Service Center Staffing with Cross-Trained Agents and Heterogeneous Customers

We model a real-world service center with cross-trained agents serving customer requests that are heterogeneous with respect to complexity and priority levels: High priority requests preempt low priority requests and low-skilled agents can only serve less complex requests, while high skilled agents can serve all requests. Our main aim is to dynamically assign requests to agents considering the priority and complexity levels of requests. We model this system as a Markov chain that is infinite in multiple dimensions and thus is not amenable to exact analysis. We therefore apply approximation and bounding techniques to develop a tractable, novel algorithm using the Matrix Analytic Method. Our algorithm closely approximates the operations of the real-world service system under a simple but effective threshold-based request-assignment policy. Extensive computational results demonstrate the usefulness of our algorithm to minimize costs given an existing staffing configuration, as well as in helping to make long-term staffing decisions. In addition, our algorithm also has at least two orders of magnitude shorter computation times than each replication of simulation. Hence, it is both fast and accurate.