −2.4 | 73% | 85% | 8.6% |
| Nov | 22.9 | 22 | −0.9 | 82% | 89% | 6.4% |
| Dec | 18.2 | 22 | +3.8 | 98% | 98% | 0.9% |
Annual call-weighted service level is 81.2% under Erlang C and 89.4% under Erlang A. The month-by-month spread, not the annual figure, is what the client experiences. The full model, its intake and an interactive sensitivity explorer are in Wiki:Packs/Dedicated Pool Performance.
See also
- Wiki:Packs/Dedicated Pool Performance — the deployable analysis pack (CP-WFM-020)
- Capacity Planning Methods
- Power of One
- Erlang Sensitivity and the Staffing Cliff
- Pooling Architecture in Service Workforces
- The Flaw of Averages
- Business Process Outsourcing
- Scenario Planning and Contingency Staffing
- Workforce Cost Modeling
References
- ↑ Savage, S. L. (2009). The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty. Hoboken, NJ: John Wiley & Sons.
- ↑ Gans, N., Koole, G., & Mandelbaum, A. (2003). "Telephone call centers: Tutorial, review, and research prospects". Manufacturing & Service Operations Management 5(2), 79–141.
- ↑ Borst, S., Mandelbaum, A., & Reiman, M. I. (2004). "Dimensioning large call centers". Operations Research 52(1), 17–34.
- ↑ Garnett, O., Mandelbaum, A., & Reiman, M. (2002). "Designing a call center with impatient customers". Manufacturing & Service Operations Management 4(3), 208–227.
- ↑ Shapley, L. S. (1953). "A value for n-person games". In H. W. Kuhn & A. W. Tucker (eds.), Contributions to the Theory of Games II, Annals of Mathematics Studies 28, 307–317. Princeton University Press.
