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Empirically-Based Staffing in Call Centers Simple Models at the Service of Complex Realities Sergey Zeltyn Technion, Haifa, Israel IBM Thomas J. Watson Research Center, October 3, 2006 Joint work with Professor Avi Mandelbaum 1
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Page 1: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Empirically-Based Staffing in Call CentersSimple Models at the Service of Complex Realities

Sergey Zeltyn

Technion, Haifa, Israel

IBM Thomas J. Watson Research Center, October 3, 2006

Joint work with Professor Avi Mandelbaum

1

Page 2: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Outline

Subject/Flow of the Talk:Hierarchy of operational decisions in call centers, with emphasis onstaffing.

Main message I:Simple Models can be excellent tools at the service ofComplex Realities.

Supported by:Erlang-A Model and the QED operational regime applied to callcenter staffing.

Main message II:Empirically-Based Analysis is a Prerequisite for Research, Teachingand Practice of service operations.

Supported by:DataMOCCA – Data MOdel for Call Center Analysis.

2

Page 3: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Outline

Subject/Flow of the Talk:Hierarchy of operational decisions in call centers, with emphasis onstaffing.

Main message I:Simple Models can be excellent tools at the service ofComplex Realities.

Supported by:Erlang-A Model and the QED operational regime applied to callcenter staffing.

Main message II:Empirically-Based Analysis is a Prerequisite for Research, Teachingand Practice of service operations.

Supported by:DataMOCCA – Data MOdel for Call Center Analysis.

2

Page 4: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Outline

Subject/Flow of the Talk:Hierarchy of operational decisions in call centers, with emphasis onstaffing.

Main message I:Simple Models can be excellent tools at the service ofComplex Realities.

Supported by:Erlang-A Model and the QED operational regime applied to callcenter staffing.

Main message II:Empirically-Based Analysis is a Prerequisite for Research, Teachingand Practice of service operations.

Supported by:DataMOCCA – Data MOdel for Call Center Analysis.

2

Page 5: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Call Centers Industry

U.S. Statistics• Over 60% of annual business volume via the telephone• 70,000 – 200,000 call centers• 3 – 6.5 million employees (3% – 6% workforce)• 20% annual growth rate• $100 – $300 billion annual expenditures• 1000’s agents in a “single" call center.

Quality/Efficiency Tradeoff

• 65 – 80% personnel costs• Over 90% U.S. consumers form company image via call center

experience.

Objective:Having the right number of appropriately skilled agents when needed.

3

Page 6: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Call Centers Industry

U.S. Statistics• Over 60% of annual business volume via the telephone• 70,000 – 200,000 call centers• 3 – 6.5 million employees (3% – 6% workforce)• 20% annual growth rate• $100 – $300 billion annual expenditures• 1000’s agents in a “single" call center.

Quality/Efficiency Tradeoff

• 65 – 80% personnel costs• Over 90% U.S. consumers form company image via call center

experience.

Objective:Having the right number of appropriately skilled agents when needed.

3

Page 7: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Call Centers Industry

U.S. Statistics• Over 60% of annual business volume via the telephone• 70,000 – 200,000 call centers• 3 – 6.5 million employees (3% – 6% workforce)• 20% annual growth rate• $100 – $300 billion annual expenditures• 1000’s agents in a “single" call center.

Quality/Efficiency Tradeoff

• 65 – 80% personnel costs• Over 90% U.S. consumers form company image via call center

experience.

Objective:Having the right number of appropriately skilled agents when needed.

3

Page 8: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Staffing Problem

Determination of load-dependent number of agents.

Prevailing method:SIPP (Stationary Independent Period-by-Period),a constant number of agents over each period (15, 30 or 60 min).

Agents and customers are assumed homogeneous.In particular, every agent can potentially serve every customer.

Main Approaches to Staffing

Constraint Satisfaction: find minimal number of agents n∗ thatsatisfies some performance goal(s) (e.g. less than 3% abandonment).Prevalent in practice, Service-Level Agreements (SLA) in outsourcing.

Cost/Revenue Optimization: find n∗ that optimizes service revenuesand costs of staffing, abandonment and waiting.

4

Page 9: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Staffing Problem

Determination of load-dependent number of agents.

Prevailing method:SIPP (Stationary Independent Period-by-Period),a constant number of agents over each period (15, 30 or 60 min).

Agents and customers are assumed homogeneous.In particular, every agent can potentially serve every customer.

Main Approaches to Staffing

Constraint Satisfaction: find minimal number of agents n∗ thatsatisfies some performance goal(s) (e.g. less than 3% abandonment).Prevalent in practice, Service-Level Agreements (SLA) in outsourcing.

Cost/Revenue Optimization: find n∗ that optimizes service revenuesand costs of staffing, abandonment and waiting.

4

Page 10: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

M/M/n+M (Erlang-A, Palm): Main Staffing Model

Call Center:Schematic Representation

arrivals

lost calls

retrials

retrials

abandonment

returns

queueACD

agentsbusy

1

2

n

…1 2 3 k

lost calls

Erlang-A Queue

agents

arrivals

abandonment

λ

µ

1

2

n

queue

θ

Erlang-A Assumptions:• λ – Poisson arrival rate• µ – Exponential service rate• n – number of service agents• θ – Exponential individual abandonment rate

• No busysignals

• First ComeFirst Served.

