WP_ContactCenterPlanningMethodologies_whitepaper_laser

Contact Center Planning Calculations and Methodologies
A Comparison of Erlang-C and Simulation Modeling
Ric Kosiba, Ph.D.
Vice President
Interactive Intelligence, Inc.
Bayu Wicaksono
Manager, Operations Research
Interactive Intelligence, Inc.

© 2014 Interactive Intelligence, Inc. 2 Contact Center Planning
Calculations and Methodologies
Contents
Introduction ......................................................................................................................................... 3
Methodology ........................................................................................................................................ 4
Service Prediction Comparison ............................................................................................................ 5
Staffing Requirement Comparison ....................................................................................................... 9
Summary and Operational Implications ............................................................................................ 12
Appendix A: Auto Insurance Call Type Charts .................................................................................... 13
Service Performance Comparisons .............................................................................................. 13
Staffing Requirements FTE Comparisons .................................................................................... 14
Appendix B: Retail Call Type Charts ................................................................................................... 15
Appendix C: Preferred Service Call Type Charts ................................................................................. 17
Appendix D: Credit Card Call Type Charts .......................................................................................... 19
Appendix E: Member Services Call Type Charts ................................................................................. 21
Appendix F: Loans Call Type Charts ................................................................................................... 23
Staffing Requirement FTE Comparisons ...................................................................................... 24
Authors ............................................................................................................................................... 25
Copyright © 2014 Interactive Intelligence, Inc. All rights reserved.
Brand, product, and service names referred to in this document are the trademarks or registered trademarks of their respective companies.
Interactive Intelligence, Inc. 7601 Interactive Way Indianapolis, Indiana 46278 Telephone (800) 267-1364 www.ININ.com
Publish date 10/14

Introduction
Contact centers are a major US industry, employing approximately 2.1 million phone agents. They are sophisticated operations, using state-of-the-art contact routing, contact monitoring, and agent staffing systems. These operations are expensive, and contact center agent costs often represent one of the top costs for many companies. Correct staffing for contact centers is important and well-studied. Surprisingly, there is little documentation available on the accuracy of the standard staffing algorithms. This paper focuses on the relative accuracy of two workforce staffing calculations and methodologies most often used in the contact center industry.
The traditional contact center planning algorithm has been the Erlang-C calculation. Developed by Agner Erlang in 1917, telephone companies used it to determine the number of operators needed in early switchboard operations. It is compact, easy to use, and easy to code in software or embed into spreadsheets. In fact, its ease of use is responsible for its incredible adoption rate. For many years, it was the only option available for developing agent schedules or contact center budgets, because alternative methods were too demanding for the computers of the day. Improvements to the original formula have been made over the years to overcome Erlang-C’s most significant weakness: It does not account for caller abandonment and assumes that callers wait indefinitely in the ACD queue. These improvements did not completely address the caller abandonment issue due to simplifying assumptions on the distribution of caller patience. Despite the limitations, it is still widely used today in workforce management or planning systems and in contact center planning spreadsheets.
The Erlang-C formula solves two specific and interrelated problems:
1. How many agents does the operation require in order to handle calls within a specific timeframe?
2. What service will the operation deliver given a specific staffing headcount?
Correct answers to these questions are critical in planning for and running an efficient and effective contact center operation.
Is the Erlang-C equation accurate enough to answer these questions? This paper demonstrates the range of the Erlang-C equation’s accuracy using a survey of real-world call center data and compares it to newer simulation models that have begun to make headway in determining staffing for contact centers.

