Landmark Papers in Contact Center Operations Research

From WFM Labs

Landmark Papers in Contact Center Operations Research identifies and examines the most influential academic publications that shaped the science of contact center workforce management. These papers established the mathematical foundations, empirical methods, and conceptual frameworks that underpin modern WFM practice. Each entry provides the full citation, a summary of its contribution, an assessment of its impact, and its influence on subsequent research and industry practice.

The papers are presented in approximate chronological order by publication date, reflecting the intellectual lineage of the field.

Dantzig (1954): The Birth of Shift Scheduling Optimization

Citation: Dantzig, G. B. (1954). "A comment on Edie's 'Traffic delays at toll booths'." Journal of the Operations Research Society of America, 2(3), 339–341.[1]

Contribution: In this brief but foundational comment, George Dantzig demonstrated that the problem of selecting shifts to cover time-varying demand could be formulated as a linear program. Responding to Leslie Edie's paper on staffing toll booths at the Port of New York Authority, Dantzig showed that if shifts are predefined and the objective is to minimize total staffing cost while meeting minimum coverage requirements in each time period, the problem reduces to a set-covering LP that his recently developed simplex method could solve efficiently.

Why it matters: This two-page paper launched an entire subfield. Before Dantzig's formulation, shift scheduling was done heuristically — supervisors manually constructed schedules guided by experience and rules of thumb. The LP formulation demonstrated that mathematical optimization could produce provably minimum-cost staffing plans, establishing the intellectual foundation for every commercial WFM scheduling engine that followed.

Influence on practice: Every modern WFM platform (NICE, Verint, Calabrio, Aspect, Genesys) contains a shift optimization engine whose conceptual architecture traces directly to Dantzig's set-covering formulation. The integer programming extensions required for practical scheduling (indivisible shifts, minimum rest periods, consecutive day-off requirements) built on Dantzig's original continuous relaxation. Henderson and Mason (1998) later showed how to extend the approach with column generation for very large shift sets.[2]

Erlang (1917/1948): The Foundation of Queueing Theory

Citation: Erlang, A. K. (1917). "Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges." Elektroteknikeren, 13, 5–13. English translation in Brockmeyer, E., Halstrøm, H. L., & Jensen, A. (1948). The Life and Works of A. K. Erlang. Copenhagen Telephone Company.[3]

Contribution: Agner Krarup Erlang, a Danish mathematician working for the Copenhagen Telephone Company, derived the probability formulas for call blocking and waiting in telephone systems. His Erlang B formula gives the probability that all servers are busy (call is lost) in a system with no waiting capacity. His Erlang C formula gives the probability that a call must wait in a system with infinite queue capacity, assuming callers never abandon.

Why it matters: Erlang's formulas remain the most widely used capacity planning tools in contact centers over a century after their derivation. The Erlang C formula, in particular, is computed millions of times daily by WFM systems worldwide to determine required staffing levels for target service levels. Despite known limitations — the no-abandonment assumption, the stationarity assumption, the single-skill assumption — Erlang C endures because of its simplicity, transparency, and reasonable accuracy for basic voice queue dimensioning.

Influence on practice: Erlang C is the default staffing calculator in virtually every WFM platform and is taught in every contact center management training program globally. Its ubiquity has been both a strength (common language for capacity planning) and a limitation (over-reliance on a model that ignores abandonment, time-variation, and multi-skill routing).

Halfin and Whitt (1981): The QED Regime

Citation: Halfin, S., & Whitt, W. (1981). "Heavy-traffic limits for queues with many exponential servers." Operations Research, 29(3), 567–588.[4]

Contribution: Halfin and Whitt identified a critical operating regime for multi-server queues — the Quality-and-Efficiency-Driven (QED) regime — where the number of servers exceeds the offered load by an amount proportional to the square root of the offered load. In this regime, both service quality (short waits) and efficiency (high utilization) are simultaneously achievable, and the system exhibits a phase transition in performance characteristics.

Why it matters: The Halfin-Whitt regime provided the first rigorous justification for the empirical observation that large contact centers are inherently more efficient than small ones. The square-root staffing rule — staff = offered load + β√(offered load), where β controls the quality-efficiency tradeoff — gave practitioners a powerful heuristic that captures the essential nonlinearity of queueing systems without requiring full Erlang C computation.