5

Page 11: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Erlang-A Model: Calculations

Performance measures can be calculated relatively easily.

4CallCenters - A Personal Tool for Workforce Management.Based on the M.Sc. thesis of Ofer Garnett.http://iew3.technion.ac.il/serveng2006S/4CallCenters/Downloads.htm

6

Page 12: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Time Scale: Arrival to a Call Center in 1999

Strategic Tactical

Arrival Process, in 1999

Yearly Monthly

Daily Hourly

Arrival Process, in 1999

Yearly Monthly

Daily Hourly Operational Stochastic

Arrival Process, in 1999

Yearly Monthly

Daily Hourly

Arrival Process, in 1999

Yearly Monthly

Daily Hourly

7

Page 13: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Queueing Science:

Arrival to a Call Center in 1976

Arrival Process, in 1976 (E. S. Buffa, M. J. Cosgrove, and B. J. Luce,

“An Integrated Work Shift Scheduling System”)

Yearly Monthly

Daily Hourly

8

Page 14: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Service Times: Distribution and Psychology

Histogram of Service Times in an Israeli Call Center

January-October November-December

Beyond Data Averages Short Service Times

AVG: 200 STD: 249

AVG: 185 STD: 238

7.2 % ? Jan – Oct:

Log-Normal AVG: 200 STD: 249

Nov – Dec:

27

Beyond Data Averages Short Service Times

AVG: 200 STD: 249

AVG: 185 STD: 238

7.2 % ? Jan – Oct:

Log-Normal AVG: 200 STD: 249

Nov – Dec:

27

• Lognormal service times prevalent in call centers

• 7.2% Short-Services: Agents’ “Abandon" (improve bonus, rest)• Distributions, not only Averages, must be measured.

9

Page 15: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Service Times: Distribution and Psychology

Histogram of Service Times in an Israeli Call Center

January-October November-December

Beyond Data Averages Short Service Times

AVG: 200 STD: 249

AVG: 185 STD: 238

7.2 % ? Jan – Oct:

Log-Normal AVG: 200 STD: 249

Nov – Dec:

27

Beyond Data Averages Short Service Times

AVG: 200 STD: 249

AVG: 185 STD: 238

7.2 % ? Jan – Oct:

Log-Normal AVG: 200 STD: 249

Nov – Dec:

27

• Lognormal service times prevalent in call centers• 7.2% Short-Services: Agents’ “Abandon" (improve bonus, rest)• Distributions, not only Averages, must be measured.

9

Page 16: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Erlang-A: Modelling (Im)Patience

• Patience Time: τ ∼ exp(θ)Time a customer is willing to wait for service.

• Offered Wait: VTime a customer is required to wait for service.(= Waiting time of a customer with infinite patience.)

• If τ ≤ V then customer abandons, else served.• Actual Wait Wq = min(τ, V ).

Patience data is censored: 2% abandoning implies 98% censored!

10

Page 17: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Erlang-A: Modelling (Im)Patience

• Patience Time: τ ∼ exp(θ)Time a customer is willing to wait for service.

• Offered Wait: VTime a customer is required to wait for service.(= Waiting time of a customer with infinite patience.)

• If τ ≤ V then customer abandons, else served.• Actual Wait Wq = min(τ, V ).

Patience data is censored: 2% abandoning implies 98% censored!

10

Page 18: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Measuring Patience

Hazard Rates of Patience in an Israeli Bank:Regular over VIP Customers

14

16

• VIP customers are more patient (needy).• Why the peaks in abandonment? Announcements!• Call-by-call data required to obtain this graph (+Uncensoring).

11

Page 19: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Measuring Patience

Hazard Rates of Patience in an Israeli Bank:Regular over VIP Customers

14

16

• VIP customers are more patient (needy).• Why the peaks in abandonment? Announcements!• Call-by-call data required to obtain this graph (+Uncensoring).

11

Page 20: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Estimating Patience: P{Ab} ∝ E[Wq] Relation

In queues with exp(θ) patience: P{Ab} = θ · E[Wq] .

Israeli Bank: Yearly Data

Hourly Data Aggregated

0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Average waiting time, sec

Pro

bab

ility

to

ab

and

on

0 50 100 150 200 250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Average waiting time, sec

Pro

bab

ility

to

ab

and

on

Graphs are based on 4158 hour intervals.

Estimate of mean patience: 250/0.55 ≈ 450 seconds.

12

Page 21: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Building block: Interrelation

Average Service Time over the Day – Israeli Bank

Figure 12: Mean Service Time (Regular) vs. Time-of-day (95% CI) (n =

42613)

Time of Day

Mea

n S

ervi

ce T

ime

10 15 20

100

120

140

160

180

200

220

240

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

3011

Prevalent: Longest services at peak-loads (10:00, 15:00). Why?

Explanations:• Prevalent: Service protocol different (longer) at congestion• Operational: The needy abandon less during peak loads;

hence the VIP remain on line, with their longer service times.13

Page 22: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Erlang-A: Fitting a Simple Model to a Complex Reality

• Small Israeli bank (10 agents)• Patience estimated via P{Ab} / E[Wq]

• Graphs: hourly performance vs. Erlang-A predictions, over 1year, aggregating groups with 40 similar hours.