Methodology
Multiple contact centers supplied historical ACD performance data to help determine a model’s service prediction accuracy. This data provides known values for the number of calls, agent work hours, call handle times, and service levels for specific 60-minute intervals. The differences between a model’s predictions and actual results are plotted and summarized at the daily and weekly level. The results for an Erlang-C equation and a discrete-event simulation model are compared.
A reverse analysis is also performed. Actual service levels are used as a model’s service level goal, and the number of staff required to achieve this service is then determined. The differences between the actual staffing (the number of ACD work hours) and a model’s prediction of the number of staff required is plotted and summarized at the daily and weekly level. These differences are extrapolated to determine wages wasted due to model error.
Empirical data gathered from call centers includes retail, banking, and financial service companies. The sample of call types within these operations varies in size from an average of three FTE (fulltime equivalent agents) per hour to an average of 228 FTE per hour. The samples vary from 3 weeks to 6 months due to data availability. The call types evaluated are presented in Table 1. Industry Call Type Size (Avg. Staff in FTE Hrs.) Insurance Auto Insurance 228
Retail
Retail
95 Banking Preferred Service 44
Banking
Credit Card Service
15 Banking Member Services 6
Finance
Loans
3
Table 1: Sample Call Types Evaluated
Simulation models for each of the call types were created, taking into account customer patience profiles, historical average service level threshold, delays, and staffing inefficiencies (e.g. idle times, scheduling inefficiencies etc.). These parameters are optimized in order to get the best steady-state simulation models given the available data.

Service Prediction Comparison
After the simulation models were created, a back-casting exercise was performed to quantify model error by comparing predicted to actual performance across the historical date ranges. Table 2 summarizes the average daily error rates for each call type. Call Type Avg. Error Sim Avg. Error Erlang-C Avg. Abn. Rate (%) Avg. SL (%) Loans 0.01% 21.34% 9.11% 76.45%
Member Services
0.04%
21.60%
7.48%
84.70% Preferred Services 0.15% 23.51% 2.76% 73.55%
Retail
0.17%
2.18%
1.43%
93.79% Credit Card -0.11% 9.46% 7.01% 56.03%
Auto Insurance
-0.01%
-3.93%
1.16%
87.20%
Average
0.04%
12.36%
4.83%
78.62%
Table 2: Daily Level Summary of Avg. Service Level, Actual Avg. Service Level, and Actual Abandonment Rate.
The results indicate that predicted Erlang-C service level inaccuracies increase with large abandonment rates. This makes sense because Erlang-C assumes that no customers will get impatient and abandon regardless of wait time (i.e. customers have infinite patience). In contrast, the simulation prediction accuracy does not vary significantly with abandonment. This is expected because the simulation models take customer patience profiles into account.
Furthermore, Erlang-C results tend to underestimate performance, as actual results are better than predictions. Again, this is most significant with higher abandonment rates. This could occur when the contact center is severely understaffed relative to its goal. In contrast, average error rates for the simulation models are less than one percent and tend to converge to zero. Properly modeled, simulations tend to balance over and under prediction across the evaluated time horizon.
The Erlang-C prediction is most accurate when the number of agents is large, and utilization is low due to low to no abandonment – also indicated by very high service levels (see Retail and Auto Insurance data in Table 2).

Figure 1 shows actual performance vs. predicted performance of simulation and Erlang-C for daily service levels of the Preferred Services call type.
Figure 1: Daily service level summary of Preferred Service Call Type
Even though the average error summary presented in Table 2 is a good indicator of the average accuracy and overall average bias of both prediction methods. It is also important to show the magnitude of the prediction error.
Table 3 summarizes the absolute error for each call type across the evaluated date range summarized at the daily level. Absolute error is defined as the absolute value of the service level predictions minus actual service levels. Custom simulation modeling significantly outperforms the Erlang-C calculation as measured by the absolute error of both prediction methods. Call Type Simulation Service Level Prediction Erlang-C Service Level Prediction Avg. Abs. Error Std. Dev. Abs. Error Avg. Abs. Error Std. Dev. Abs. Error
Loans
2.75%
1.53%
21.34%
10.25% Member Services 3.04% 2.68% 22.12% 10.38%
Preferred Services
4.11%
3.01%
23.51%
7.62% Retail 5.21% 6.50% 4.76% 7.42%
Credit Card
1.42%
1.44%
9.47%
5.58% Auto Insurance 5.89% 6.02% 6.08% 4.78%
Average
3.74%
3.53%
14.55%
7.67%
Table 3: Summary of the absolute error for each call type across the evaluated date range summarized at the daily level
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SERVICE LEVEL (%)
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Preferred Service: Service Level Comparison Simulation vs. Erlang-C vs. Actual (Daily Summary)
SL Actual
SL Sim
SL Erlang

