Call volume forecasting per operator

A large international banking group operates a multi-channel customer service center handling thousands of inbound calls daily. Accurate call volume estimation at the operator level is critical to ensure adequate staffing and service levels, optimize workforce planning, avoid over- or under-utilization of agents, and control operational costs while maintaining customer satisfaction.

The challenge was to predict the number of calls handled per operator over a given time period, accounting for differences in schedules, experience, and operating conditions.

As a first baseline, a linear regression model was considered due to its simplicity and interpretability. However, exploratory data analysis quickly revealed structural issues: call volumes are discrete counts (0, 1, 2, …), not continuous; predictions from linear regression could be negative or non-integer, which is not meaningful in this context; and variance increased with the mean, violating linear regression assumptions. These observations indicated a model–data mismatch.

Given the nature of the target variable (call counts), the problem was reframed using a count-based probabilistic model. The approach started with Poisson regression as a natural framework for count data, using a log-link function to ensure strictly positive predictions. An exposure offset accounted for different working durations (e.g., hours worked per operator), and a hierarchical structure modeled systematic differences between operators while sharing information across the population.

The final solution was implemented as a Bayesian hierarchical count model using PyMC, allowing for operator-level random effects (experience, efficiency, behavioral differences), global effects from contextual variables (shift type, workload indicators, tenure), and full uncertainty quantification via posterior distributions.

When over-dispersion was detected, the model was extended to a Negative Binomial formulation, improving robustness and predictive performance. This approach aligns the statistical assumptions of the model with the real-world data-generating process.