P{Ab} E[Wq] P{Wq > 0}

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

Probability to abandon (Erlang−A)

Pro

babi

lity

to a

band

on (

data

)

0 50 100 150 200 2500

50

100

150

200

250

Waiting time (Erlang−A), sec

Wai

ting

time

(dat

a), s

ec

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of wait (Erlang−A)

Pro

babi

lity

of w

ait (

data

)

14

Page 23: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Erlang-A:

Fitting a Simple Model to a Complex Reality II

Large U.S. Bank

Retail. P{Wq > 0} Telesales. E[Wq]

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of wait (QED: aggregated)

Pro

babi

lity

of w

ait (

data

: agg

rega

ted)

0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

60

70

80

90

Average wait (QED: aggregated), secA

vera

ge w

ait (

data

: agg

rega

ted)

, sec

Partial success, in some cases Erlang-A does not work well(Networking, SBR).

Large Israeli call center – underway.

15

Page 24: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Erlang-A:

Fitting a Simple Model to a Complex Reality III

We have learned:• Arrival process can by approximated by Poisson• Service times are not exponential (typically close to lognormal)• Patience times are not exponential (various patterns are

observed).

Question: why Erlang-A works with non-exponential patience andservice times?

Answer: via study of operational regimes in call centers.

16

Page 25: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Erlang-A:

Fitting a Simple Model to a Complex Reality III

We have learned:• Arrival process can by approximated by Poisson• Service times are not exponential (typically close to lognormal)• Patience times are not exponential (various patterns are

observed).

Question: why Erlang-A works with non-exponential patience andservice times?

Answer: via study of operational regimes in call centers.

16

Page 26: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Operational Regimes: Motivating Example

Health Insurance. ACD Report.

Time Calls Answered Abandoned% ASA AHT Occ% # of agents

Total 20,577 19,860 3.5% 30 307 95.1%

8:00 332 308 7.2% 27 302 87.1% 59.38:30 653 615 5.8% 58 293 96.1% 104.19:00 866 796 8.1% 63 308 97.1% 140.49:30 1,152 1,138 1.2% 28 303 90.8% 211.110:00 1,330 1,286 3.3% 22 307 98.4% 223.110:30 1,364 1,338 1.9% 33 296 99.0% 222.511:00 1,380 1,280 7.2% 34 306 98.2% 222.011:30 1,272 1,247 2.0% 44 298 94.6% 218.012:00 1,179 1,177 0.2% 1 306 91.6% 218.312:30 1,174 1,160 1.2% 10 302 95.5% 203.813:00 1,018 999 1.9% 9 314 95.4% 182.9

13:30 1,061 961 9.4% 67 306 100.0% 163.4

14:00 1,173 1,082 7.8% 78 313 99.5% 188.9

14:30 1,212 1,179 2.7% 23 304 96.6% 206.1

15:00 1,137 1,122 1.3% 15 320 96.9% 205.815:30 1,169 1,137 2.7% 17 311 97.1% 202.216:00 1,107 1,059 4.3% 46 315 99.2% 187.116:30 914 892 2.4% 22 307 95.2% 160.0

17:00 615 615 0.0% 2 328 83.0% 135.0

17:30 420 420 0.0% 0 328 73.8% 103.518:00 49 49 0.0% 14 180 84.2% 5.8

17

Page 27: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Efficiency-Driven (ED) Regime

Time Calls Answered Abandoned% ASA AHT Occ% # of agents

13:30 1,061 961 9.4% 67 306 100.0% 163.4

• 100% occupancy• High P{Ab}

• Considerable waiting time• P{Wq > 0} ≈ 1.

Offered load:

RED∆=

λ

µ= 1061 :

1800306

= 180.37 .

Characterization:

n = RED · (1− γ) , γ > 0.

Service grade

γ = 1− nRED

= 1− 163.4180.37

= 0.094 ≈ P{Ab} .

ED regime captured by Fluid-Model.

18

Page 28: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Efficiency-Driven (ED) Regime

Time Calls Answered Abandoned% ASA AHT Occ% # of agents

13:30 1,061 961 9.4% 67 306 100.0% 163.4

• 100% occupancy• High P{Ab}

• Considerable waiting time• P{Wq > 0} ≈ 1.

Offered load:

RED∆=

λ

µ= 1061 :

1800306

= 180.37 .

Characterization:

n = RED · (1− γ) , γ > 0.

Service grade

γ = 1− nRED

= 1− 163.4180.37

= 0.094 ≈ P{Ab} .

ED regime captured by Fluid-Model.

18

Page 29: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Efficiency-Driven (ED) Regime

Time Calls Answered Abandoned% ASA AHT Occ% # of agents

13:30 1,061 961 9.4% 67 306 100.0% 163.4

• 100% occupancy• High P{Ab}

• Considerable waiting time• P{Wq > 0} ≈ 1.

Offered load:

RED∆=

λ

µ= 1061 :

1800306

= 180.37 .

Characterization:

n = RED · (1− γ) , γ > 0.

Service grade

γ = 1− nRED

= 1− 163.4180.37

= 0.094 ≈ P{Ab} .

