Presentation

Service Engineering:
Data-Based Science & Teaching
in support of Service Management
Avishai Mandelbaum
Technion, Haifa, Israel
http://ie.technion.ac.il/serveng
Based on joint work with Sergey Zeltyn, . . .
Technion SEE Center / Lab: Paul Feigin, Valery Trofimov, RA’s, . . .
1
Main Messages
1. Simple Useful Models at the Service of Complex Realities.
Note: Useful must be Simple; Simple often rooted in Deep analysis.
2. Data-Based Research & Teaching is a Must & Fun.
Supported by DataMOCCA = Data MOdels for Call Center Analysis.
Initiated with Wharton, developed at Technion, available for adoption.
3. Back to the Basic-Research Paradigm (Physics, Biology, . . .):
Measure, Model, Experiment, Validate, Refine, etc.
4. Ancestors & Practitioners often knew/apply the “right answer":
simply did/do not have our tools/desire/need to prove it so.
Supported by Erlang (1915), Palm (1945),..., thoughtful managers.
5. Scientifically-based design principles and tools (software),
that support the balance of service quality, process efficiency and
business profitability, from the (often-conflicting) views of
customers, servers, managers: Service Engineering .
Background Material (Downloadable)
I
Technion’s ‘‘Service-Engineering" Course (≥ 1995):
http://ie.technion.ac.il/serveng
I
Gans (U.S.A.), Koole (Europe), and M. (Israel):
“Telephone Call Centers: Tutorial, Review and Research
Prospects." MSOM, 2003.
I
Brown, Gans, M., Sakov, Shen, Zeltyn, Zhao:
“Statistical Analysis of a Telephone Call Center: A
Queueing-Science Perspective." JASA, 2005.
I
Trofimov, Feigin, M., Ishay, Nadjharov:
"DataMOCCA: Models for Call/Contact Center Analysis."
Technion Report, 2004-2006.
I
M. “Call Centers: Research Bibliography with Abstracts."
Version 7, December 2006.
3
The First Prerequisite: Data & Measurements
Empirical “Axiom": The data one needs is never there for one to
use – always problems with historical data (eg. lacking,
contaminated, averaged, . . .)
Averages Prevalent.
But I need data at the level of the Individual Transaction: For each
service transaction, its operational history – time-stamps of events.
(Towards integrating with marketing / financial history.)
Sources: “Service-floor" (vs. Industry-level, Surveys, . . .)
I
I
I
I
Administrative (Court, via “paper analysis")
Face-to-Face (Bank, via bar-code readers)
Telephone (Call Centers, via ACD)
Future: Hospitals (via RFID)
Measurements: Face-to-Face Services
23 Bar-Code Readers at a Bank Branch
Bank – 2nd Floor Measurements
5
Telephone Service:Call-by-Call
Call-by-Call Data
Measurements: Telephone
Data (Log-File)
vru+line call_id customer_id priority type date
vru_entry vru_exit vru_time q_start
q_exit
q_time outcome ser_start ser_exit ser_time server
AA0101 44749 27644400
2
PS 990901 11:45:33 11:45:39 6
11:45:39 11:46:58 79
AGENT 11:46:57 11:51:00 243
DORIT
AA0101 44750 12887816
AA0101 44967 58660291
1
2
PS 990905 14:49:00 14:49:06 6
PS 990905 14:58:42 14:58:48 6
14:49:06 14:53:00 234
