Scheduling inbound calls in call centers

Scheduling inbound calls, namely assigning calls to Customer Service Representatives (CSRs) and sequencing the calls waiting for each CSR, is a key task in call center operations. In most call center this is achieved using simple priority rules, but in this dissertation we show that performance can be significantly improved by employing an optimization approach. Specifically, we formulate three different Integer Programming (IP) problems for such call scheduling, with objective functions of 1) minimizing the Total Flow Time (TFT), 2) minimizing the Maximum Flow Time (MFT) of any call, and 3) minimizing the Maximum Deviation of Cumulative Assigned Workload (MDCAW) for CSRs. 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. Our findings indicate that optimization is most valuable under realistic scenarios involving specialized but broadly trained CSRs and high call centre utilization rates. Furthermore, both the flow time and workload related objective functions are found to be useful, depending on the characteristics of the call center and the performance measures that are most important to call center management. We explore several solution techniques such as IP reformulation, Lagrangian relaxation and duality, cutting plane algorithm, and heuristic approach for solving the formulated IPs. For those solution algorithms, the qualities of the solution and the computational times of solving the IPs using a standard solver are compared to signify the effective approaches that make the optimization a competitive approach for scheduling inbound calls. Numerical results show that the heuristics optimization approach is preferable to any other solution investigated in terms of solution quality while the cutting plane algorithm is preferable in terms of computational times. Additionally, a case study comparing performances of a call center as resulted from using its current routing method with the performance resulted from the suggested solution techniques is presented