DDBA 8561 Week 6 Access Center Staffing Model Example

Callers Who Hang Up Come Back Elsewhere: A Staffing Model for a Patient Access Center Testing Its Monday Schedule Against Half-Hourly Demand With an Erlang A Queue and Following Abandoned Calls Into Retrials and Portal Messages

Student Name

Walden University

DDBA 8561: Seminar in Managing Healthcare Delivery Systems

Instructor Name

Month Day, Year

Callers Who Hang Up Come Back Elsewhere: A Staffing Model for a Patient Access Center Testing Its Monday Schedule Against Half-Hourly Demand With an Erlang A Queue and Following Abandoned Calls Into Retrials and Portal Messages

The Center and the Claim

The patient access center of a composite health system in Kansas City schedules appointments for 140 clinics, answering about 2,900 calls on a typical Monday between 7:00 a.m. and 5:00 p.m. Its managers report daily service as adequate: on a daily average, the center's 22 agents at full staffing can handle the volume. But the center counts callers who hang up before reaching an agent as lost demand. This model argues they are demand that returns, by calling again or by sending messages through the patient portal, and that the schedule's morning gap creates much of it.

The Mismatch

Calls arrive unevenly. Forecasts from twelve Mondays show volume rising from 60 calls in the 7:00 half hour to a peak of 170 at 9:00 and falling to about 100 by 11:30. The schedule, built around shift starts that suit staff, places 10 agents on the phones at 7:00, adding agents through the morning to reach 22 at 10:00. The result is too few agents from 8:00 to 9:30 and more than enough from 10:30 onward.

The Model

Most staffing tools use the Erlang C formula, which assumes callers wait indefinitely. When demand exceeds capacity in an interval, Erlang C predicts an unbounded queue and cannot say what happens. Garnett et al. (2002) developed the Erlang A model, which adds caller patience: each waiting caller abandons after a random time. They showed that ignoring abandonment can lead to serious errors in staffing, and Gans et al. (2003) reviewed evidence that abandonment is a central feature of real call centers. This model uses Erlang A with an average handle time of 4.5 minutes and average caller patience of 3 minutes, both drawn from the center's telephony data. The staffing target is abandonment of 5 percent or less and average wait of 30 seconds or less.

[after]

From 8:00 to 9:30, the schedule falls 8 to 11 agents short, and about a third of callers hang up. After 10:30, the center has more agents than it needs.

Table 1

Monday Morning Staffing, Scheduled Versus Needed

Where Abandoned Calls Go

About 190 callers abandon between 8:00 and 10:00 on a typical Monday. The center's call records, matched by phone number, show that about 60 percent call again within an hour, adding roughly 114 calls to the late morning, when the center is staffed to handle them but agents spend time on repeat callers who are already frustrated. Aguir et al. (2004) showed that retrials can substantially change call center performance and that models ignoring them misjudge both load and service. About 20 percent of abandoning callers, roughly 38 on a Monday, send a portal message instead, which goes to clinic nurses who must then call the patient back. The remainder do not reappear in either record; some may have reached the clinic another way, and some may have given up.

What Follows

Shifting four agents' start times from 10:00 to 8:00 would cover most of the morning gap without adding staff, since the late morning has slack. A model that counted abandoned calls as lost would understate both the need and the cost borne by clinic nurses.

Why the Daily Average Misleads

On a daily basis, the center answers about 2,900 calls with agents whose combined capacity, spread evenly, would be ample. That is why the center's monthly report shows acceptable service. The average hides the morning, when a third of callers hang up, and the late morning, when agents spend their time on retrials. A model built on the daily average reports enough staff and misses the problem entirely. The half-hourly view is not a refinement of the daily one; it is a different picture of the same day, and only it shows where demand and capacity diverge.

Limits

Patience is assumed to follow a single average; real patience varies by caller. Retrial and portal shares come from matching phone numbers and patient identifiers, which miss callers using different phones.

References

Aguir, S., Karaesmen, F., Aksin, O. Z., & Chauvet, F. (2004). The impact of retrials on call center performance. OR Spectrum, 26(3), 353-376. https://doi.org/10.1007/s00291-004-0165-7

Gans, N., Koole, G., & Mandelbaum, A. (2003). Telephone call centers: Tutorial, review, and research prospects. Manufacturing & Service Operations Management, 5(2), 79-141. https://doi.org/10.1287/msom.5.2.79.16071

Garnett, O., Mandelbaum, A., & Reiman, M. (2002). Designing a call center with impatient customers. Manufacturing & Service Operations Management, 4(3), 208-227. https://doi.org/10.1287/msom.4.3.208.7753