A Logarithmic Safety Staffing Rule For Contact Centers with Service Blending

Contact centers, i.e., call centers that handle more than one type of jobs simultaneously, such as inbound and outbound calls or telephony and online chatting, are of growing significance. In particular, most businesses place outbound as well as inbound calls, although these two types of calls may be performed by separate groups of agents. In this paper we consider contact centers in which one pool of agents handles inbound and outbound calls simultaneously, a process commonly referred to as call blending. We propose a logarithmic safety staffing rule, combined with a threshold control policy, ensuring that agents’ utilization is very close to one at all times, but that there are practically always idle agents present. Agent’s availability ensures that inbound customers rarely need to wait in queue and that outbound calls are not dropped. (Dropped outbound calls are a significant issue in the automated environment of modern contact centers.) Specifically, we show that, in addition to satisfying the target throughput rate of outbound calls, it is possible to have practically all inbound calls answered immediately upon their arrival, with at most a negligible proportion of outbound calls dropped. The main managerial insight of this paper is that call blending is a good alternative for costly overstaffing in large contact centers, when compared to the splitting setting. Here, “splitting” refers to a situation in which the two types of customers (inbound and outbound) are handled by two distinct service pools, each dedicated to one customer type. Specifically, when the goals are to satisfy desired service-quality constraints for the inbound calls, while maintaining a pre-specified long-run throughput rate of outbound calls with a negligible proportion of dropped calls, then blending can achieve these goals with a substantially smaller number of agents than the number needed for splitting.