Flexibility Structure and Capacity Design with Human Resource Considerations

Most service systems consist of multidepartmental structures with multiskill agents that can deal with several types of service requests. The design of flexibility in terms of agents' skill sets and assignments of requests is a critical issue for such systems. The objective of this study was to identify preferred flexibility structures when demand is random and capacity is finite. We compare structures recommended by the flexibility literature to structures we observe in practice within call centers. To enable a comparison of flexibility structures under optimal capacity, the capacity optimization problem for this setting is formulated as a two-stage stochastic optimization problem. A simulation-based optimization procedure for this problem using sample-path gradient estimation is proposed and tested, and used in the subsequent comparison of the flexibility structures being studied. The analysis illustrates under what conditions on demand, cost, and human resource considerations, the structures found in practice are preferred.