In a series of predictions, absolute error measures the difference from the correct value, while standard deviation measures the range in which the prediction will most likely occur, or how spread-out the predictions are. Average absolute error is a measure of overall accuracy. The closer to zero, the more accurate the prediction, while standard deviation is a measure of precision (Figure 2).
Figure 2: Accuracy vs. precision (taken from http://climatica.org.uk/climate-science-information/uncertainty)
Looking at the Loans call type in Table 3, any given prediction of the simulated service level would most likely be 2.75% off the actual value. Additionally, the prediction is a bit spread out. Not only would it be 2.75% away from the actual value, but chances are the prediction could be as inaccurate as ±4.28% (2.75% + 1.53%) away from the actual value, or as accurate as within ±1.22% (2.75% - 1.53%) from the actual value.
For long-term planning purposes, it is a best and common industry practice to summarize the accuracy and precision to the weekly level, as hiring and staffing decisions are made at this level of detail. Call Type Simulation Service Level Prediction Erlang-C Service Level Prediction Avg. Err Avg. Abs. Err Std. Dev. Abs. Err Avg. Err Avg. Abs. Err Std. Dev. Abs. Err
Loans
0.59%
0.78%
0.65%
22.42%
22.42%
4.61% Member Services 0.24% 1.19% 1.20% 25.97% 25.97% 5.56%
Preferred Services
-1.27%
2.21%
1.75%
24.11%
24.11%
4.67% Retail 0.86% 2.66% 1.39% 3.36% 4.03% 4.85%
Credit Card
0.31%
1.01%
1.08%
9.99%
9.99%
3.41% Auto Insurance 1.20% 2.45% 2.27% -3.46% 3.46% 1.59%
Average
0.32%
1.72%
1.39%
13.73%
15.00%
4.12%
Table 4: Weekly Level Summary of Avg. and Std. Dev. of Error and Absolute Error of Service Level by Call Type
At the weekly level, the advantage of simulation over Erlang-C is more apparent with even less variability (Table 4). This is not observed in the Erlang-C results. Properly developed simulation models minimize variability over less granular time intervals due to their steady-state assumptions. This is why the simulated predictions produce better results compared to Erlang-C.

Figure 3 illustrates the differences between weekly service levels of actual performance compared to simulation and Erlang-C predictions. For more visual comparisons of each of the call types between historical actuals vs. simulation and Erlang-C, please refer to the appendices at the end of this document.
Figure 3: Weekly Service Level Summary Comparison for Preferred Service Call Type
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Preferred Service: Service Level Comparison Simulation vs. Erlang-C vs. Actuals (Weekly Summary)
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Staffing Requirement Comparison
The modeling technique used to predict service performance, whether simulation or Erlang, is most often used to determine the number of available contact center agents required to meet a specific servicing standard. To compare staffing prediction accuracy between Erlang-C and simulation models, a similar validation exercise is developed.
Using the same models as the previous analyses, a reverse calculation is performed to determine the accuracy of staffing requirement predictions given a service level goal. In both cases, it is assumed that the historical service level is the same as the servicing goal the planner would set.
The average prediction error percentage listed in Table 5 is the relative error from the actual staffing value, calculated as (퐴푐푡푢푎푙−푃푟푒푑푖푐푡푖표푛) 퐴푐푡푢푎푙 ∗100%. The actual average daily staff value (in hours) is also listed for a frame of reference. Call Type Avg. Sim Req. Error % Avg. Erlang Req. Error % Avg. Daily Staff (Hrs) Loans 2.26% -42.36% 35.24
Member Services
-1.86%
-20.54%
60.95 Preferred Services -1.79% -16.84% 1,054.73
Retail
2.01%
8.81%
1,335.10 Credit Card 0.93% -11.44% 309.29
Auto Insurance
3.14%
9.81%
5,043.52
Average
0.78%
-12.09%
1,306.47
Table 5: Daily Summary of Average Relative Error of the Staff Requirement Prediction (in Hours) by Call Type
Similar to our previous service level predictions, the relative error for the simulated staffing requirement is relatively low, averaging within 1% to 3% of historic staffing. In contrast, the Erlang-C-developed requirement is often too high, especially where abandon rates are high (Loans, Member Services, and Credit Card in Table 5). This corresponds directly to Erlang-C’s under-prediction of service level.
The average absolute error and standard deviation is calculated and summarized in Table 6.
Table 6: Daily Summary of Average and Std. Dev. of Absolute Error of the Staff Requirement Prediction by Call Type Call Type Simulation Requirement Erlang-C Requirement Avg. Daily Staff (Hrs) Avg. Abs. Rel. Err (%) Std. Dev. Abs. Rel. Error (%) Avg. Abs. Rel. Error (%) Std. Dev. Abs. Rel. Error (%)
Loans
4.01%
3.60%
42.36%
14.22%
35.24 Member Services 4.90% 5.75% 20.54% 28.25% 60.95
Preferred Services
3.06%
4.47%
16.84%
12.07%
1,054.73 Retail 5.35% 4.93% 9.26% 5.14% 1,335.10
Credit Card
2.81%
2.76%
11.44%
8.22%
309.29 Auto Insurance 4.59% 5.78% 10.34% 6.57% 5,043.52
Average
4.12%
4.55%
18.46%
12.41%
1,119.83

