Practical scheduling for call center operations

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.