ED regime captured by Fluid-Model.

18

Page 30: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Efficiency-Driven (ED) Regime

Time Calls Answered Abandoned% ASA AHT Occ% # of agents

13:30 1,061 961 9.4% 67 306 100.0% 163.4

• 100% occupancy• High P{Ab}

• Considerable waiting time• P{Wq > 0} ≈ 1.

Offered load:

RED∆=

λ

µ= 1061 :

1800306

= 180.37 .

Characterization:

n = RED · (1− γ) , γ > 0.

Service grade

γ = 1− nRED

= 1− 163.4180.37

= 0.094 ≈ P{Ab} .

ED regime captured by Fluid-Model.18

Page 31: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Quality-Driven (QD) Regime

Time Calls Answered Abandoned% ASA AHT Occ% # of agents

17:00 615 615 0.0% 2 328 83.0% 135.0

• Occupancy far below 100%• Negligible P{Ab}

• Very short waiting time• P{Wq > 0} ≈ 0.

Offered load:

RQD =λ

µ= 615 :

1800328

= 112.07 .

Characterization:

n = RQD · (1 + γ) , γ > 0.

Service grade

γ =n

RQD− 1 =

135112.07

− 1 = 0.205 .

19

Page 32: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Quality and Efficiency-Driven (QED) Regime

Time Calls Answered Abandoned% ASA AHT Occ% # of agents

14:30 1,212 1,179 2.7% 23 304 96.6% 206.1

• High occupancy, but not 100%• P{Wq > 0} ≈ α, 0 < α < 1.

• Small P{Ab} and waiting

Offered load: RQED =λ

µ= 1212 :

1800304

= 204.69 .

Characterization: n = RQED + β√

RQED , −∞ < β < ∞ .

Service grade

β =n − RQED√

RQED=

206.1− 204.69√204.69

= 0.10 .

Square-Root Staffing Rule: Described by Erlang in 1924!

Awaited the seminal formulation of Halfin-Whitt in 1981.

20

Page 33: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Quality and Efficiency-Driven (QED) Regime

Time Calls Answered Abandoned% ASA AHT Occ% # of agents

14:30 1,212 1,179 2.7% 23 304 96.6% 206.1

• High occupancy, but not 100%• P{Wq > 0} ≈ α, 0 < α < 1.

• Small P{Ab} and waiting

Offered load: RQED =λ

µ= 1212 :

1800304

= 204.69 .

Characterization: n = RQED + β√

RQED , −∞ < β < ∞ .

Service grade

β =n − RQED√

RQED=

206.1− 204.69√204.69

= 0.10 .

Square-Root Staffing Rule: Described by Erlang in 1924!

Awaited the seminal formulation of Halfin-Whitt in 1981.

20

Page 34: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Quality and Efficiency-Driven (QED) Regime

Time Calls Answered Abandoned% ASA AHT Occ% # of agents

14:30 1,212 1,179 2.7% 23 304 96.6% 206.1

• High occupancy, but not 100%• P{Wq > 0} ≈ α, 0 < α < 1.

• Small P{Ab} and waiting

Offered load: RQED =λ

µ= 1212 :

1800304

= 204.69 .

Characterization: n = RQED + β√

RQED , −∞ < β < ∞ .

Service grade

β =n − RQED√

RQED=

206.1− 204.69√204.69

= 0.10 .

Square-Root Staffing Rule: Described by Erlang in 1924!

Awaited the seminal formulation of Halfin-Whitt in 1981.

20

Page 35: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Operational Regimes: Performance.

Assume that offered load R is not small (λ →∞).

ED regime: n ≈ R − δR , 0.1 ≤ δ ≤ 0.25 .

• Essentially all customers are delayed• %Abandoned ≈ δ (10-25%)• Average wait ≈ 30 seconds - 2 minutes.

QD regime: n ≈ R + γR , 0.1 ≤ γ ≤ 0.25 .Essentially no delays.

QED regime: n ≈ R + β√

R, −1 ≤ β ≤ 1 .

• %Delayed between 25% and 75%• %Abandoned is 1-5%• Average wait is one-order less than average service time

(seconds vs. minutes).

21

Page 36: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Erlang-A Queue: QED Approximations

Assume that offered load R is not small (λ →∞).

Let β = β

õ

θ, h(·) =

φ(·)1− Φ(·)

= hazard rate of N (0, 1).

• Delay probability:

P{Wq > 0} ∼

[1 +

√θ

µ· h(β)

h(−β)

]−1

,

• Probability to abandon:

P{Ab|Wq > 0} =1√n·

√θ

µ·[h(β)− β

]+ o

(1√n

).

• Linear relation between P{Ab} and E[Wq]:

P{Ab}E[Wq]

= θ.

22

Page 37: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Generally Distributed Patience:

M/M/n+G Model

agents

arrivals

abandonment

λ

µ

1

2

n

queue

G

Back to puzzle of “Why Erlang-A works?"Assume patience times are generally distributed.

Density of patience time: g = {g(x), x ≥ 0}, where g(0)∆= g0 > 0.

QED regime: n ≈ R + β√

R.

QED approximations: use Erlang-A, with g0 replacing θ.

