A practical spreadsheet-based scheduling method is developed to determine the optimal allocation of service agents to candidate tour types and start times in an inbound call center. A stationary Markovian queueing model with customer abandonment is employed to determine required staffing levels for a sequence of time intervals with varying call volumes, handling times, and relative agent availabilities. These staffing requirements populate a quadratic programming model for determining the distribution of agent tours that will maximize the fraction of offered calls beginning service within a target response time, subject to side constraints on tour type quantities. The optimal distribution is scaled to reflect the total number of scheduled agents, and a near-optimal integer solution is derived using rounding thresholds found by successive one-dimensional searches. This novel approach has been successfully implemented in large service centers at Qwest Communications and could easily be adapted to other operational environments.