14:58:48 15:02:31 223
AGENT 14:52:59 14:54:29 90
AGENT 15:02:31 15:04:10 99
ROTH
ROTH
AA0101 44968 0
0
NW 990905 15:10:17 15:10:26 9
15:10:26 15:13:19 173
HANG 00:00:00 00:00:00 0
NO_SERVER
AA0101 44969 63193346
2
PS 990905 15:22:07 15:22:13 6
15:22:13 15:23:21 68
AGENT 15:23:20 15:25:25 125
STEREN
AA0101 44970 0
0
NW 990905 15:31:33 15:31:47 14
00:00:00 00:00:00 0
AGENT 15:31:45 15:34:16 151
STEREN
AA0101 44971 41630443
2
PS 990905 15:37:29 15:37:34 5
15:37:34 15:38:20 46
AGENT 15:38:18 15:40:56 158
TOVA
AA0101 44972 64185333
2
PS 990905 15:44:32 15:44:37 5
15:44:37 15:47:57 200
AGENT 15:47:56 15:49:02 66
TOVA
AA0101 44973 3.06E+08
1
PS 990905 15:53:05 15:53:11 6
15:53:11 15:56:39 208
AGENT 15:56:38 15:56:47 9
MORIAH
AA0101 44974 74780917
2
NE 990905 15:59:34 15:59:40 6
15:59:40 16:02:33 173
AGENT 16:02:33 16:26:04 1411
ELI
AA0101 44975 55920755
2
PS 990905 16:07:46 16:07:51 5
16:07:51 16:08:01 10
HANG 00:00:00 00:00:00 0
NO_SERVER
AA0101 44976 0
0
NW 990905 16:11:38 16:11:48 10
16:11:48 16:11:50 2
HANG 00:00:00 00:00:00 0
NO_SERVER
AA0101 44977 33689787
2
PS 990905 16:14:27 16:14:33 6
16:14:33 16:14:54 21
HANG 00:00:00 00:00:00 0
NO_SERVER
AA0101 44978 23817067
2
PS 990905 16:19:11 16:19:17 6
16:19:17 16:19:39 22
AGENT 16:19:38 16:21:57 139
TOVA
AA0101 44764 0
0
PS 990901 15:03:26 15:03:36 10
00:00:00 00:00:00 0
AGENT 15:03:35 15:06:36 181
ZOHARI
AA0101 44765 25219700
2
PS 990901 15:14:46 15:14:51 5
15:14:51 15:15:10 19
AGENT 15:15:09 15:17:00 111
SHARON
AA0101 44766 0
AA0101 44767 58859752
0
2
PS 990901 15:25:48 15:26:00 12
PS 990901 15:34:57 15:35:03 6
00:00:00 00:00:00 0
15:35:03 15:35:14 11
AGENT 15:25:59 15:28:15 136
AGENT 15:35:13 15:35:15 2
ANAT
MORIAH
AA0101 44768 0
0
PS 990901 15:46:30 15:46:39 9
00:00:00 00:00:00 0
AGENT 15:46:38 15:51:51 313
ANAT
AA0101 44769 78191137
2
PS 990901 15:56:03 15:56:09 6
15:56:09 15:56:28 19
AGENT 15:56:28 15:59:02 154
MORIAH
AA0101 44770 0
0
PS 990901 16:14:31 16:14:46 15
00:00:00 00:00:00 0
AGENT 16:14:44 16:16:02 78
BENSION
AA0101 44771 0
0
PS 990901 16:38:59 16:39:12 13
00:00:00 00:00:00 0
AGENT 16:39:11 16:43:35 264
VICKY
AA0101 44772 0
0
PS 990901 16:51:40 16:51:50 10
00:00:00 00:00:00 0
AGENT 16:51:49 16:53:52 123
ANAT
AA0101 44773 0
0
PS 990901 17:02:19 17:02:28 9
00:00:00 00:00:00 0
AGENT 17:02:28 17:07:42 314
VICKY
AA0101 44774 32387482
1
PS 990901 17:18:18 17:18:24 6
17:18:24 17:19:01 37
AGENT 17:19:00 17:19:35 35
VICKY
AA0101 44775 0
0
PS 990901 17:38:53 17:39:05 12
00:00:00 00:00:00 0
AGENT 17:39:04 17:40:43 99
TOVA
AA0101 44776 0
0
PS 990901 17:52:59 17:53:09 10
00:00:00 00:00:00 0
AGENT 17:53:08 17:53:09 1
NO_SERVER
AA0101 44777 37635950
2
PS 990901 18:15:47 18:15:52 5
18:15:52 18:16:57 65
AGENT 18:16:56 18:18:48 112
ANAT
AA0101 44778 0
0
NE 990901 18:30:43 18:30:52 9
00:00:00 00:00:00 0
AGENT 18:30:51 18:30:54 3
MORIAH
AA0101 44779 0
0
PS 990901 18:51:47 18:52:02 15
00:00:00 00:00:00 0
AGENT 18:52:02 18:55:30 208
TOVA
AA0101 44780 0
0
PS 990901 19:19:04 19:19:17 13