Influence on practice: Square-root staffing became the standard "back of the envelope" capacity planning method in the industry. The Halfin-Whitt regime also provided the theoretical foundation for understanding economies of scale in contact center consolidation: merging two 50-seat centers into one 100-seat center yields a staffing reduction of approximately √50 ≈ 7 agents while maintaining equivalent service levels. Borst, Mandelbaum, and Reiman (2004) extended the framework to include per-agent and per-call costs, making the economic implications explicit.[5]

Garnett, Mandelbaum, and Reiman (2002): The Erlang-A Model

Citation: Garnett, O., Mandelbaum, A., & Reiman, M. I. (2002). "Designing a call center with impatient customers." Manufacturing & Service Operations Management, 4(3), 208–227.[6]

Contribution: This paper introduced the Erlang-A model (M/M/n+M), which extends the classical Erlang C model by incorporating customer abandonment — callers who hang up after waiting too long. The addition of exponentially distributed patience times fundamentally changes system behavior: the queue is always stable (no infinite queue buildup), and the model produces finite performance metrics even when offered load exceeds capacity. The paper derived closed-form expressions for key performance measures and analyzed the system's behavior across different operating regimes.

Why it matters: Customer abandonment is an empirical reality that Erlang C ignores. In practice, 2-10% of callers abandon before reaching an agent, and this fraction increases substantially during peak periods. Ignoring abandonment causes Erlang C to systematically overstate staffing requirements — a well-documented bias that the Erlang-A model corrects. The paper demonstrated that accounting for abandonment changes not just the quantitative staffing answer but the qualitative nature of system design: the Erlang-A model reveals that moderate understaffing is far less catastrophic than Erlang C suggests, because abandonment provides a natural safety valve.

Influence on practice: The Erlang-A model has been adopted by advanced WFM platforms (NICE IEX was among the first) as a superior alternative to Erlang C for staffing calculation. The abandonment correction is particularly important for planning during peak periods and for organizations with higher-than-average abandonment rates. Mandelbaum and Zeltyn (2004) subsequently provided comprehensive analysis of the M/M/n+G model with general patience distributions.[7]

Gans, Koole, and Mandelbaum (2003): The Definitive Survey

Citation: Gans, N., Koole, G., & Mandelbaum, A. (2003). "Telephone call centers: Tutorial, review, and research prospects." Manufacturing & Service Operations Management, 5(2), 79–141.[8]

Contribution: This 63-page survey provided the first comprehensive academic treatment of call center operations, bridging the gap between industry practice and academic research. It covered the full spectrum of call center operations: arrival process modeling, queueing models, staffing and scheduling, routing, performance measurement, and human resource management. The paper identified open research problems across all domains and provided a unified mathematical framework for analyzing call center operations.

Why it matters: Before this survey, call center operations research was fragmented across queueing theory, integer programming, and human resource management literatures. Gans, Koole, and Mandelbaum unified these streams into a coherent intellectual framework. The paper legitimized call centers as a serious academic research domain — previously, many operations researchers viewed call center problems as straightforward applications of existing theory rather than sources of novel research questions.

Influence on practice: With over 2,400 citations (Google Scholar), this is the most-cited paper in contact center operations research. It became the standard reference for researchers entering the field and for industry practitioners seeking to understand the scientific foundations of their work. The research agenda it articulated — particularly around time-varying demand, skill-based routing, and human factors — shaped a generation of subsequent research. It catalyzed significant academic investment in call center research, particularly in Israel (Technion), the Netherlands (VU Amsterdam), and the United States (Wharton, Columbia).

Ernst et al. (2004): The Scheduling Survey

Citation: Ernst, A. T., Jiang, H., Krishnamoorthy, M., & Sier, D. (2004). "Staff scheduling and rostering: A review of applications, methods and models." European Journal of Operational Research, 153(1), 3–27.[9]

Contribution: This survey cataloged the mathematical methods applied to staff scheduling across industries, providing a taxonomic framework that distinguished between task scheduling, shift scheduling, tour scheduling, and roster construction. The paper reviewed exact methods (integer programming, constraint programming), heuristic approaches (constructive heuristics, meta-heuristics), and decomposition strategies, situating contact center scheduling within the broader workforce scheduling literature.

Why it matters: By positioning contact center scheduling as an instance of a broader class of workforce scheduling problems, the paper enabled cross-pollination of solution methods. Techniques developed for nurse rostering, airline crew scheduling, and transit driver scheduling became accessible to WFM researchers and vendors. The taxonomic framework also helped clarify which aspects of contact center scheduling were truly unique (real-time demand responsiveness, sub-hourly granularity) versus standard applications of known methods.

