An Integer Programming approach for scheduling inbound calls in call centres

Scheduling inbound calls is a key task in call centre operations. In most call centres this is achieved using simple priority rules, but in this paper we show that performance can be significantly improved by employing an optimisation approach. Specifically, we formulate three different Integer Programming (IP) problems with objective functions of minimising the Total Flow Time, the Maximum Flow Time and the Maximum Deviation of Cumulative Assigned Workload. We also report the results of a numerical experiment designed to evaluate under what conditions these IP formulations give superior performance and which objective should be chosen.