00:00:00 00:00:00 0
AGENT 19:19:15 19:20:20 65
MEIR
AA0101 44781 0
AA0101 44782 0
0
0
PS 990901 19:39:19 19:39:30 11
NW 990901 20:08:13 20:08:25 12
00:00:00 00:00:00 0
00:00:00 00:00:00 0
AGENT 19:39:29 19:41:42 133
AGENT 20:08:28 20:08:41 13
BENSION
NO_SERVER
AA0101 44783 0
0
PS 990901 20:23:51 20:24:05 14
00:00:00 00:00:00 0
AGENT 20:24:04 20:24:33 29
BENSION
AA0101 44784 0
0
NW 990901 20:36:54 20:37:14 20
00:00:00 00:00:00 0
AGENT 20:37:13 20:38:07 54
BENSION
AA0101 44785 0
0
PS 990901 20:50:07 20:50:16 9
00:00:00 00:00:00 0
AGENT 20:50:15 20:51:32 77
BENSION
AA0101 44786 0
0
PS 990901 21:04:41 21:04:51 10
00:00:00 00:00:00 0
AGENT 21:04:50 21:05:59 69
TOVA
AA0101 44787 0
0
PS 990901 21:25:00 21:25:13 13
00:00:00 00:00:00 0
AGENT 21:25:13 21:28:03 170
AVI
AA0101 44788 0
0
PS 990901 21:50:40 21:50:54 14
00:00:00 00:00:00 0
AGENT 21:50:54 21:51:55 61
AVI
AA0101 44789 9103060
2
NE 990901 22:05:40 22:05:46 6
22:05:46 22:09:52 246
AGENT 22:09:51 22:13:41 230
AVI
AA0101 44790 14558621
2
PS 990901 22:24:11 22:24:17 6
22:24:17 22:26:16 119
AGENT 22:26:15 22:27:28 73
VICKY
AA0101 44791 0
0
PS 990901 22:46:27 22:46:37 10
00:00:00 00:00:00 0
AGENT 22:46:36 22:47:03 27
AVI
AA0101 44792 67158097
2
PS 990901 23:05:07 23:05:13 6
23:05:13 23:05:30 17
AGENT 23:05:29 23:06:49 80
VICKY
AA0101 44793 15317126
2
PS 990901 23:28:52 23:28:58 6
23:28:58 23:30:08 70
AGENT 23:30:07 23:35:03 296
DARMON
AA0101 44794 0
0
PS 990902 00:10:47 00:12:05 78
00:00:00 00:00:00 0
HANG 00:00:00 00:00:00 0
NO_SERVER
AA0101 44795 0
0
PS 990902 07:16:52 07:17:01 9
00:00:00 00:00:00 0
AGENT 07:17:01 07:17:44 43
ANAT
AA0101 44796 0
0
PS 990902 07:50:05 07:50:16 11
00:00:00 00:00:00 0
AGENT 07:50:16 07:53:03 167
STEREN
6
Averages Prevalent
ACD Report: Health Insurance
Time
Total
8:00
8:30
9:00
9:30
10:00
10:30
11:00
11:30
12:00
12:30
13:00
13:30
14:00
14:30
15:00
15:30
16:00
16:30
17:00
17:30
18:00
Calls
20,577
332
653
866
1,152
1,330
1,364
1,380
1,272
1,179
1,174
1,018
1,061
1,173
1,212
1,137
1,169
1,107
914
615
420
49
Answered
19,860
308
615
796
1,138
1,286
1,338
1,280
1,247
1,177
1,160
999
961
1,082
1,179
1,122
1,137
1,059
892
615
420
49
Abandoned%
3.5%
7.2%
5.8%
8.1%
1.2%
3.3%
1.9%
7.2%
2.0%
0.2%
1.2%
1.9%
9.4%
7.8%
2.7%
1.3%
2.7%
4.3%
2.4%
0.0%
0.0%
0.0%
7
ASA
30
27
58
63
28
22
33
34
44
1
10
9
67
78
23
15
17
46
22
2
0
14
AHT
307
302
293
308
303
307
296
306
298
306
302
314
306
313
304
320
311
315
307
328
328
180
Occ%
95.1%
87.1%
96.1%
97.1%
90.8%
98.4%
99.0%
98.2%
94.6%
91.6%
95.5%
95.4%
100.0%
99.5%
96.6%
96.9%
97.1%
99.2%
95.2%
83.0%
73.8%
84.2%
# of agents
59.3
104.1
140.4
211.1
223.1
222.5
222.0
218.0
218.3
203.8
182.9
163.4
188.9
206.1
205.8
202.2
187.1
160.0
135.0
103.5
5.8
quantiles of waiting times to those of the exponential (the straight line at the right plot). The t is reasonable
up to about 700 seconds. (The p-value for the Kolmogorov-Smirnov test for Exponentiality is however 0 {
not that surprising in view of the sample size of 263,007).