Influence on practice: The paper has been cited over 1,700 times and remains the standard reference for workforce scheduling methodology. Its taxonomic framework is used in WFM vendor product specifications and academic textbooks. Van den Bergh et al. (2013) subsequently published an updated survey covering the 2004-2013 period.[10]

Brown et al. (2005): The JASA Call Center Data Analysis

Citation: Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Shen, H., Zeltyn, S., & Zhao, L. (2005). "Statistical analysis of a telephone call center: A queueing-science perspective." Journal of the American Statistical Association, 100(469), 36–50.[11]

Contribution: Using a massive dataset from an Israeli bank's call center (over 300,000 calls), this paper performed a rigorous statistical analysis of call center operations, testing the assumptions underlying standard queueing models against empirical evidence. Key findings included: arrival processes are not Poisson at the daily level (overdispersion due to day-to-day randomness), service times are approximately lognormal (not exponential as assumed by Erlang models), patience times are approximately lognormal, and there are significant time-of-day and day-of-week effects on all processes. The paper introduced the concept of "queueing science" — the integration of statistical methodology with queueing theory.

Why it matters: This paper was a wake-up call for both academics and practitioners. It demonstrated empirically that the convenient assumptions underlying standard models (Poisson arrivals, exponential service times, exponential patience) are systematically violated in real call centers. This mattered because the violations are not minor: the overdispersion in arrivals, for instance, means that Erlang-based models underestimate the variability in staffing requirements. The paper established that data-driven validation of model assumptions is essential, not optional.

Influence on practice: The paper influenced a shift toward more empirically grounded models in both academic research and vendor products. The demonstration that service time distributions are lognormal rather than exponential led several WFM platforms to incorporate more realistic distributional assumptions. The dataset itself, shared publicly, became a benchmark for testing new models and methods. The paper received the American Statistical Association's Outstanding Statistical Application Award and has been cited over 800 times.

Aksin, Armony, and Mehrotra (2007): The Modern Call Center Survey

Citation: Aksin, Z., Armony, M., & Mehrotra, V. (2007). "The modern call center: A multi-disciplinary perspective on operations management research." Production and Operations Management, 16(6), 665–688.[12]

Contribution: This survey updated and extended the Gans et al. (2003) review, focusing on developments in the intervening four years and expanding the scope to include multi-disciplinary perspectives from marketing, human resources, and information systems. The paper introduced a comprehensive framework organizing call center research into three temporal scales: long-term (capacity planning, technology selection), medium-term (staffing and scheduling), and short-term (real-time routing and management). It also highlighted emerging challenges including multi-channel operations, outsourcing, and the integration of customer relationship management with operational decisions.

Why it matters: While Gans et al. (2003) established the field, Aksin et al. (2007) mapped its evolution and identified the research frontier for the next decade. The multi-disciplinary framing was particularly influential: it demonstrated that call center operations cannot be optimized purely through queueing theory and integer programming but require integration with marketing science (customer value-based routing), organizational behavior (agent motivation and retention), and information systems (technology architecture).

Influence on practice: The paper has been cited over 1,100 times. Its temporal framework (long/medium/short-term) became the standard organizing principle for WFM curriculum and vendor product architecture. The emphasis on multi-disciplinary integration influenced the development of workforce engagement management (WEM) platforms that combine scheduling optimization with quality management, performance analytics, and agent experience tools. Vijay Mehrotra's involvement — as both an academic (University of San Francisco) and former industry practitioner (Blue Pumpkin/Witness Systems) — ensured the review maintained practical relevance.

Green, Kolesar, and Whitt (2007): Time-Varying Demand

Citation: Green, L. V., Kolesar, P. J., & Whitt, W. (2007). "Coping with time-varying demand when setting staffing requirements for a service system." Production and Operations Management, 16(1), 13–39.[13]

Contribution: This paper addressed the fundamental challenge that demand in service systems varies over time, but most queueing models assume stationarity. The authors developed and validated the Stationary Independent Period by Period (SIPP) approach and its variants for setting staffing requirements in systems with time-varying arrival rates. They showed when the common practice of treating each time period independently (applying steady-state Erlang formulas to each interval's arrival rate) works well and when it fails — specifically, it fails during rapid demand transitions where the system's transient behavior differs significantly from steady-state predictions.

Why it matters: The SIPP method is the actual computational engine inside most WFM staffing calculations, yet before this paper, its validity conditions were not well understood. Green, Kolesar, and Whitt identified conditions under which SIPP produces significant errors — particularly when staffing intervals are long relative to the rate of demand change — and proposed corrections. The paper provided the theoretical underpinning for a practice that had been used heuristically for decades.

