Expanding Service Capabilities Through an On-Demand Workforce

An on-demand workforce can greatly benefit a traditional call center by allowing it to adjust its service capacity on demand quickly. Despite its conceptual elegance, the operationalization of this process is challenging due to the various sources of randomness involved. The purpose of this paper is to help call centers enhance service levels while keeping operating expenses low by taking advantage of an on-call pool of temporary agents in day-to-day operations. For that purpose, we develop a two-stage decision model in which the first stage seeks the optimal mix of permanent and on-call staff, and the second stage seeks a joint on-demand staffing and call scheduling policy to minimize the associated cost given the base staffing level and the size of the on-call pool. Because the exact analysis of the two-stage decision model seems analytically intractable, we resort to an approximation in a suitable asymptotic regime. In that regime, we characterize the system dynamics of the service operation and derive an optimal joint on-demand staffing and call scheduling policy for the second-stage problem, which in turn is used to find an approximate solution to the first-stage problem. In particular, the derived policy for the second-stage problem involves tapping into the on-call pool to procure a team of on-demand agents when the number of calls to be processed exceeds a certain threshold and dismissing them when it falls below another threshold; additionally, the call scheduling rule shows an unusual pattern due to the interplay between staffing and scheduling decisions. Extensive numerical studies under realistic parameter settings show that the solution approach we propose can achieve significant cost savings.