Beyond Averages: Waiting Times in a Call Center
9: Distribution of waiting time (1999) Large U.S. Bank
Small IsraeliFigure
Bank
Chart1
29.1 %
20
18
Relative frequencies, %
600
Mean = 98
SD = 105
13.4 %
8.8 %
200
6.9 %
400
Exp quantiles
20 %
5.4 %
3.9 %
3.1 %
2.3 %
16
14
12
10
8
6
4
2
1.7 %
0
0
2
5
8
11
14
17
20
23
26
29
Time
0
30
60
90
120
150
180
210
240
270
300
0
200
Time
400
Waiting time given agent
600
Page 1
Medium Israeli Bank
waitwait
0.9
Relative frequencies, %
0.8 exponentials: Interestingly, the means and standard deviations in Table
Remark on mixtures of independent
19 are rather close, both annually0.7and across all months. This suggests also an exponential distribution
for each month separately, as was0.6indeed veried, and which is apparently inconsistent with the observerd
annual exponentiality. The phenomenon
recurs later as well, hence an explanation is in order. We shall be
0.5
satised with demonstrating that 0.4
a true mixture W of independent random varibles Wi , all of which have
coeÆcients of variation C (Wi ) = 1,0.3can also have C (W ) 1. To this end, let Wi denote the waiting time in
month i, and suppose it is exponentially distributed with mean mi . Assume that the months are independent
0.2
and let pi be the fraction of calls performed in month i (out of the yearly total). If W denotes the mixture
0.1
of these exponentials (W = Wi with
probability pi , that is W has a hyper-exponential distribution), then
0.0
20 40 60 2
80 100 120 140 160 1802200 220 240 260 280 300 320 340 360 380
C (W ) = 1Time
+ 2(Resolution
C (M ); 1 sec.)
where M stands for a ctitious random variable, dened to be equal mi with probability pi . One concludes
that if the mi 's do not vary much relative to their mean (C (M )8 << 1), which is the case here, then C (W ) 1,
Page 1
32
35
The Second Prerequisite: Models
Through Examples Only.
Each example starts with a Complex Reality and ends with a useful
insight due to a Simple Model.
‘‘Theorem": A useful model must be simple (yet not too simple).
Models in decreasing simplicity-levels:
I
Conceptual: Service Networks = Queueing Networks
I
Descriptive: Averages, Histograms
I
Explanatory: Comparative, Regression
I
Analytical/Mathematical: Little’s Law, Fluid Models, Queueing
Models, Diffusion Refinements.
“Corollary": To be useful, a simple model sometimes requires deep
analysis.
9
Conceptual Model: Face-to-Face Services
Bank Branch = Queueing Network
/
/
Manager
Entrance
Xerox
Teller
Tourism
/
Bottleneck!
10
23
Descriptive Model:
Transition Probabilities (Averages)
Bank: A Queuing Network
Transition Frequencies Between Units in The Private and Business Sections:
Private Banking
To Unit Bankers
From Unit
Bankers
Private
Authorized
Personal
Banking Compensations
Authorized Compens -
Business
Tellers
Tellers Overdrafts Authorized
Personal
- ations
1%
1%
4%
4%
5%
4%
6%
18%
12%
7%
4%
Tellers
6%
0%
1%
Tellers
0%
0%
0%
90%
0%
0%
0%
73%
6%
0%
0%
1%
64%
1%
0%
0%
0%
90%
1%
0%
2%
94%
5%
8%
64%
11%
69%
1%
0%
0%
0%
2%
0%
1%
1%
19%
Authorized
Personal
2%
1%
0%
1%
11%
5%
Full Service
1%
0%
0%
0%
8%
1%
2%
Entrance
13%
0%
3%
10%
58%
2%
0%
0%-5%
5%-10%
10% -15% >15%
Dominant Paths - Business:
Unit
Parameter
Station 1
Tourism
Station 2
Teller
Total
Dominant Path
Service Time
12.7
4.8
17.5
Waiting Time
Total Time
8.2
20.9
6.9
11.7
15.1
32.6
Service Index
0.61
0.41
0.53
11
Exit
Service
Services Overdrafts
