Revolutionizing Workforce Planning for Today’s Contact Centers with Erlang-O

By Ted Lango

Outdated Staffing Models: Why Traditional Methods Fall Short

Erlang-C and Erlang-A have been fundamental in understanding the optimized staff required to handle forecasted workloads and achieve service level objectives. However, these models struggle with the dynamic nature of modern call centers, which require real-time staffing adjustments, multi-channel communications, and the ability to handle variability and volatility in call arrivals.

Traditional models operate on the premise that activities like coaching, training, breaks, lunches, and alternative channel work should be scheduled ahead of time. This pre-planning approach, while logical in a less complex environment, falls short in today’s fast-paced contact centers. Metrics such as Schedule Adherence are derived from this fine-tuned approach, where any deviation can threaten service levels. The concept of “The Power of One,” introduced by Penny Reynolds, illustrates how quickly service level drops when even a single agent is missing.

To visualize this, consider a base Erlang-C model where we calculate the service level and average speed of answer for 150 calls offered in a 30-minute interval with an average handling time of 450 seconds. With a service level objective of answering 80% of calls in 30 seconds or less, 43 agents are required. However, any shortage in staff dramatically impacts service levels and average speed of answer:

Number of Staff	Service Level	Average Speed of Answer (seconds)
43	80%	24
42	72%	37
41	63%	61
40	50%	107
39	33%	221
38	12%	815

This can be described as a classic example of a queueing system reaching its capacity. In such systems, when the number of staff is sufficient to handle incoming calls, the service level can be maintained at or above 80% in the 30-second target. In our example, precisely 43 agents would answer 80% of calls in 30 seconds or less. However, once the staff number falls below a critical point necessary to manage the call volume, the service level declines rapidly.

This behavior is often modeled using queueing theory, in which the system’s performance is stable until a tipping point is reached. Past this tipping point, even a small reduction in resources (in this case, staff) leads to a non-linear and disproportionate decrease in service level performance.

This kind of relationship is sometimes called a “cliff effect” because the performance remains high and stable until it suddenly drops, much like a cliff’s edge. In practical terms, this indicates that there’s a minimum threshold of staffing required to maintain a high service level, and staffing below this threshold can result in a dramatic reduction in service quality.

Such an effect underscores the importance of maintaining a buffer of additional staff above the critical threshold to accommodate unexpected variances and ensure service levels remain consistent. Yet, the term “buffer” is often thought of as waste that results in increased expenses, the result of a sub-optimal plan.

Understanding and Harnessing Variance and Volatility

Variation in contact centers refers to natural fluctuations in call volumes and handling times, influenced by factors such as time of day, day of the week, and seasonal trends. Minimal Interval Variance (MV) plays a critical role in the Erlang-O methodology, representing natural variance within a call center queue due to the randomness of call arrivals.

where: FC is the forecasted call volume for the interval.

MV acknowledges that a contact center with a higher call volume per interval will experience a lower MV due to the statistical ‘smoothing’ effect observed in larger systems.

When incorporating MV into Erlang-O calculations, we adjust the base staffing levels required to accommodate the natural unpredictability of call arrivals. This adjustment ensures that service levels are maintained even when natural variance swings lead to agent shortages relative to call demand.

Unpredictable Volatility (VX) represents sudden, unforeseeable spikes in call volume that disrupt normal operations. Unlike fluctuations accounted for by MV, VX events are significant deviations that cannot be anticipated through traditional forecasting methods. By incorporating VX, Erlang-O adds resilience to the staffing model, ensuring that call centers can handle unexpected spikes in demand.

Erlang-O Unleashed: A New Era of Staffing Calculations

Erlang-O builds on traditional models but introduces several enhancements to address modern contact center challenges. It incorporates MV, VX, and Intraday Shrinkage (IS) into staffing calculations. By leveraging real-time data and automation, Erlang-O dynamically adjusts staffing levels throughout the day, ensuring optimal staffing and operational efficiency.

Breaking Down Erlang-O: Key Components of the New Staffing Model

Erlang-O addresses three core components not considered in previous staffing models:

• Minimal Interval Variance (MV): This algorithm accounts for the inherent unpredictability in call arrivals and ensures the staffing model can dynamically adjust to expected changes in call volume associated with minimal interval variance.
• Forecast Volatility (VX): Beyond minimal interval variance, the algorithm extends overhead to account for volatility or spikes outside the minimal interval variance. Incorporating volatility in the base staffing model adds additional resilience to the environment.
• Intraday Shrinkage (IS): The algorithm acknowledges that pre-scheduling productive off-phone shrinkage (training, coaching, and other activities) can be more effectively managed in real-time with automation. By dynamically delivering time allocated for non-phone activities and less time-sensitive channel allocation, Erlang-O ensures an optimal allocation of agent resources.

