The goal of capacity planning is to determine the number of agents to be assigned at each time slot so that a desired customer satisfaction (e.g. short waiting time and low abandon rate) is achieved at low operational cost (fewer number of agents), given the forecasted future arrivals, service times, time a customer is willing to wait, as well as the routing policy at the automatic call distributor (ACD). As we have seen in Section 8.3.1, capacity planning consists of (iterations of) modeling, analysis, and simulation.
When a contact center is operated in a simple manner, for example when calls are served by homogeneous agents in the FCFS order, the contact center can be modeled in such way that it can be analyzed efficiently and accurately, and such analytical methods are found to be quite useful in capacity planning at contact centers [58]. Analytical methods not only quickly provide the number of agents to be assigned, but also allow us to study the performance under a wide range of parameter settings, which is useful in designing routing policies as we will see in Section 8.3.3.
Recently, however, it has become popular to prioritize calls (value-based routing) and to route particular calls to particular agents (skill-based routing). Under value-based or skill-based routing, a contact center can be modeled as a multidimensional Markov chain, for which only coarse approximations exist in the literature. Below, we discuss how the analytical tools developed in this thesis can support modeling and analysis in capacity planning at contact centers today.