Legend:
Full
Personal
88%
14%
0%
Conceptual Model: Hospital (ED) Network
(Marmur, Sinreich)
proportion of patients
process requires bed
01
Else
Lab
Imaging
02
Nurse
reception
Physician
04 triage
03
vital signs
E.C.G
06
05
07
handling
patient&family
initial
examination
09
10
08
11
Labs
100%
consultation
bloodwork
14
13
25,26
32,33
34
labs
decision
35
18
consultation
21
29
17
16
treatment 19
treatment
decision
ultrasound
28
15
imaging
27
23
24
imaging
20
Xray
36
22
labs
37
38
decision
39
40
CT
30
treatment
31
observation
43
45
46
follow up
every 15 minutes
48
hospitalization/
discharge
49
52
50
awaiting
evacuation
51
discharge
53
instructions
prior discharge
55
discharge /
hospitalization
else
54
56
estimated max time
60
probability of events
10%
decision point for alternative processes
reference point
Figure 2. The Unified Patient Process Chart
12
42
treatment
follow up
47
every 15 minutes
awaiting
discharge
41
44
else
12
consultation
imaging /consultation /
treatment
Hours
Descriptive Model: Service Times (Averages) or,
Even “Doctors" Can Manage
Operations Time - Morning (by Hour) vs. Afternoon (by Case):
6
AM
5
Hours
4
PM
3
2
1
0
EEG
Orthopedics
Surgery
Blood Surgery
Plastic Surgery
Department
Afternoon,
by Case
Morning,
by Hour
13
Heart/Chest
Surgery
Neuro-Surgery
Eyes
E.I. Surgery
Conceptual Model: The “Production of Justice"
“Production” Of Justice
The Labor-Court Process in Haifa, Israel
Open File
Allocate
Prepare
Activity
Mile Stone
Proceedings
Queue
Phase
Phase Transition
Closure
Avg. sojourn time ≈ in months / years
Processing time ≈ in mins / hours / days
Appeal
14
Analytical Model: Little’s Law in Court (still Averages)
Judges:
Judges:
Operational
Performance
Performance
Analysis
– Base Case
Judges:
Performance
byAnalysis
Case-Type
Judges:
Performance
Operational
Performance:
Rate
λ & Time W
Case Type 0
Case Type 01
Case Type 3
10
Average Number of Months - W
9
Judge1
Judge2
Judge3
Judge4
Judge5
0
0
01
8
7
. 45
(6.2, 7.4)
. 100
(13.5, 7.4)
3
3
01
3
6
5
(7.2, 4.6)
01
4
.
3
33
0
59
(12, 4.9)
.
0
0
118
(26.3, 4.5)
3
.
01
01
3
2
1
0
0
5
10
15
20
Average Number of Cases / Month - λ
15
25
30
Expertise “invite" Skills-Base-Routing (SBR)
Operational Performance:
Judges’
Heterogeneity
Judges:
Judges:
Operational
Performance
Performance
Analysis
– Base Case(Best / Worse)
Judges:
Performance
byAnalysis
Case-Type
Judges:
Performance
Case Type 0
Case Type 01
Case Type 3
10
Average Number of Months - W
9
Judge1
Judge2
Judge3
Judge4
Judge5
0
0
01
8
7
. 45
(6.2, 7.4)
. 100
(13.5, 7.4)
3
3
01
3
6
5
(7.2, 4.6)
01
4
.
3
33
0
59
(12, 4.9)
.
0
0
118
(26.3, 4.5)
3
.
01
01
3
2
1
0
0
5
10
15
20
Average Number of Cases / Month - λ
16
25
30
Analytical Model: Little’s Law in Court (still Averages)
Judges:
Performance
Analysis
Judges’
Profiles
(Operational)
Case Type 0
Case Type 01
Case Type 3
10
9
0
0
8
Avg. Months - W
Judge1
Judge2
Judge3
Judge4
Judge5
01
7
. (6.2, 7.4)
. (13.5, 7.4)
3
3
01
3
6
5
(7.2, 4.6)
.
3
01
4
.
(12, 4.9)
0
0
3
(26.3, 4.5)
.
0
01
01
3
2
1
0
0
5
10
15
Avg. Cases / Month - λ
17
20
25
30
Analytical Model: Little’s Law in Court (still Averages)
Judges: Performance Analysis
Judges: The Best/Worst (Operational) Performer
Case Type 0
Case Type 01
Case Type 3
10
9
0
0
8
Avg. Months - W
Judge1
Judge2
Judge3
Judge4
Judge5
01
7
. (6.2,
45 7.4)
3
3
. (13.5,
100 7.4)
01
3
6
5
(7.2, 4.6)
01
4
.
3
33
0
59
(12, 4.9)
.
0
0
118
(26.3, 4.5)
3
.
