O.R./Analytics in Action Blog

Whether in the 911 call center serving New York City during Hurricane Irene or at the help desk in the local utilities department of a one-square-mile town, managers are constantly faced with one decision: how many agents should be staffed for answering phone calls? Making the staffing decision is never easy, due to the intrinsic uncertainty of each individual (agent or caller), and in fact this is getting even trickier with the increasing sophistication of technologies and also of people -- yes, more and more callers know they can immediately press 0 the moment their call gets through.

As operations researchers, my collaborators and I use mathematical models and analytics to tackle this challenge. More specifically, we take a stochastic modeling approach. Based on a widely used call center model, the Erlang A stochastic queueing model (named after A.K. Erlang, the Danish inventor, or perhaps co-inventor, of the fields of traffic engineering and queueing theory), we have developed a computational method, namely, Refined Square-Root Staffing (RSRS), for determining the optimal staffing level subject to different service-level constraints.

Consider the example of 911 call center during Hurricane Irene. Our computational method takes some key system characteristics, such as average call arrival rate and duration, as input, and quickly searches for the lowest staffing level needed to ensure 98% of the calls are answered within 10 seconds.

Take a revenue-generating call center, such as one that processes credit card applications, as another example. In this situation a particularly important performance measure is the long-run proportion of callers who hang up before their calls are answered, also known as caller abandonment probability. This performance measure is important because these abandoning customers may never call back and as a result potential revenue opportunities can go unrealized. Our proposed RSRS method can be applied to efficiently compute the optimal staffing level subject to a service-level constraint on the caller abandonment probability, thereby striking the tradeoff between potential revenue losses and staffing costs.

We hasten to admit that our stochastic modeling approach to call center staffing is by no means novel. What distinguishes our method from others is its balanced combination of computational scalability, accuracy, and structural lucidity.

While call centers can be of any size and appear in a variety of places, large call centers, i.e., those with hundreds or thousands of agents, are especially prevalent these days. A really usable staffing algorithm should be able to determine the optimal staffing level quickly not only for a small town’s utilities help desk -- often simply faced with the choice between one and two agents -- but also for large call centers, with a wide range of feasible staffing levels all at the order of thousands of agents. This is what we have referred to as computational scalability.

Our computational method achieves such scalability by exploiting the fact that certain system characteristics, e.g., call durations, do not differ much between large call centers and small ones (assuming they provide the same type of service).

In addition, our method yields significant accuracy improvement over the best existing approach, namely, Square-Root (Safety) Staffing --- hence the word “refined” in the name of our method. For example, both methods can be used to prescribe the most cost-effective staffing level to meet a given targeted service level. However, when the call center under consideration mainly serves customers who tend not to wait long to speak with an agent, the conventional Square-Root Staffing approach can incur an understaffing error of up to 60 agents, whereas our method is able to completely correct that error and be right on target. In our paper, we have carefully explored the mathematical foundations underlying both methods and explained why ours guarantees higher accuracy.

In its simplest form, our method can be illustrated by a three-column table. The first column shows the desired service level. The second and third columns, computed by our RSRS method, each provide a parameter, say, beta and b, corresponding to the service level in the first column. Specifically, if the staffing level has the form

staffing level = workload incoming rate + b + beta x √(workload incoming rate)

then the corresponding service level is achieved at optimality.

By building such a lucid table which highlights the key operational tradeoffs, operations researchers can help call center managers run their businesses more efficiently. This is the analytics of better.

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Bo Zhang, 2010 Nicholson Prize winner, blogs on his award-winning research. For a copy of the research paper, please visit his personal web page: http://www2.isye.gatech.edu/~bzhang34.

Operations research, analytics, and management science are making a major impact in business, government, and the research world. Read further to learn about award-winning projects that exemplify how operations research is helping decision-makers and people like you. Bloggers include winners and finalists in INFORMS competitions and INFORMS Community competitions, as well as recipients of grants. If you’re interested in submitting a blogpost, contact the INFORMS Public Information Committee (PIC) at picchair@mail.informs.org. Guidelines for submission are below.

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