23

Page 38: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Generally Distributed Patience:

M/M/n+G Model

agents

arrivals

abandonment

λ

µ

1

2

n

queue

G

Back to puzzle of “Why Erlang-A works?"Assume patience times are generally distributed.

Density of patience time: g = {g(x), x ≥ 0}, where g(0)∆= g0 > 0.

QED regime: n ≈ R + β√

R.

QED approximations: use Erlang-A, with g0 replacing θ.

23

Page 39: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Generally Distributed Patience:

Fitting Erlang-A

Israeli Bank: Yearly Data

Hourly Data Aggregated

0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Average waiting time, sec

Pro

bab

ility

to

ab

and

on

0 50 100 150 200 250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Average waiting time, sec

Pro

bab

ility

to

ab

and

on

TheoryErlang-A: P{Ab} = θ · E[Wq]. M/M/n+G: P{Ab} ≈ g0 · E[Wq].

Recipe:In both cases, use Erlang-A, with θ = P{Ab}/E[Wq] (slope above).

24

Page 40: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Generally Distributed Patience:

Fitting Erlang-A

Israeli Bank: Yearly Data

Hourly Data Aggregated

0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Average waiting time, sec

Pro

bab

ility

to

ab

and

on

0 50 100 150 200 250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Average waiting time, sec

Pro

bab

ility

to

ab

and

on

TheoryErlang-A: P{Ab} = θ · E[Wq]. M/M/n+G: P{Ab} ≈ g0 · E[Wq].

Recipe:In both cases, use Erlang-A, with θ = P{Ab}/E[Wq] (slope above).

24

Page 41: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Generally Distributed Service Times

Established: M/M/n+M ≈ M/M/n+G (θ = g0).

Next: M/M/n+G ≈ M/G/n+G (same mean service).

Numerical Experiments: Whitt (2004), Rosenshmidt (2006)demonstrate a good fit for typical call-center parameters.

Lognormal (CV=1) vs. Exponential Service Times, QED regime;100 agents, mean patience = mean service

Fraction Abandoning Delay Probability

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Service grade

Frac

tion

aban

doni

ng

Exponential Lognormal

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Service grade

Del

ay p

roba

bilit

y

Exponential Lognormal

25

Page 42: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Generally Distributed Service Times

Established: M/M/n+M ≈ M/M/n+G (θ = g0).

Next: M/M/n+G ≈ M/G/n+G (same mean service).

Numerical Experiments: Whitt (2004), Rosenshmidt (2006)demonstrate a good fit for typical call-center parameters.

Lognormal (CV=1) vs. Exponential Service Times, QED regime;100 agents, mean patience = mean service

Fraction Abandoning Delay Probability

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Service grade

Frac

tion

aban

doni

ng

Exponential Lognormal

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Service grade

Del

ay p

roba

bilit

y

Exponential Lognormal

25

Page 43: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Generally Distributed Service Times

Established: M/M/n+M ≈ M/M/n+G (θ = g0).

Next: M/M/n+G ≈ M/G/n+G (same mean service).

Numerical Experiments: Whitt (2004), Rosenshmidt (2006)demonstrate a good fit for typical call-center parameters.

Lognormal (CV=1) vs. Exponential Service Times, QED regime;100 agents, mean patience = mean service

Fraction Abandoning Delay Probability

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Service grade

Frac

tion

aban

doni

ng

Exponential Lognormal

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Service grade

Del

ay p

roba

bilit

y

Exponential Lognormal

25

Page 44: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Simple Model for Complex Realities:

More on Applications of the QED Regime

• Simple performance approximations that are robust also inthe ED and QD regimes: Mandelbaum, Zeltyn.

• Optimal staffing for cost/revenue optimization problems(staffing, abandonment and waiting costs): Borst, Mandelbaum,Reiman, Zeltyn.

• General service times: Puhalskii, Reiman; Jelencovic,Mandelbaum, Momcilovic.

• Generalizations to time-varying queues: Jennings, Feldman,Mandelbaum, Massey, Whitt.

• Generalizations to system with non-homogeneous customersand/or servers (Skills-Based Routing): Armony, Gurvich,Mandelbaum; Atar, Shaikhet.

• Load-balancing: Dai, Tezcan.

26

Page 45: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

The QED Regime and Stochastic-Ignorant Staffing:

The Right Answer for the Wrong Reasons

If β = 0, QED staffing prescribes:

n = R ,

R = offered load (minutes of work that arrive per minute).

In word: Assign number of agents that equals offered load,which is common practice.

No abandonment: queue “explodes".

With abandonment, n = 400, reasonable (im)patience:

• %Delayed ≈ 50%• %Abandoned ≈ 2%• E[Wq] ≈ 2% · E[S], few seconds.

Very good service level.

27

Page 46: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Call Centers: Hierarchical Operational ViewForecasting Customers (Statistics), Agents (HRM) Staffing: Queueing Theory (Erlang-A based) Service Level, Costs # FTE’s (Seats) per unit of time Shifts: IP, Combinatorial Optimization; LP Union constraints, Costs Shift structure Rostering: Heuristics, AI (Complex) Individual constraints

Agents Assignments

Skills-based Routing: Stochastic Control (of Q's)

1

28

Page 47: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

DataMOCCA = Data MOdel for Call Center Analysis

Project Goal: Designing and Implementing a (universal)data-base/data-repository and interface for storing, retrieving,analyzing and displaying Call-by-Call-Data.