01
01
3
2
1
0
0
5
10
15
Avg. Cases / Month - λ
18
20
25
30
Call-Center Network: Gallery of Models
Index
Service Engineering: Multi-Disciplinary Process View
(75% in Banks)
Information Design
Marketing,
Operations Research
Lost Calls
(
Waiting Time
Return Time)
Organization Design:
Parallel (Flat)
Sequential (Hierarchical)
Sociology/Psychology,
Operations Research
Agents
Queue
Redial
Function
Scientific Discipline
Multi-Disciplinary
Call Center Design
Service Completion
Experts
(Consultants)
(Invisible)
(Retrial)
Computer-Telephony
Integration - CTI
MIS/CS
Busy
(Rare)
Good
or
Arrivals
(Business Frontier
Bad
Job Enrichment
Training, Incentives
Human Resource
Management
of the
21th Century)
VRU/
IVR
Forecasting
Statistics
Internet
Chat
Email
Fax
Customers
Interface Design
Human Factors
Engineering
New Services
Design (R&D)
Operations,
Marketing
Agents
(CSRs)
To Avoid
Starvation Skill Based Routing
(SBR) Design
Marketing,
Human Resources,
To Avoid Operations Research,
MIS
Delay
Customers
Segmentation CRM
Marketing
Tele-Stress
Psychology
(Turnover up to
200% per Year)
(Sweat Shops
of the
21th Century)
Psychological
Process
Archive
Expect 3 min
Willing 8 min
Perceive 15 min
Back-Office
VIP
VIP Queue
(Training)
Service Process
Design
Abandonment
Psychology,
Logistics
Statistics
Lost Calls
Positive: Repeat Business
Negative: New Complaint
19
Operations/
Business
Process
Archive
Database
Design
Data Mining:
MIS, Statistics,
Operations
Research,
Marketing
Service
Completion
(If Required 15 min,
then Waited 8 min)
(If Required 6 min,
then Waited 8 min)
Psychology,
Operations
Research,
Marketing
The “Phases of Waiting" for Service
Common Experience:
I Expected to wait 5 minutes, Required to 10
I Felt like 20, Actually waited 10 (hence Willing ≥ 10)
An attempt at “Modeling the Experience":
1. Time that a customer expects to wait
2.
willing to wait
3.
required to wait
4.
actually waits
5.
perceives waiting.
Experienced customers
“Rational" customers
⇒
⇒
((Im)Patience: τ )
(Offered Wait:V )
(Wq = min(τ, V ))
Expected = Required
Perceived = Actual.
Then left with (τ, V ).
20
Call Center Data: Hazard Rates (Un-Censored)
Required/Offered Wait V
(Im)Patience Time τ
−3
5
x 10
4.5
4
Israel
hazard rate
3.5
3
2.5
2
1.5
1
0.5
0
0
50
100
150
200
time, sec
actuarial estimate
spline smoother
16
0.3
14
0.25
12
hazard rate
U.S.
hazard rate
0.35
0.2
0.15
10
8
6
0.1
4
0.05
0
0
2
10
20
30
time, sec
40
50
0
0
60
21
10
20
30
time, sec
40
50
60
A Patience Index
Quantifying (Im)Patience: “Willing to wait 15 min" = Patient?
Willing to wait
E[τ ]
=
,
Expected to wait
E[V ]
“assuming" Experienced; further “assuming" that τ and V are
Exponential, the M-L estimate of Index is the easily-measurable:
∆
Theoretical Patience-Index =
∆
Empirical Patience-Index =
% Served
% Abandoning
Index Validation: Theoretical vs. Empirical
10
9
Theoretical Index
8
7
6
5
4
3
2
1
0
2
3
4
5
6
Empirical Index
7
8
9
Predicting Performance
Model Primitives:
I
I
I
I
Arrivals to service (random process)
(Im)Patience while waiting τ (r.v.)
Service times (r.v.)
# Servers / Agents (parameter / r.v.)
Model Output: Offered-Wait V (r.v.)
Operational Performance Measure calculable in terms of (τ, V ).
I
I
eg.
eg.
Average Wait = E[min{τ, V }]
% Abandonment = P{τ < V }
Application: Staffing – How Many Agents? (When? Who?)
23
The Basic Staffing Model: Erlang-A (M/M/n +M)
agents
1
arrivals
queue
2
λ
…
n
µ
abandonment θ
Erlang-A Parameters:
I
I
I
I
λ – Arrival rate (Poisson)
µ – Service rate (Exponential)
θ – Impatience rate (Exponential)
n – Number of Service-Agents.