Influence on practice: The paper directly influenced how WFM platforms compute staffing requirements. The identification of SIPP failure conditions led to recommendations for shorter planning intervals (15 minutes rather than 30 or 60) during periods of rapid demand change. The modified SIPP approaches proposed in the paper were implemented in several commercial WFM systems. Green, Kolesar, and Whitt's earlier work on the same topic, particularly their 2001 paper on the "Pointwise Stationary Fluid Flow Approximation" (PSFFA), provided complementary methods for extreme non-stationarity.[14]

Koole and Mandelbaum (2002): Queueing Models of Call Centers

Citation: Koole, G., & Mandelbaum, A. (2002). "Queueing models of call centers: An introduction." Annals of Operations Research, 113(1-4), 41–59.[15]

Contribution: This introductory paper provided an accessible bridge between classical queueing theory and contact center practice. It covered the essential models (Erlang B, Erlang C, Erlang A), introduced the key performance metrics, and explained the operational context that drives modeling choices. The paper served as the opening article for a special issue of Annals of Operations Research dedicated to call center operations.

Why it matters: While less cited than Gans et al. (2003), this paper was influential in making queueing theory accessible to operations management researchers who lacked deep backgrounds in stochastic processes. It demonstrated that call centers are queueing networks, not just single queues, and that the network structure (skill-based routing, overflow groups, virtual queuing) creates modeling challenges that go beyond classical theory.

Influence on practice: The special issue that this paper introduced brought together researchers from queueing theory, optimization, and statistics, catalyzing the interdisciplinary research community that would produce most of the landmark work in the following decade.

Avramidis, Deslauriers, and L'Ecuyer (2004): Simulation for Staffing

Citation: Avramidis, A. N., Deslauriers, A., & L'Ecuyer, P. (2004). "Modeling daily arrivals to a telephone call center." Management Science, 50(7), 896–908.[16]

Contribution: This paper addressed the empirically observed overdispersion in call arrival counts — the phenomenon that arrival variability exceeds what a Poisson process predicts. The authors proposed doubly stochastic models where the daily arrival rate is itself random, drawn from a distribution that captures day-to-day uncertainty. They tested several distributional models against real call center data and found that a Gaussian copula model with gamma-distributed marginals for each period provided the best fit.

Why it matters: Overdispersion matters operationally because it means that demand uncertainty is larger than standard models suggest. Staffing plans based on Poisson arrival assumptions will underestimate the probability of extreme busy or slow periods, leading to service level violations during busy realizations and overstaffing during slow realizations. The doubly stochastic framework provides a principled method for incorporating this additional uncertainty into staffing calculations.

Influence on practice: The paper influenced the development of simulation-based staffing approaches in WFM platforms, which can incorporate arbitrary arrival process models. It also contributed to the growing recognition that point forecasts are insufficient — probabilistic forecasts that quantify demand uncertainty are necessary for robust staffing decisions. Jongbloed and Koole (2001) independently documented similar overdispersion findings using a different analytical approach.[17]

Bassamboo, Harrison, and Zeevi (2006): Data-Driven Staffing

Citation: Bassamboo, A., Harrison, J. M., & Zeevi, A. (2006). "Design and control of a large call center: Asymptotic analysis of an LP-based method." Operations Research, 54(3), 419–435.[18]

Contribution: This paper developed an LP-based framework for jointly optimizing staffing and routing in large-scale call centers with multiple customer classes and agent types. Using asymptotic analysis (many-server heavy-traffic limits), the authors showed that a deterministic LP provides near-optimal staffing recommendations when the system is large, with corrections of order √n (square root of the system size) needed for exact optimization. The framework elegantly connected the Halfin-Whitt regime to practical multi-skill staffing decisions.

Why it matters: Multi-skill staffing — determining how many agents of each skill type to schedule — is the core planning problem in modern contact centers but is computationally much harder than single-queue staffing. This paper showed that the problem becomes tractable in the many-server limit and that LP-based solutions provide near-optimal performance, giving practical algorithms that scale to realistic system sizes.

Influence on practice: The LP-based staffing framework influenced the development of skills-based staffing modules in commercial WFM platforms. The asymptotic optimality result provided theoretical justification for the common industry practice of solving an LP relaxation of the staffing problem and then rounding to integer solutions.

Summary and Legacy

These landmark papers collectively established contact center operations research as a mature scientific discipline. Their contributions can be organized into three intellectual streams:

Mathematical foundations: Erlang (1917), Halfin and Whitt (1981), Garnett et al. (2002), and Green et al. (2007) built the queueing-theoretic foundation for capacity planning.

