WrightForge Lab — Interactive Tool

The balance between call demand and agent supply defines everything.

WFM Equilibrium is an interactive workforce management visualizer that lets you see, feel, and understand the forces that shape contact centre performance — powered by real Erlang C queuing mathematics.

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The Challenge

Workforce management is the invisible engine of every contact centre.

Every day, contact centres face the same fundamental tension: calls arrive unpredictably, but agents cost money whether they're on the phone or not. Staff too few, and callers wait, abandon, and churn. Staff too many, and you're burning budget on idle time.

The discipline of Workforce Management exists to navigate this tension — to forecast demand, schedule supply, and continuously balance service quality against operational cost. But the relationships between these variables are non-linear and unintuitive. Adding five agents doesn't improve service level by a fixed amount — it depends on current traffic intensity, handle times, shrinkage, and a dozen other factors.

This is why the math matters. And why seeing it — not just reading a table of numbers — changes how you think about your operation.

Call Volume

Handle Time

Workload

Agents

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Shrinkage

Capacity

When workload exceeds capacity, service degrades.
Erlang C tells you exactly how much.

Understanding the Domain

What is Contact Centre Workforce Management?

Workforce management in a contact centre is the practice of aligning the right number of agents, with the right skills, at the right time, to meet a forecasted volume of customer interactions — while hitting service level targets and controlling cost.

It encompasses four interconnected disciplines: forecasting (predicting how many calls will arrive and when), scheduling (assigning agent shifts to cover the forecast), real-time adherence (monitoring whether agents are following the plan), and continuous improvement (learning from variance to sharpen future accuracy).

The underlying mathematics rely on queuing theory — specifically the Erlang C model, which calculates the probability that an arriving call must wait given a known arrival rate, handle time, and number of agents. From that single probability, we can derive service level, average speed of answer, agent occupancy, and predicted abandonment. Every WFM decision — whether to approve a vacation request, add overtime, or adjust an IVR — ultimately flows through this equation.

The challenge is that these relationships are deeply non-linear. A contact centre operating at 85% occupancy might deliver an 82% service level. Push occupancy to 92% by removing just a few agents, and service level can collapse below 50%. Small input changes cascade through the model in ways that spreadsheets and static reports struggle to communicate.

The Tool

Four ways to see your operation.

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Demand vs Supply

An area chart showing call volume overlaid with agent capacity across the day, week, or month. Where the curves diverge, service suffers. Where they align, the operation hums. Hover any interval to see Erlang C outputs in context.

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Call Flow Sankey

Trace every call from arrival through IVR, queue, agent, and outcome. See the proportions: how many self-serve, how many wait, how many abandon, how many resolve on first contact. The widths tell the story.

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Balance & KPIs

A service level gauge with red/amber/green zones, surrounded by six outcome KPI cards — service level, ASA, abandon rate, occupancy, cost per call, and effective staff. The executive summary at a glance.

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Live Particle Flow

The signature view. Every call is a particle — spawning, flowing, queuing, being served, or abandoning in real time. Colors shift from green to amber to red as wait times climb. You don't just read the numbers — you feel them.

Real Erlang C

Not an approximation. The full Erlang C queuing model with Poisson arrivals, exponential service times, and logarithmic factorial handling for large agent pools. Abandon rate modeled via exponential caller patience overlay.

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Every Lever Connected

Call volume, AHT, headcount, shift length, shrinkage, after-call work, break time, service level target — adjust any input and watch all four views and every KPI respond in real time. Cause and effect, made visible.

How to Use It

Explore the equilibrium.

WFM Equilibrium is designed for anyone who wants to understand the dynamics of a contact centre — whether you're a WFM analyst, an operations manager, or someone new to the domain trying to build intuition.

Set your demand

Dial in your daily call volume and average handle time. These two numbers define your total workload — the amount of agent-time your callers need.

Configure your supply

Set your agent headcount, shift length, shrinkage rate, break and after-call time. Watch the effective staff number respond — this is what you actually have on the phones.

Watch the cascade

Flip between the four visualization tabs. See where demand outpaces supply on the gap chart, trace calls through the Sankey, check your KPI gauge, then watch the particle flow to feel the operation in motion.

Test scenarios

What happens if AHT rises 30 seconds? If three agents call in sick? If call volume doubles? Drag the sliders and see — in real time — how fragile or resilient your staffing model really is.