24
Erlang-A: Fitting a Simple Model to a Complex Reality
Hourly Performance vs. Erlang-A Predictions (1 year)
% Abandon
E[Wait]
%{Wait > 0}
1
250
0.9
0.5
0.8
0.4
0.3
0.2
Probability of wait (data)
Waiting time (data), sec
Probability to abandon (data)
200
150
100
0.7
0.6
0.5
0.4
0.3
0.2
50
0.1
0.1
0
0
0.1
0.2
0.3
0.4
0.5
Probability to abandon (Erlang−A)
I
I
0.6
0
0
50
100
150
200
Waiting time (Erlang−A), sec
250
0
0
0.2
0.4
0.6
Empirically-Based & Theoretically-Supported Estimation of
(Im)Patience: θ̂ = P{Ab}/E[Wq ])
Small Israeli Bank (more examples in progress)
25
0.8
Probability of wait (Erlang−A)
1
Testing the Erlang-A Primitives
I
I
I
Arrivals: Poisson?
Service-durations: Exponential?
(Im)Patience: Exponential?
Validation: Support? Refute?
26
May 1959!
Arrivals to Service: only Poisson-Relatives
Time
24 hrs
Arrival Rate to Three Call Centers
(Lee A.M., Applied Q-Th)
Dec. 1995 (U.S. 700 Helpdesks)
May 1959
(England)
Q-Science
Arrival Process, in 1999
Arrival
Rate
% Arrivals
Yearly
Monthly
Dec 1995!
May 1959!
Time
24 hrs
Time
24 hrs
(Help Desk Institute)
November 1999 (Israel)
28
(Lee A.M., Applied Q-Th)
Daily
Hourly
% Arrivals
Dec 1995!
Observation:
Peak Loads at 10:00 & 15:00
27
Time
24 hrs
Service Durations: LogNormal Prevalent
Israeli Bank
Log-Histogram
Survival-Functions
Service
Time
by Service-Class
Survival curve, by Types
900
800
700
NW (New) = 11
PS (Regular) = 1
600
500
Survival
Frequency
Means (In Sec
Average = 2.24
St.dev. = 0.42
400
300
NE (Stocks) = 2
IN (Internet) =
200
100
0
0.8
1
1.2 1.4 1.6 1.8
2
2.2 2.4 2.6 2.8
3
3.2 3.4 3.6 3.8
Log(service time)
frequency
Time
normal curve
3
I
I
New Customers: 2 min (NW);
Regulars: 3 min (PS);
I
I
Stock: 4.5 min (NE);
Tech-Support: 6.5 min (IN).
Observation: VIP require longer service times.
28
(Im)Patience while Waiting (Palm 1943-53)
Irritation ∝ Hazard Rate of (Im)Patience Distribution
Regular over VIP Customers – Israeli Bank
16
I
14
I
Peaks of abandonment at times of Announcements
Call-by-Call Data (DataMOCCA) required (& Un-Censoring).
Observation: VIP are more patient (Needy)
29
A “Service-Time" Puzzle at a Small Israeli Bank
'
$
Inter-related Primitives
Figure 12: Mean Service Time (Regular) vs. Time-of-day (95% CI) (n =
42613)
180
160
100
120
140
Mean Service Time
200
220
240
Average Service Time over the Day – Israeli Bank
7
&
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
%
Time of Day
11
30
Prevalent: Longest services at peak-loads (10:00, 15:00). Why?
Explanations:
I Common: Service protocol different (longer) during peak times.
I Operational: The needy abandon less during peak times;
hence the VIP remain on line, with their long service times.
30
Erlang-A: Simple, but Not Too Simple
Experience:
I Arrival process not pure Poisson (time-varying, σ 2 too large)
I Service times not exponential (typically close to lognormal)
I Patience times not exponential (various patterns observed).
I Customers and Servers not homogeneous (classes, skills)
Questions naturally arise:
1. Why does Erlang-A practically work? justify robustness.
2. When does it fail? chart boundaries.
3. Generalize: time-variation, SBR, networks, uncertainty , . . .
Answers via Asymptotic Analysis, as load- and staffing-levels ↑ ,
which captures model-essentials:
I
I
Efficiency-Driven (ED) regime: Fluid models (deterministic).
Quality- and Efficiency-Driven (QED) regime: Diffusion
refinements (eg. revealing that the patience-density at the origin
is “all" that is needed).
31
DataMOCCA = Data MOdels for Call Center Analysis
I
I
I
Technion: P. Feigin, V. Trofimov, Statistics / SEE Laboratory.
Wharton: L. Brown, N. Gans, H. Shen (UNC).
industry:
I
I
U.S. Bank: 2.5 years, 220M calls, 40M by 1000 agents.