System Components:• Clean Databases: operational-data of individual calls, agents

and operations.• Friendly yet powerful Online Interface: enables convenient fast

access to (mostly) operational and (some) administrative data(but no marketing/business data).

Current Databases:• Medium-sized U.S. Bank (2.5 years; 220M calls, 40M via

agents; 800 agents at peaks) – Completed.• Israeli Cell-Phone Company (2 years; 110M calls, 25M via

agents; 400 agents at peaks) – Ongoing.• Large Israeli Bank – Pilot.

DataMOCCA will now be used to illustrate the hierarchy ofoperational decisions, from forecasting to SBR.

29

Page 48: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

DataMOCCA = Data MOdel for Call Center Analysis

Project Goal: Designing and Implementing a (universal)data-base/data-repository and interface for storing, retrieving,analyzing and displaying Call-by-Call-Data.

System Components:• Clean Databases: operational-data of individual calls, agents

and operations.• Friendly yet powerful Online Interface: enables convenient fast

access to (mostly) operational and (some) administrative data(but no marketing/business data).

Current Databases:• Medium-sized U.S. Bank (2.5 years; 220M calls, 40M via

agents; 800 agents at peaks) – Completed.• Israeli Cell-Phone Company (2 years; 110M calls, 25M via

agents; 400 agents at peaks) – Ongoing.• Large Israeli Bank – Pilot.

DataMOCCA will now be used to illustrate the hierarchy ofoperational decisions, from forecasting to SBR.

29

Page 49: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

DataMOCCA = Data MOdel for Call Center Analysis

Project Goal: Designing and Implementing a (universal)data-base/data-repository and interface for storing, retrieving,analyzing and displaying Call-by-Call-Data.

System Components:• Clean Databases: operational-data of individual calls, agents

and operations.• Friendly yet powerful Online Interface: enables convenient fast

access to (mostly) operational and (some) administrative data(but no marketing/business data).

Current Databases:• Medium-sized U.S. Bank (2.5 years; 220M calls, 40M via

agents; 800 agents at peaks) – Completed.• Israeli Cell-Phone Company (2 years; 110M calls, 25M via

agents; 400 agents at peaks) – Ongoing.• Large Israeli Bank – Pilot.

DataMOCCA will now be used to illustrate the hierarchy ofoperational decisions, from forecasting to SBR.

29

Page 50: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

DataMOCCA = Data MOdel for Call Center Analysis

Project Goal: Designing and Implementing a (universal)data-base/data-repository and interface for storing, retrieving,analyzing and displaying Call-by-Call-Data.

System Components:• Clean Databases: operational-data of individual calls, agents

and operations.• Friendly yet powerful Online Interface: enables convenient fast

access to (mostly) operational and (some) administrative data(but no marketing/business data).

Current Databases:• Medium-sized U.S. Bank (2.5 years; 220M calls, 40M via

agents; 800 agents at peaks) – Completed.• Israeli Cell-Phone Company (2 years; 110M calls, 25M via

agents; 400 agents at peaks) – Ongoing.• Large Israeli Bank – Pilot.

DataMOCCA will now be used to illustrate the hierarchy ofoperational decisions, from forecasting to SBR.

29

Page 51: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Arrivals to Service: Predictable vs. RandomArrival Rates on Tuesdays in a September – U.S. Bank

0

500

1000

1500

2000

2500

3000

3500

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00

Time (Resolution 30 min.)

Arrival rate

04.09.2001 11.09.2001 18.09.2001 25.09.2001

• Tuesday, September 4th: Heavy, following Labor Day• Tuesdays, September 18 & 25: Normal

• Tuesday, September 11th, 2001.

30

Page 52: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Arrivals to Service: Predictable vs. RandomArrival Rates on Tuesdays in a September – U.S. Bank

0

500

1000

1500

2000

2500

3000

3500

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00

Time (Resolution 30 min.)

Arrival rate

04.09.2001 11.09.2001 18.09.2001 25.09.2001

• Tuesday, September 4th: Heavy, following Labor Day• Tuesdays, September 18 & 25: Normal• Tuesday, September 11th, 2001.

30

Page 53: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Agent Status

Erlang-A Model ⇒ optimal Staffing Level n.

n = overall number-of-agents that come to work? No!

Israeli Bank, Agent Status: Monthly Averages

0

50

100

150

200

250

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00

Time

Number of agents

Long Break Medium Break Short BreakOther Activities Outgoing Call AvailableIncoming Call

Staffing Level (FTE) = Busy with “Incoming Calls" + “Available" forservice.

31

Page 54: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Shifts Scheduling

Integer Programming given interval-based Staffing Levels.

Example of a shift scheduling problem:should we bring agents early, given a predictable arrival peak?

U.S. Bank: Queue-length and Staffing on May 3, 2002

0

50

100

150

200

250

300

350

400

07:00

08:00

09:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

18:00

19:00

20:00

21:00

22:00

23:00

24:00

:00

Num

ber o

f Age

nts

0

20

40

60

80

100

120

Que

ue L

engt

h

Offered Load Number of Agents Queue length

32

Page 55: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Rostering

Assigning individual agents to schedules.Typically, heuristics used to accommodate individual constraints.

