MSHR 6610 Week 4 Erlang C Staffing Model Example

From Calls to Seats to People: An Erlang C Staffing Model for a Utility Contact Center That Converts Agents Needed on the Phones Into Agents Scheduled, With Every Assumption Printed Beside Its Number

Student Name

Walden University

MSHR 6610: Aligning Human Resources with Business Operations

Instructor Name

Month Day, Year

From Calls to Seats to People: An Erlang C Staffing Model for a Utility Contact Center That Converts Agents Needed on the Phones Into Agents Scheduled, With Every Assumption Printed Beside Its Number

The Model

The demand analysis established how many calls Northfork Power & Light's contact center receives in each half hour and how long they take. This model asks how many agents each interval needs. It uses Erlang C, the queuing formula most commonly used to staff inbound call centers (Gans et al., 2003). Erlang C treats calls as arriving at random and waiting in a single queue until an agent is free. Given the number of calls, the average handle time and a number of agents, it estimates the share of calls that will wait and how long they will wait. The model is run with increasing numbers of agents until the result meets the service target. Here the target is the center's existing standard: 80 percent of calls answered within thirty seconds.

Agents Needed on the Phones

The workload column is the number of agents that would be needed if every agent were busy every second; the extra agents in the next column are what it takes to keep waits short when calls arrive unevenly. The gap is proportionally larger in smaller intervals, which is why evening and Saturday intervals need relatively more agents per unit of workload than the Monday morning peak.

Table 1

Erlang C Results for Selected Intervals

Composite utility. Inputs are illustrative; outputs calculated with the Erlang C formula for a 30-second target.

From Seats to People

Agents needed on the phones are not the same as agents on the schedule. Some scheduled time is always lost to breaks, training, team meetings, coaching and absence. The center's records put this shrinkage at about 35 percent of scheduled time. To have 37 agents on the phones at 6:00 p.m., the center must schedule about 37 divided by 0.65, or 57 agents. For the Monday 8:00 a.m. peak, it must schedule about 80.

Table 2

Assumptions Behind the Model

Composite utility. Sensitivities are approximate.

Limits of Erlang C

Erlang C assumes that callers never hang up and that every agent can take every call. Neither is true here. Callers who wait too long abandon, which lowers the load the remaining agents face, so the model tends to overstate the agents needed slightly when service is poor. More importantly, calls involving balances need a billing-certified agent, and only some agents are certified. Koole (2013) describes how skill-based routing complicates staffing models; this model treats all agents as interchangeable, so it understates the need for certified agents on billing-heavy intervals. The constraint brief later in the course addresses that directly.

Checking the Model

The model's predictions can be checked against last quarter's actual results. On evenings when about 33 agents were on the phones at 6:00 p.m., the center recorded service levels in the high thirties, close to what the model predicts for that staffing. That agreement gives some confidence in the inputs, though a single interval is a narrow test.

What the Model Shows

The model confirms what the demand analysis suggested. Evening intervals need about 31 to 41 agents on the phones, or about 48 to 64 scheduled, while the current evening roster schedules about 50 at 5:00 p.m. and fewer later. Mornings are adequately covered. The shortfall is concentrated in the evenings, and it is a scheduling problem as much as a hiring one. Aksin et al. (2007) note that staffing and scheduling are usually solved together; the next step is to compare the model's requirements with the actual schedule, interval by interval.

References

Aksin, Z., Armony, M., & Mehrotra, V. (2007). The modern call center: A multi-disciplinary perspective on operations management research. Production and Operations Management, 16(6), 665-688. https://doi.org/10.1111/j.1937-5956.2007.tb00288.x

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

Koole, G. (2013). Call center optimization. MG Books.