Dimensioning Large Call Centers

Abstract

We develop a framework for asymptotic optimization of a queueing system. The motivation is the sta ng problem of call centers with 100's of agents or more. Such a call center is modeled as an M M N queue, where the number of agents N is large. Within our framework, we determine the asymptotically optimal sta ng level N that trades o agents' costs with service quality: the higher the latter, the more expensive is the former. As an alternative t o this optimization, we also develop a constraint satisfaction approach where one chooses the least N that adheres to a given constraint o n w aiting cost. Either way, the analysis gives rise to three regimes of operation: quality-driven, where the focus is on service quality; e ciencydriven, which emphasizes agents' costs; and a rationalized regime that balances, and in fact uni es, the other two. Numerical experiments reveal remarkable accuracy of our asymptotic approximations: over a wide range of parameters, from the very small to the extremely large, N is exactly optimal, or it is accurate to within a single agent. We demonstrate the utility o f our approach b y revisiting the square-root safety sta ng principle, which is a long-existing ruleof-thumb for sta ng the M M N queue. In its simplest form, our rule is as follows: if c is the hourly cost of an agent, and a is the hourly cost of customers' delay, then N = R + y a c p R, where R is the o ered load, and y is a function that is easily computable.2000 Mathematics Subject Classi cation: 60K25 primary, 90B22 secondary.

When Promotions Meet Operations: Cross-Selling and Its Effect on Call Center Performance

“…The asymptotic regime that we use has been shown to be extremely robust even in relatively small systems (see Borst et al [8]); Consistent with this finding we give strong numerical evidence to support the claim that this robustness is also typical in our setting. We note however, that the existing methods of establishing steady-state convergence in this asymptotic framework were not sufficient for proofs in our framework.…”

“…In particular, we follow the asymptotic optimality framework approach first used by Borst et al [8], and adapted later to more complex settings ( [3], [4], [5], [6], [15] and [19]). …”

A Method for Staffing Large Call Centers Based on Stochastic Fluid Models

“…To apply our method in a given real-world context, the main task is to estimate the demand distribution F defined by (4). A reasonable procedure for doing this, which accords well with the estimation methods commonly used in call center practice, is the following.…”

“…A widely-used rule-of-thumb that emerges from the Erlang-C formula is the square-root safety staffing rule, cf. Kolesar and Green [16], which recommends a server pool size of the form [4]. They refine the square-root rule by optimizing over β to balance queueing and staffing costs.…”

Managing Response Time in a Call-Routing Problem with Service Failure

“…5% delay probability). As the arrival rate increases, the size of the call center would increas in a way that follows the square-root staffing rule (e.g., see Borst, Mandelbaum, and Reiman [6]). One difficulty is that these rules are not derived for the heterogeneous servers, callback loops, and priority rules that are essential in our model.…”