Israeli Technical Support Call Center: Online Shift Bidding

Shift-bidding starts at 18:00.

• 60% of agents are registered till 18:00• 80% till 18:24; 90% till 22:00; registration closed at 5:23am.

33

Page 56: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Introduction to Skills Based Routing

General Setup

10

Introduction

Multi-queue parallel-server system = schematic depiction of a telephone call-center:

λ1 λ2 λ3 λ4

θ1 1 θ2 2 3 θ3 4 θ4

µ1 µ2 µ3 µ4 µ5 µ6 µ7 µ8 S1 S2 S3

Here the λ's designate arrival rates, the µ's service rates, the θ's abandonment rates, and the S's are the

number of servers in each server-pool.

Skills-Based Design:

- Queue: "customer-type" requiring a specific type of service;

- Server-Pool: "skills" defining the service-types it can perform;

- Arrow: leading into a server-pool define its skills / constituency.

For example, a server with skill 2 (S2) can serve customers of type 3 (C3)

at rate µ6 customers/hour.

Customers of type 3 arrive randomly at rate λ3 customers/hour, equipped with

an impatience rate of θ3.

Major Control Decisions• Customer Routing: If an agent turns idle and there are queued

customers, which customer (if any) should be routed to thisagent.

• Agent Scheduling: If a customer arrives and there are idleagents, which agent (if any) should serve this customer.

• Load Balancing: Routing of customers to distributed callcenters (eg. nation-wide).

34

Page 57: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Customers Relationship/Revenue Management (CRM)

NationsBank CRM relationship groups:• RG1: high-value customers• RG2: marginally profitable customers (with potential)• RG3: unprofitable customer.

NationsBank’s Design of the Service Encounter

Examples of Specifications: Assignable Grade Of Service

6

3

NationsBank CRM: What are the relationship groups?

The groups– RG1 : high-value customers– RG2 : marginally profitable customers (with potential)– RG3 : unprofitable customer

What does it mean for a customer in each group to be profitable? Customer Revenue Management

5

NationsBank’s Design of the Service Encounter

90% of calls85% of calls70% of callsVRU Target

within 8 business dayswithin 2 business daysduring callProblem Resolution

basic productproduct expertsuniversalRep. Training

< 9%< 5%< 1%Abandonment rate

mailcall / mailcall / faxTrans. Confirmation

FCFSFCFSrequest rep / callbackRep. Personalization

2 min. average4 min. averageno limitAverage Talk Time

50% in 20 seconds80% in 20 seconds100% in 2 ringsSpeed of Answer

RG3RG2RG1

Examples of Specifications: Assignable Grade Of Service (AGOS)

35

Page 58: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Priorities and Economies-of-ScaleU.S. Bank. Regular vs. VIP Customers. December 2002

Average Wait Staffing Level

0

5

10

15

20

25

30

35

40

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00

Time (Resolution 30 min.)

Average Waiting Time, sec

Retail Premier

0

50

100

150

200

250

300

350

400

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00

Time (Resolution 30 min.)

Number of Agents

Retail Premier

Premier customers do not get a better service level.

Number of agents assigned to Premier is small and they do not getenough help from regular agents.

Challenge: enable better service level for Premier and still servemost of them by a small dedicated group of agents.

36

Page 59: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Priorities and Economies-of-ScaleU.S. Bank. Regular vs. VIP Customers. December 2002

Average Wait Staffing Level

0

5

10

15

20

25

30

35

40

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00

Time (Resolution 30 min.)

Average Waiting Time, sec

Retail Premier

0

50

100

150

200

250

300

350

400

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00

Time (Resolution 30 min.)

Number of Agents

Retail Premier

Premier customers do not get a better service level.

Number of agents assigned to Premier is small and they do not getenough help from regular agents.

Challenge: enable better service level for Premier and still servemost of them by a small dedicated group of agents.

36

Page 60: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Priorities and Routing Protocols I

Israeli Bank. Regular vs. VIP Customers. October 2004

Delay Probability Average Wait

0

10

20

30

40

50

60

70

80

90

100

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00

Time (Resolution 30 min.)

Delay Probability, %

Private Private Platinum

0

5

10

15

20

25

30

35

40

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00

Time (Resolution 30 min.)

Average Wait, sec

Private Private Platinum

More Platinum customers have to wait, but their average wait isshorter. How to explain?

37

Page 61: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Priorities and Routing Protocols II

Histograms of Waiting Times. October 2004

Private Private Platinumprivate_hist

Page 1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

2 14 26 38 50 62 74 86 98

Time (Resolution 1 sec.)

Relative frequencies, %

platinum_hist

Page 1

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

2 14 26 38 50 62 74 86

Time (Resolution 1 sec.)

Relative frequencies, %

After 25 seconds of wait, Platinum are routed to Regular agentsgetting high priority. Hence, almost no long waiting times forPlatinum.

38

Page 62: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Dynamic Priority-Upgrade

Large Israeli Bank: Histogram of Waiting Timeswaitwait

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380

Time (Resolution 1 sec.)

Relative frequencies, %

Peaks every 60 seconds. Why?