Optimization methods: Dantzig (1954), Ernst et al. (2004), and Bassamboo et al. (2006) established the mathematical programming frameworks for scheduling and staffing.

Empirical methodology: Brown et al. (2005), Avramidis et al. (2004), and the two major surveys (Gans et al. 2003, Aksin et al. 2007) grounded the field in data and established its interdisciplinary scope.

The field's next landmark papers will likely address the integration of AI agents into service delivery, the application of machine learning to forecasting and routing, and the development of governance frameworks for algorithmic workforce management — problems surveyed in Open Problems in Workforce Management Research.

See also

  1. ↑ Dantzig, G. B. (1954). "A comment on Edie's 'Traffic delays at toll booths'." Journal of the Operations Research Society of America, 2(3), 339–341.
  2. ↑ Henderson, S. G., & Mason, A. J. (1998). "Rostering by iterating integer programming and simulation." Proceedings of the 1998 Winter Simulation Conference, 1, 677–683.
  3. ↑ Erlang, A. K. (1917). "Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges." Elektroteknikeren, 13, 5–13. English translation in Brockmeyer, E., Halstrøm, H. L., & Jensen, A. (1948). The Life and Works of A. K. Erlang. Copenhagen Telephone Company.
  4. ↑ Halfin, S., & Whitt, W. (1981). "Heavy-traffic limits for queues with many exponential servers." Operations Research, 29(3), 567–588.
  5. ↑ Borst, S., Mandelbaum, A., & Reiman, M. I. (2004). "Dimensioning large call centers." Operations Research, 52(1), 17–34.
  6. ↑ Garnett, O., Mandelbaum, A., & Reiman, M. I. (2002). "Designing a call center with impatient customers." Manufacturing & Service Operations Management, 4(3), 208–227.
  7. ↑ Mandelbaum, A., & Zeltyn, S. (2004). "The impact of customers' patience on delay and abandonment: Some results for the G/G/n + G queue." Working Paper, Technion Israel Institute of Technology. (Later published as Zeltyn, S., & Mandelbaum, A. (2005). "Call centers with impatient customers: Many-server asymptotics of the M/M/n + G queue." Queueing Systems, 51(3-4), 361–402.)
  8. ↑ Gans, N., Koole, G., & Mandelbaum, A. (2003). "Telephone call centers: Tutorial, review, and research prospects." Manufacturing & Service Operations Management, 5(2), 79–141.
  9. ↑ Ernst, A. T., Jiang, H., Krishnamoorthy, M., & Sier, D. (2004). "Staff scheduling and rostering: A review of applications, methods and models." European Journal of Operational Research, 153(1), 3–27.
  10. ↑ Van den Bergh, J., Beliën, J., De Bruecker, P., Demeulemeester, E., & De Boeck, L. (2013). "Personnel scheduling: A literature review." European Journal of Operational Research, 226(3), 367–385.
  11. ↑ Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Shen, H., Zeltyn, S., & Zhao, L. (2005). "Statistical analysis of a telephone call center: A queueing-science perspective." Journal of the American Statistical Association, 100(469), 36–50.
  12. ↑ Aksin, Z., Armony, M., & Mehrotra, V. (2007). "The modern call center: A multi-disciplinary perspective on operations management research." Production and Operations Management, 16(6), 665–688.
  13. ↑ Green, L. V., Kolesar, P. J., & Whitt, W. (2007). "Coping with time-varying demand when setting staffing requirements for a service system." Production and Operations Management, 16(1), 13–39.
  14. ↑ Green, L. V., Kolesar, P. J., & Soares, J. (2001). "Improving the SIPP approach for staffing service systems that have cyclic demands." Operations Research, 49(4), 549–564.
  15. ↑ Koole, G., & Mandelbaum, A. (2002). "Queueing models of call centers: An introduction." Annals of Operations Research, 113(1-4), 41–59.
  16. ↑ Avramidis, A. N., Deslauriers, A., & L'Ecuyer, P. (2004). "Modeling daily arrivals to a telephone call center." Management Science, 50(7), 896–908.
  17. ↑ Jongbloed, G., & Koole, G. (2001). "Managing uncertainty in call centres using Poisson mixtures." Applied Stochastic Models in Business and Industry, 17(4), 307–318.
  18. ↑ Bassamboo, A., Harrison, J. M., & Zeevi, A. (2006). "Design and control of a large call center: Asymptotic analysis of an LP-based method." Operations Research, 54(3), 419–435.
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