Ger Koole

Ger Koole is a Dutch mathematician and full professor at Vrije Universiteit Amsterdam (VU Amsterdam), specializing in queueing theory, optimization, and workforce management for service operations. He is the author of Call Center Optimization (2013), widely regarded as the definitive academic textbook on workforce management mathematics. Koole co-founded CCmath with Auke Pot in 2005, building a WFM software company directly from academic research, and developed the Erlang X model — an extension of Erlang C that incorporates abandonment, retrials, line capacity limits, and arrival variance into a single framework.

Overview

Ger Koole bridges the gap between academic operations research and practical contact center management more directly than perhaps any other living researcher. His textbook translates complex queueing mathematics into operational guidance that WFM analysts can apply. His software company, CCmath, commercializes that research into tools used by contact centers globally. And his Erlang X model addresses the key limitations of Erlang C that practitioners have long recognized but lacked a rigorous alternative for.

Koole co-authored the landmark 2003 survey "Telephone Call Centers: Tutorial, Review, and Research Prospects" with Noah Gans and Avishai Mandelbaum — the paper that established call center operations research as a recognized academic field.

Early Life and Education

Koole is a mathematician by training, with deep expertise in applied probability theory, Markov decision processes, and queueing models. He completed his doctoral research in mathematics, focusing on optimization in stochastic systems, before joining the faculty at VU Amsterdam. His academic career has been characterized by a consistent focus on applying rigorous mathematical methods to real-world service operations — particularly contact centers and healthcare.

Career

VU Amsterdam

As a full professor in the Department of Mathematics at VU Amsterdam, Koole built a research program centered on the application of queueing theory and optimization to service industries. He teaches Business Analytics and Optimization courses and has supervised numerous doctoral students whose dissertations have advanced contact center science. His research extends beyond call centers into healthcare operations and revenue management, but workforce management remains his primary domain of impact.

CCmath (2005–Present)

In 2005, Koole co-founded CCmath with Auke Pot, a fellow PhD from VU Amsterdam. CCmath represents a rare example of a WFM software company built directly on original academic research. The company provides forecasting and workforce scheduling software for contact centers, with algorithms grounded in the queueing models Koole developed in his research. CCmath's tools include native Excel integrations for Erlang C, Erlang X, chat staffing, and blending calculations. Wout Bakker currently serves as president of CCmath.

Adscience

Koole also co-founded Adscience, an internet advertising optimization company, demonstrating the versatility of his optimization expertise beyond contact centers.

Key Contributions

The Erlang X Model

Main article: Erlang X

The Erlang X model is Koole's most significant contribution to WFM practice. While the Erlang-A model (developed by Avishai Mandelbaum) extended Erlang C by adding customer abandonment, Erlang X goes further by incorporating multiple real-world phenomena into a single model:

• Abandonment — Customers who hang up before being served
• Retrials — Customers who abandon but call back, creating additional demand
• Line capacity limits — Finite trunk lines that produce busy signals (connecting to Erlang B concepts)
• Arrival variance — Non-Poisson arrival patterns that deviate from standard assumptions

By integrating these effects, Erlang X provides staffing estimates that account for the circular dependencies between service level, abandonment, and retrials — dependencies that simpler models miss entirely. When service degrades, more customers abandon; some of those customers retry, increasing load; increased load further degrades service. Erlang X captures this feedback loop mathematically.

Call Center Optimization (2013)

Koole's textbook is the most comprehensive academic treatment of WFM mathematics available. It covers the complete WFM cycle — forecasting, staffing, scheduling, and real-time management — with mathematical rigor that is absent from practitioner-oriented guides but remains accessible to technically inclined analysts. The book treats Erlang B, Erlang C, Erlang A, and Erlang X in a unified framework, making it essential reading for anyone seeking to understand the mathematical foundations underlying commercial WFM software.

The 2003 Landmark Survey

The "Telephone Call Centers" survey paper, co-authored with Gans and Mandelbaum, was published in Manufacturing & Service Operations Management and ran 62 pages covering every aspect of call center operations research. The paper has been cited thousands of times and remains the standard entry point for researchers entering the field. It identified open problems in forecasting, routing, staffing, and scheduling that have driven two decades of subsequent research.

Markov Decision Process Applications

Koole has published extensively on the application of Markov decision processes (MDPs) to service operations, including optimal routing policies for multi-skill contact centers and dynamic scheduling under uncertainty. This work provides the theoretical foundation for the optimization algorithms used in advanced WFM and ACD routing systems.

Legacy and Impact

Koole's impact is distinctive because it operates simultaneously in three domains: academic research, commercial software, and practitioner education. His textbook trained a generation of researchers. His company, CCmath, puts his algorithms into production. And his Erlang X model gives practitioners a more realistic alternative to the standard Erlang C calculations that most WFM tools still rely on.

The Erlang X model is particularly important because it addresses a complaint that experienced WFM analysts have raised for decades: Erlang C overstaffs because it ignores abandonment, but Erlang A understaffs because it ignores retrials. Erlang X accounts for both, producing staffing recommendations that better match real-world outcomes.

Connection to Workforce Management

Koole's work is directly embedded in WFM practice through multiple channels. CCmath's software is used by contact centers for forecasting and scheduling. The Erlang X calculator, freely available on Koole's website, is used by analysts worldwide. His textbook is the mathematical reference that WFM software developers consult when implementing staffing algorithms. And his research on multi-skill optimization and arrival process modeling has influenced the design of scheduling engines across the industry.

For WFM practitioners, Koole represents the rare academic who not only understands the mathematics but also understands the operational context in which those mathematics must be applied.

Selected Publications

• Koole, G. Call Center Optimization. MG Books, 2013.
• Gans, N., Koole, G., and Mandelbaum, A. "Telephone Call Centers: Tutorial, Review, and Research Prospects." Manufacturing & Service Operations Management, 5(2), 2003, pp. 79–141.
• Koole, G. and Mandelbaum, A. "Queueing Models of Call Centers: An Introduction." Annals of Operations Research, 113, 2002, pp. 41–59.
• Koole, G. Call Center Optimization: A Deep Dive into WFM. Online resource, gerkoole.com.
• Pot, A., Bhulai, S., and Koole, G. "A Simple Staffing Method for Multi-Skill Call Centers." Manufacturing & Service Operations Management, 10(3), 2008, pp. 421–428.

See Also

• CCmath
• Erlang C
• Erlang B
• Erlang-A
• Operations Research in Workforce Management
• Avishai Mandelbaum
• Noah Gans
• Forecasting Methods