• System: Priority-Upgrade (unrevealed) every 60 seconds• Human: Voice-Announcement every 60 seconds.

Served Customers Abandoning Customerswaithandled

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380

Time (Resolution 1 sec.)

Relative frequencies, %

waitab

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340

Time (Resolution 1 sec.)

Relative frequencies, %

39

Page 63: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Dynamic Priority-Upgrade

Large Israeli Bank: Histogram of Waiting Timeswaitwait

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380

Time (Resolution 1 sec.)

Relative frequencies, %

Peaks every 60 seconds. Why?• System: Priority-Upgrade (unrevealed) every 60 seconds• Human: Voice-Announcement every 60 seconds.

Served Customers Abandoning Customerswaithandled

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380

Time (Resolution 1 sec.)

Relative frequencies, %

waitab

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340

Time (Resolution 1 sec.)

Relative frequencies, %

39

Page 64: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Dynamic Priority-Upgrade

Large Israeli Bank: Histogram of Waiting Timeswaitwait

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380

Time (Resolution 1 sec.)

Relative frequencies, %

Peaks every 60 seconds. Why?• System: Priority-Upgrade (unrevealed) every 60 seconds• Human: Voice-Announcement every 60 seconds.

Served Customers Abandoning Customerswaithandled

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380

Time (Resolution 1 sec.)

Relative frequencies, %

waitab

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340

Time (Resolution 1 sec.)

Relative frequencies, %

39

Page 65: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Network Balancing via Interqueue in a U.S. Bank

73

Distributed Call Center (U.S. Bank)

NY 1

RI 3

PA 2

MA 4

179+5

619+3

11+1

74+7

8+1

19+1

20

508+2

101+2

2

External arrivals:2092 2063(98.6%Served)+29(1.4%Aban)

Not Interqueued:1209(57.8%)

• Served: 1184(97.9/56.6)

• Aban: 25(2.1/1.2) Interqueued :883(42.2) • Served

here:174(19.7/8.3)

• Served at 2: 438(49.6/20.9) S d t 3

External arrivals: 16941687(99.6%

Served)+7( 0.4% Aban)

Not Interqueued: 1665(98.3)

• Served: 1659 (99.6/97.9)

• Aban: 6 (0.4/04) Interqueued:28+1 (1.7)

• Served here: 17(58.6/1)

• Served at 1: 3(10.3/0.2)

External arrivals: 122 112(91.8

Served)+10(8.2 Aban)

Not Interqueued: 93 (76.2)

• Served: 85 (91.4/69.7)

• Aban: 8 (8.6/6.6) Interqueued:27+2

(23.8) • Served here:

14(48.3/11.5) • Served at 1: 6

External arrivals: 1770 1755(99.2

Served)+15(0.8 Aban)

Not Interqueued: 1503(84.9)

• Served: 1497 (99.6/84.6)

• Aban: 6 (0.4/0.3) Interqueued:258+9

(15.1) • Served here: 110

(41.2/6.2) • Served at 1:58

(21 7/3 3)

Internal arrivals: 224

• Served at 1: 67 (29.9)

• Served at 2: 41 (18.3)

• Served at 3: 87 (38.8)

• Served at 4:

Internal arrivals: 643

• Served at 1: 157 (24.4)

• Served at 2: 195 (30.3)

• Served at 3: 282 (43.9)

• Served at 4: 4 (0.6)

• Aban at 1: 3

Internal arrivals: 81

• Served at 1: 17(21)

• Served at 3: 42(51.9)

• Served at 4: 15(18 5)

Internal arrivals: 613• Served at 1:

41(6.7) • Served at 2:

513(83.7) • Served at 3:

55(9.0) • Aban at 1:

2(0.3)

10 AM – 11 AM (03/19/01): Interflow Chart Among the 4 Call C t f Fl t B k

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Page 66: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Network Balancing Protocols and Performance Level

U.S. Bank: Histograms of Waiting Times

Retail BusinessChart1

Page 1

0

2

4

6

8

10

12

14

16

18

20

2 5 8 11 14 17 20 23 26 29 32 35

Time

Relative frequencies, %

Sheet3 Chart 1

Page 1

0

2

4

6

8

10

12

2 8 14 20 26 32 38 44 50 56 62 68 74 80 86 92

Time

Relative frequencies, %

Why do we observe a peak for Retail service (10 seconds)?After 10 seconds of wait Retail customers were sent into theinterqueue.

Business customers – peak at 5 seconds, for the same reason.Second peak – unclear, maybe priority-upgrade.

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Page 67: Empirically-Based Staffing in Call Centersiew3.technion.ac.il/serveng/References/emp_staff06_watson_presentation.pdf · Empirically-Based Staffing in Call Centers Simple Models

Main Research and Practical Challenges

• Skills-Based Routing: Convergence of Practice and Theory• Uncertainty: in Reality, Model Parameters, Forecasting• Time-Varying Queues: Time-Stable Performance• General Service-Times: Theory• Economic Models: Operations (Dimensioning), Marketing• Human Dimensions:

Measure, Model, Experiment, Validate, Refine, etc.

All of the above in a Network of distributed call centers.

See our Service Engineering site for downloads:http://iew3.technion.ac.il/serveng

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