Capacity sizing in the presence of a common shared resource: dimensioning an inbound call center

This paper studies a capacity sizing problem for service systems where capacity is determined by multiple types of resources that are required simultaneously in order to provide service. In addition to the simultaneous use of resources, the systems are characterized by the presence of a common resource that is shared across multiple types of customers. The paper focuses on inbound call centres as an important example of such systems. The capacity sizing problem in this context is one where the optimal number of servers that need to be allocated to different call types is determined. Optimality is defined as the number of servers that maximize revenues net of staffing costs. For the case where customers do not wait, it is shown that a greedy allocation procedure yields the optimal server allocation. Heuristics are proposed for the case with waiting customers that can exhibit impatience. The numerical analysis illustrates that for systems experiencing heavy loads and serving a diverse set of customers, the proposed heuristics outperform current methods that ignore the role of a shared resource in these types of dimensioning problems.