Again, simulation modeling holds an advantage with accuracy and precision within ±5% per day. Prediction variability is also lower compared to Erlang-C. Almost all of Erlang-C’s predictions are consistently overstaffing by more than 10% from the actual historical staffing (the exception being Retail). Predictions are also less precise with a spread of more than 5%. Figure 4 charts the comparison for the Credit Card call type.
Figure 4: Daily Staffing Requirement Comparison for Credit Card Call Type
As with service performance in the previous analysis, a weekly summary (Table 7) is also created. As most long-term staffing decisions are developed with a week-over-week view, this is the appropriate level of detail to evaluate algorithms for strategic capacity planning. Call Type Simulation Requirement Erlang-C Requirement Avg. Weekly Staff (Hrs.) Avg. Rel. Error (%) Avg. Abs. Rel. Err (%) Stdev. Abs. Rel. Error (%) Avg. Rel. Error (%) Avg. Abs. Rel. Error (%) Stdev. Abs. Rel. Error (%)
Loans
1.04%
2.29%
1.53%
-42.72%
42.72%
7.30%
158.59 Member Services -1.61% 2.15% 3.20% -14.32% 14.32% 5.55% 319.98
Preferred Services
-0.83%
1.34%
1.21%
-12.73%
12.73%
2.93%
6,873.92 Retail 3.36% 4.03% 4.85% 9.98% 9.98% 5.26% 8,307.51
Credit Card
0.04%
2.20%
2.92%
-11.75%
11.75%
5.79%
1,615.20 Auto Insurance 2.66% 2.89% 2.87% 10.43% 10.43% 3.73% 32,362.59
Average
0.78%
2.48%
2.76%
-10.19%
16.99%
5.09%
7,091.11
Table 7: Weekly Summary Error Statistics of the Weekly Staff Requirement Prediction by Call Type
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Credit Card: Staffing Requirement Comparison Simulation vs. Erlang-C vs. Actuals (Daily Summary)
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Simulation Requirement
Erlang-C Requirement

