|M.Sc Student||Aldor-Noiman Sivan|
|Subject||Forecasting Demand for a Telephone Call Center: Analysis of|
Desired versus Attainable Precision
|Department||Department of Industrial Engineering and Management||Supervisors||Professor Paul Feigin|
|Professor Avishai Mandelbaum|
Today's call centers managers face multiple operational decision making tasks. One of their most common chores is determining the weekly staffing levels to ensure customer satisfaction and needs while minimizing service costs. An initial step for producing the weekly schedule is forecasting the future system loads comprising both the predicted arrival counts and the average service times.
After obtaining the forecasted system load, in large call centers, a manager can implement the QED (Quality-Efficiency Driven) regime ``square-root staffing'' rule to allow balancing between the offered load per server and quality of service. Implementing this staffing rule requires that the forecasted values maintain certain levels of precision. One of the aims of this thesis is to determine whether or not these levels can be achieved by practical algorithms.
In this thesis we introduce two arrival count models which are based on a mixed Poisson process approach. The first model uses the Normal-Poisson stabilization transformation in order to employ linear mixed model techniques. The model is implemented and analyzed on two different data sets. In one of the call centers the data include billing cycles information and we also demonstrate how to incorporate it as exogenous variables in this model. We develop different goodness-of-fit criteria that help determine the models performance under the QED regime. These show that during most hours of the day the model can reach the desired precision levels. Actually, whenever the QED regime and square root staffing formula are appropriate, the model performs well. We also demonstrate the effect the forecasting lead time (that is, the time between the last learning data and the first forecasted time) has on this model precision.
We also demonstrate how our mixed model can achieve very similar levels of precision when compared to other models. This similarity holds even though our model's predictions are based on smaller amounts of learning data.
Our second model employs the Bayesian approach, implementing Gibbs sampling techniques, and using `OpenBugs' software, to produce the predictive distributions for the future arrival counts. Due to computational limitations we only show a `proof of concept' for this model by applying it to predicting a single day's arrivals and comparing it to the mixed model results.
We also develop a fairly simple quadratic regression model to predict the average service times needed for producing the future system loads.