Calculation of the Erlang-O Model

The Erlang-O model enhances traditional Erlang formulas by incorporating variance, volatility and shrink overhead directly into the staff line. Unlike its predecessors, Erlang-O integrates variables representing Minimal Interval Variance (MV) and Volatility (VX) to recalculate the base staff and then incorporates Intraday Shrinkage (IS) alongside traditional inputs such as call arrival rates, traffic intensity, and servicing time objectives.

Where:

• ErlangC (Adjusted Calls, AdjustedAHT, SL) calculates the base number of agents required using the Erlang-C formula based on adjusted Calls, adjustedAHT, for the desired service level objective.
• Adjusted Calls = Forecasted Calls * (1+MV+VX1), calculating the adjusted call volume by incorporating Minimal Interval Variance (MV) and any additional volatility (VX). We will later describe OV=(VX+MV) representing total Operational Variance, a composite of both volatility and minimal interval variance.
• AdjustedAHT = Forecasted AHT * (1+VX2), calculating the adjusted call AHT by incorporating additional volatility (VX2) for handling time. 
• Intraday Shrink: IS (DPS, OS, AC) is Intraday Shrinkage, factoring in Discounted Productive Shrinkage (DPS) from all non-scheduled off-phone activities such as training, coaching, breaks & other developmental activities, Other Shrinkage (OS) such as absenteeism and unaccountable shrink, and Alternative Channel (AC) work, to reflect the time to allocate for work queues with multi-hour or multi-day service level objectives.

Hands-On with Erlang-O: Sample Interval Calculation

Working through a sample interval calculation, we leverage an interval for which we are offered 150 calls with an expected AHT duration of 460 seconds and assume our service level objective is to answer at least 80% of the calls in 30 seconds or less.

For our base FTE required using Erlang-C, we calculate 44 agents are necessary:

ErlangBase (Calls, AHT, SL) = 44

Here find we need to incorporate 6.5% based on the interval calls forecasted of 150. This means that each interval could be as low as ~140 calls and as high as ~160 calls.

We now re-calculate ErlangC (Adjusted Calls, Adjusted AHT, SL) where Adjusted Calls represents the higher variance parameter, or 160 calls. Re-calculating ErlangC with 160 calls at 460 seconds determines we now need 3 additional agents to ensure we answer 80% of the calls in 30 seconds. For this example, we’ll assume a volatility analysis does not require any adjustment to our forecast.

Next, we incorporate shrinkage into the net staff line by the amount of time we intend to remove throughout the time, based on Intraday Shrinkage. This calculation is a straightforward aggregation of all non-scheduled off-phone activities, across the three areas of productive shrinkage, other shrinkage and alternative channel work, as described in the previous section. 

For our example, we’ll assume that we want to apply:

Productive Shrink: 8%, Discounted Productive Shrink: 4%

Other Shrinkage: 7%

Alternative Channel: 5%

Total Intraday Shrink (IS): 16%

We now calculate the final agents staffed for this interval to be 56.

Achieving Peak Efficiency: Service Level and Expense Optimization with Real-Time Automation

With real-time contact center automation, Erlang-O continuously analyzes agent states and queue health, making decisions to deliver productive shrinkage and alternative channel work. By delivering these off-phone activities in response to queue health, you maximize both the percentage of productive off-phone work and protect the service level objective. Leveraging variation and volatility in real-time allows for discounting the shrink factor required for training, coaching, and alternative channel work. This methodology is superior to traditional WFM planning processes, which pre-emptively optimized on and off-phone activity.

By systematically applying these steps, the Erlang-O model provides a robust methodology for staffing that is responsive to real-time conditions while being anchored in the statistical realities of call volume variance. This approach allows for a staffing strategy that is both resilient and optimized for operational efficiency.

Erlang-O: Transforming Contact Center Staffing for the Future

Erlang-O is an innovative staffing model designed for the dynamic complexities of modern contact center operations. By integrating real-life operational complexities such as overhead, variance, and volatility into its algorithm, Erlang-O offers a more nuanced approach to workforce management. The model’s capability to incorporate these factors enables it to adapt more effectively to fluctuating demands, maintaining service levels and optimizing operational efficiency.

Erlang-O’s integration of intraday automation allows for real-time adjustments based on actual operational conditions. By dynamically managing agent allocation in response to queue health, Erlang-O not only enhances the utilization of human resources but also supports continuous employee development and effective handling of alternative communication channels. This model demonstrates significant improvements in service quality and cost management, marking a paradigm shift in workforce management strategies.

Discover how Erlang-O can elevate your contact center operations to new heights. Reach out to Ted Lango for an exclusive consultation and learn how to implement this innovative model in your organization today.

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Ted Lango is Senior Vice President at Intradiem and Founder of WFM Labs, a community reinventing the next-generation approach to successfully operating contact centers. Ted may be reached at Ted.Lango@Intradiem.com.

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