In Table 7, it can be seen that with a weekly outlook both the relative and absolute error of the simulation prediction is significantly reduced. This is due to the steady-state behavior of the simulation modeling, as has been discussed in the previous section. Erlang-C results do not improve when evaluating weekly results as they retain roughly the same level of error in both daily vs. weekly models. A comparison of weekly staffing requirements for the Credit Card call type is shown in Figure 5.
Figure 5: Weekly Staffing Requirements for Credit Card Call Type
Overall, it can be concluded that staffing requirements generated by simulation are more accurate and precise than those generated by Erlang-C. A further analysis of the errors in the prediction of staffing requirements indicate additional advantages of simulation modeling over Erlang-C, as shown in Table 8. Predictive Methodology Staffing Error > 5% per 푪풖풔풕풐풎풆풓푫풂풚⁄ Staffing Error > 5% per 푪풖풔풕풐풎풆풓푾풌⁄ Simulation 4.65% 1.49%
Erlang-C
18.22%
17.31%
Table 8: Summary of Missed Staffing Requirement Prediction by more than 5% per day and week
In Table 8, the staffing requirement generated by simulation modeling has an error of more than 5% a mere 4.65% of the time at the daily level, and only around 1.5% of the time at the weekly level. Erlang-C generated requirements are off by more than 5% more than 17% of the time both at the daily and weekly levels, indicating accuracy and precision problems.
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Credit Card: Staffing Requirement Comparison Simulation vs. Erlang-C vs. Actuals (Weekly Summary)
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Summary and Operational Implications
Based on this comparative analysis, the following summary observations are arrived at:
 The Erlang-C model, on average, is pessimistically biased when measuring service performance (actual results are better than predicted), but may become optimistically biased when utilization is high and arrival rates are uncertain. Erlang-C error does not improve when models are evaluated weekly, rather than daily.
 Simulation modeling, by contrast, shows a slight optimistic bias when measuring service performance, but not at the expense of its accuracy. It is also precise as evidenced by the low variability around the mean. Simulation prediction of service performance becomes more accurate and precise as the level of granularity changes from daily to weekly.
 The Erlang-C model is most accurate when the number of agents is large and utilization is low due to the "no abandonment" assumption. In any other situation, it tends to overstaff significantly. Empirical evidence suggests by more than 10% on average, relative to the historical staffing. Simulation is accurate with any contact center size.
 Erlang-C measurement error is high when the contact center exhibits higher levels of abandonment. Simulation does not show this shortcoming as abandonment behavior can be derived from the customer patience profile.
That the Erlang-C method overstaffs contact centers is not surprising. Erlang-C equations have long been suspected of requiring too many agents or under-predicting service. The magnitude of the error is surprising, however. Extrapolating this small example, contact centers relying on Erlang-C methods may be managing their operations with as much as 16% too many agents. Waste is easy to hide, and the overstaffed contact center often loses more than the obvious extra agent costs, they lose their edge.
A subtler result from this study is that the Erlang-C method produces error rates that are not consistent. Sometimes overstaffing by a lot and sometimes by just a bit. If service consistency is important for your operation, this poses a problem.
Simulation models need to be customized in order to be accurate. Every call center is different. Different distributions of call arrivals, handle times, customer patience, efficiency, and staffing must all be represented in an accurate simulation model. For every call type, a new and different simulation model may be necessary to produce accurate results. Charts like those developed for this paper, demonstrating the accuracy of the models, are required to verify any simulation system. Without these validation charts, the models should be assumed inaccurate.
The most obvious implication of this empirical study is that Erlang-C errors result in significant and wasteful costs for most organizations using it. Erlang-C is not usable for accurate what-if analyses, and it will ensure service delivery that is inconsistent. Discrete- event simulation models exist that address these substantial, and often hidden, costs.

Appendix A: Auto Insurance Call Type Charts
Service Performance Comparisons
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Staffing Requirements FTE Comparisons
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Appendix B: Retail Call Type Charts
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Appendix C: Preferred Service Call Type Charts
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Appendix D: Credit Card Call Type Charts
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Credit Card: Service Level Comparison Simulation vs. Erlang-C vs. Actuals (Daily Summary)
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SL Sim
SL Erlang
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
1
2
3
4
5
6
7
8
9
SERVICE LEVEL (%)
WEEK #
Credit Card: Service Level Comparison Simulation vs. Erlang-C vs. Actuals (Weekly Summary)
SL Actual
SL Sim
SL Erlang

