Call Centers: A Robust Method for Workforce Optimization

Christian van Delft, Professor of Operations Management and Information Technology - July 15th, 2011
Call Centers

Christian van Delft and his co-authors have developed a method for staffing call centers that, for the first time, takes into account the uncertainty in overall daily workload. They show that giving personnel in these centers secondary tasks to perform between calls makes it possible to reduce operating costs while ensuring high-quality service.

Christian van Delft ©HEC Paris

Christian van Delft hoIds a Bachelor's of Engineering in Applied Mathematics from the Université catholique de Louvain (Belgium) and a doctorate in Operations Management from HEC (...)

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Call centers have become an integral part of many companies, and the quality of their customer service is a potential competitive advantage and selling point. Indeed, van Delft and his coauthors explain, as early as 2002, call centers handled more than 70 percent of all business/customer interactions in the United States. While their emergence on a large scale has led to the investigation of numerous problems in operations management, none of the research thus far has taken into account one of the key factors of call center sizing and shift scheduling: the high degree of uncertainty concerning the number and duration of calls from day to day. This overlooked variable complicates workload evaluations and thus leads to staffing problems. Meanwhile, as van Delft points out, “ salaries make up 70 to 75 percent of a call center’s operating costs,” so inefficiencies in this area constitute a major concern. 


“In theory, the method is supposed to be simple: managers use commercial software packages, act as though they could predict the future, and plan out days based on data that are assumed to be reliable.  They then readjust to fluctuations in real time as best they can.” This method can be efficient — if there are few forecasting errors or if workload varies relatively little from one day to the next. But these conditions do not always hold true. “For example, in areas close to the sea, we would expect that when the weather gets nice, people will go to the beach, thus changing their consumption habits by putting off telephone purchases until later in the evening. On the other hand, when the weather is less pleasant, calls will tend to be spread evenly throughout the day instead,” explains the researcher, who sees in this issue a potential application for supply chain optimization in the context of random phenomena. “As we see it, you have to integrate forecasting errors directly into the methodology—because they are definitely going to happen—and handle adaptation costs from the outset.”


As explained above, the traditional approach, which presumes a relatively accurate prediction of consumer calling habits, cannot solve the planning problems associated with factors such as weather conditions. “It’s a little like if somebody told you to go to the moon or to Mars and find the deepest crater,” he continues. “There is no efficient strategy!” To deal with this problem, van Delft and his coauthors used robust optimization, a useful concept that was first presented several years ago. “The idea is to try and find a solution with the best possible performance, looking at the worst-case scenario given a set of uncertainties that are set in advance. The huge advantage of this approach is that it frees us from having to use probability distributions to describe the missing data, which are often difficult to execute with precision due to the complexity of the mathematical models,” explains van Delft. “With robust optimization, we stick to problems of a more limited size, which we can solve more easily.” To ensure the reliability of their method, the researchers start by validating it using the simplest call centers before moving on to bigger ones.


“This work mostly allowed us to test our theories on call centers, which present specific difficulties,” van Delft continued. “The comparison between robust optimization and other approaches, notably between it and the traditional method where forecasts are assumed to be perfectly accurate, revealed significant differences in terms of the instances of over- and under-staffing. These fluctuations can be modeled quite easily, and there’s no reason not to do it in practice.” The researchers showed that performance gains depend on the amplitude of fluctuations of calls received  and of the required quality of service (fluctuations in operating costs can be reduced by as much as seven times in call centers where service quality is high). These differences are explained notably by the fact that in a highly fluctuating environment, the researchers were interested not only in mean costs and performance, but also their fluctuations around this mean. “In general, that’s where you lose the most if you don’t integrate uncertainty from the outset,” explains van Delft. “This is a well-known phenomenon, but practitioners rarely take it into account.” On the other hand, the authors suggest that when the inevitable fluctuations in customer calls is taken into account, it becomes possible to schedule additional tasks (such as processing emails), which can be performed in-between calls, thus partially attenuating the undesirable effects of uncertainty.

Based on an interview with Christian van Delft and the article “Staffing a Call Center with Uncertain Non-Stationary Arrival Rate and Flexibility” by S. Liao, G. Koole, C. van Delft and O. Jouini, published on the 24 May 2011 in OR Spectrum .

Applications For Businesses
Applications For Businesses

The optimization method that van Delft and his coauthors have created can currently be used by call center managers with a limited number of types of operators: work on more complex call centers is still in its early stages. Managers of the former can use it to size their staff and set schedules more efficiently, both in economic (cost reduction) and individual performance terms. This research also shows that it is in their interests to give staff secondary tasks to perform between calls to reduce operating costs.


The researchers created a robust optimization model in order to determine the optimal workforce (the most efficient in terms of costs and performance) on the scale of a day, for a call center that has a single team of operators. This call center handles both random calls that must be processed as quickly as possible and secondary tasks such as the processing of emails. They used data from a real case (a Dutch hospital) to compare the performance of their robust methodology with that of other commonly used approaches.