March 10, 2009 1:54 Production Planning & Control cat˙ppc˙init Production Planning & Control Vol. 00, No. 00, Month 200x, 1–14 RESEARCH ARTICLE Feedback Control Ideas for Call Centre Staﬃng M. R. Arahal, D. R. Ramirez ∗ and E. F. Camacho Dpto. de Ingenier´ ıa de Sistemas y Autom´ atica, Escuela T´ ecnica Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, s/n., 41092 Sevilla, Spain (Received 00 Month 200x; ﬁnal version received 00 Month 200x) Call centres are nowadays a widespread solution to deal with customer support and as platform for diﬀerent kind of business. Call center staﬃng is crucial to provide adequate service levels at acceptable costs. The task is usually accomplished using heuristics with the help of a human experts or with some static oﬀ-line optimization based on operations research. Simulators based on queue theory and statistical analysis are, in some cases, also used. The aim of the paper is to show that call centre staﬃng can be posed as a feedback control problem with the advantage of getting a higher level of automation, and a wealth of results from control theory that can help to obtain the best possible staﬃng. In the paper the working procedures of call centres are described and how the staﬃng is usually made. A feedback controller is proposed and assessed in simulation. The results show that good call centre staﬃng can be obtained even with a not very sophisticated controller. 1. Introduction Call centres are nowadays present in companies that have to deal with a large number of customers, and some businesses (e.g. airlines, hotels, and credit-card companies) rely almost exclusively on call centres to provide service and to obtain customer feedback (Andrews and Cunningham 1995). The capacity of a call centre is determined mostly by the human resources used. Since these are expensive, the quality of the service is often balanced with capacity, so that the call centre can provide the best service with minimum costs (Pinedo et al. 1999). A widely used approach to scheduling is to use Markov chain (Deslauriers et al. 2005) and queueing models to simulate the behavior of the call centre under diﬀerent circumstances. In Koole and Mandelbaum (2002), a survey of queueing theory applied to telephone call centres can be found with many relevant references. Forecasting techniques can be useful for predicting arrival rates (Jongbloed and Koole 2001). This information can be used by a simulator of the call centre to test diﬀerent staﬃng situa- tions, allowing the planner to produce a staﬃng plan that balance quality of service and costs. Prediction techniques can also be used in a dynamic staﬃng scheme such as in Whitt (1999). A more elaborate procedure is to compute the call centre staﬃng for a long period using static optimization, more precisely, solving an integer programming problem in which costs and service are considered through a model like the well known Erlang C formula (Gans et al. 2003, Tijms 2003). In this case, the staﬃng is applied in an open-loop manner and unpredictable ﬂuctuations in the number of incoming calls have a negative impact in the service levels. In fact, using such staﬃng forces the management staﬀ to decide on which policy to follow: a service-oriented policy in which more agents than needed on average are hired (with higher costs), or a cost oriented policy in which less agents are hired (with lower service levels). * Corresponding author. Email: danirr@cartuja.us.es ISSN: 0953-7287 print/ISSN 1366-5871 online c  200x Taylor & Francis DOI: 10.1080/0953728YYxxxxxxxx http://www.informaworld.com