0
50
100
150
200
250
300
350
400
450
500
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
DAY #
Credit Card: Staffing Requirement Comparison Simulation vs. Erlang-C vs. Actual Staff (Daily Summary)
Actual Staff
0
500
1000
1500
2000
2500
1
2
3
4
5
6
7
8
9
WEEK #
Credit Card: Staffing Requirement Comparison Simulation vs. Erlang-C vs. Actual Staff (Weekly Summary)
Actual Staff

Appendix E: Member Services Call Type Charts
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
SERVICE LEVEL (%)
DAY #
Member Services: Service Level Comparison Simulation vs. Erlang-C vs. Actuals (Daily Summary)
SL Actual
SL Sim
SL Erlang
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
1
2
3
4
SERVICE LEVEL (%)
WEEK #
Member Services: Service Level Comparison Simulation vs. Erlang-C vs. Actuals (Weekly Summary)
SL Actual
SL Sim
SL Erlang

0
10
20
30
40
50
60
70
80
90
100
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
DAY #
Member Services: Staffing Requirement Comparison Simulation vs. Erlang-C vs. Actual Staff (Daily Summary)
Actual Staff
0
100
200
300
400
500
600
1
2
3
4
WEEK #
Member Services: Staffing Requirement Comparison Simulation vs. Erlang-C vs. Actual Staff (Weekly Summary)
Actual Staff

Appendix F: Loans Call Type Charts
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
SERVICE LEVEL (%)
DAY #
Loans: Service Level Comparison Simulation vs. Erlang-C vs. Actuals (Daily Summary)
SL Actual
SL Sim
SL Erlang
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
1
2
3
4
SERVICE LEVEL (%)
WEEK #
Loans: Service Level Comparison Simulation vs. Erlang-C vs. Actuals (Weekly Summary)
SL Actual
SL Sim
SL Erlang

Staffing Requirement FTE Comparisons
0
10
20
30
40
50
60
70
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
DAY #
Loans: Staffing Requirement Comparison Simulation vs. Erlang-C vs. Actual Staff (Daily Summary)
Actual Staff
0
50
100
150
200
250
300
350
1
2
3
4
WEEK #
Loans: Staffing Requirement Comparison Simulation vs. Erlang-C vs. Actual Staff (Weekly Summary)
Actual Staff

Authors
Ric Kosiba is an expert in the field of call center management and modeling, call center strategy development, and the optimization of large-scale operational processes. He received a Ph. D in Operations Research and Engineering from Purdue University and an M.S.C.E. and B.S.C.E. from Purdue’s School of Civil Engineering. He also has obtained a patent on the application of optimal collection strategies to delinquent portfolios in addition to a patent on the application of simulation and analytics to contact center planning.
At the start of his career, Ric served as Manager of Customer Service Analytics for USAir’s Operations Research Division, and as Operations Management Senior Analyst with Northwest Airlines. Later, he moved into Customer Support at First USA, where he served as Vice President of Operations Research and guided all facets of the company’s call center process improvement, including collections strategy modeling and detailed staff plan development and call center budgeting. Ric then held a position as the Director of Management Science at Partners First, where his responsibilities included the detailed modeling of portfolio risks, in addition to predictive and prescriptive marketing and operations engineering.
Ric ultimately founded Bay Bridge Decisions, which later joined Interactive Intelligence, and now serves as Interactive’s Vice President in the strategic planning market. He continues to write for numerous contact center publications and speaks at highly acclaimed technical and contact center forums on a frequent basis.
Contact him at: ric.kosiba@inin.com or 410.224.9883.
Bayu Wicaksono is the Manager of Operations Research Department at Interactive Intelligence. He has been responsible for developing the algorithms and analytic for Interaction Decisions (formerly CenterBridge) for 10+ years, and has in-depth knowledge of contact center analytic and strategic planning/modeling/forecasting. He graduated both Bachelor's and Master's in Industrial Engineering with focus on Operations Research from Purdue University.
Bayu holds several patents relating to predictive and prescriptive simulation modeling and analytic to contact center planning. His passion is continuous learning and process improvement, programming, cloud-based solutions architecture, analytic algorithms, as well as library deployment and integration. He also loves to talk about math, programming and process improvements, and can be reached at bayu.wicaksono@inin.com or 410.224.7620.

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