Israeli Cellular: 2.5 years, 110M calls, 25M calls by 750 agents;
ongoing.
Project Goal: Designing and Implementing a (universal)
data-base/data-repository and interface for storing, retrieving,
analyzing and displaying Call-by-Call-based Data / Information.
System Components:
I Clean Databases: operational-data of individual calls / agents.
I Graphical Online Interface: easily generates graphs and tables,
at varying resolutions (seconds, minutes, hours, days, months).
Free for academic adoption: Mini version available on a DVD;
working version 7GB tables, or 20GB raw zipped, for each call
center – ask for my mini-HD.
32
Arrivals to Service: Predictable vs. Random
Arrival Rates on Tuesdays in a September – U.S. Bank
3500
3000
Arrival rate
2500
2000
1500
1000
500
0
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.)
04.09.2001
I
I
I
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.
33
A “Waiting-Times" Puzzle at a Medium Israeli Bank
waitwait
0.9
Relative frequencies, %
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380
Time (Resolution 1 sec.)
Page 1
Peaks Every 60 Seconds. Why?
I Human: Voice-announcement every 60 seconds.
I System: Priority-upgrade (unrevealed) every 60 seconds.
Served Customers
Abandoning Customers
waithandled
waitab
0.6
0.9
0.5
Relative frequencies, %
Relative frequencies, %
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.4
0.3
0.2
0.1
0.1
0.0
0.0
20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380
20
Time (Resolution 1 sec.)
40
60
80 100 120 140 160 180 200 220 240 260 280 300 320 340
Time (Resolution 1 sec.)
Page 1
Page 1
34
Priorities, Economies-of-Scale, SBR
Regular vs. VIP Customers: Cellular – March 23, 2004
Average Wait
Staffing Level
50
60
50
40
Number of agents
Average waiting time, sec
45
35
30
25
20
15
10
40
30
20
10
5
0
7:00
9:00
11:00
13:00
15:00
17:00
19:00
21:00
0
7:00
23:00
9:00
11:00
13:00
Time
Private
15:00
17:00
19:00
21:00
Time
Private Platinum
Private
Private Platinum
I
Design: VIP-dedicated agents, Regular-dedicated Agents.
VIP’s are not served better than Regular’s
I
Solutions: Add VIP agents (costly), or Re-Design.
I
35
23:00
Priorities and Routing Protocols I
Regular vs. VIP Customers: Cellular – October 2004
Average Wait
40
90
35
80
Average Wait, sec
Delay Probability, %
Delay Probability
100
70
60
50
40
30
20
25
20
15
10
5
10
0
7:00
30
9:00
0
7:00
11:00 13:00 15:00 17:00 19:00 21:00 23:00
Private
9:00
11:00 13:00 15:00 17:00 19:00 21:00 23:00
Time (Resolution 30 min.)
Time (Resolution 30 min.)
Private Platinum
Private
Private Platinum
More VIPs delayed than Regulars, yet their average wait is shorter.
What changed since last March?
36
Priorities and Routing Protocols II
Waiting-Time Histograms: Cellular – October 2004
Regular Customers
VIP (Platinum) Customers
private_hist
platinum_hist
3.0
18.0
Relative frequencies, %
Relative frequencies, %
16.0
2.5
2.0
1.5
1.0
0.5
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
0.0
2
14
26
38
50
62
74
86
98
2
Time (Resolution 1 sec.)
14
26
38
50
62
74
Time (Resolution 1 sec.)
Page 1
Page 1
After 25 seconds of wait, VIP customers are routed with high
priority to Regular agents. Hence, almost no long waiting times for
VIP’s.
37
86
Distributed via
Call Center
(U.S. Bank) at a U.S. Bank
Network Balancing
Inter-Queues
10 AM – 11 AM (03/19/01): Interflow Chart Among the 4 Call
C t
f Fl t B k
Internal arrivals:
224
•
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 t3
•
Internal arrivals:
643
•
Served at 1:
67 (29.9)
Served at 2:
41 (18.3)
Served at 3:
87 (38.8)
Served at 4:
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
•
•
•
•
2
NY
1
179
+5
619
+3
19
+1
•
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)
•
•
•
•
Served here: 110
(41.2/6.2)
Served at 1:58
(21 7/3 3)
External arrivals: 122
112(91.8
Served)+10(8.2 Aban)
M
A4
Internal arrivals: 613
•
Served: 1497
(99.6/84.6)
Aban: 6 (0.4/0.3)
Interqueued:258+9
(15.1)
•
11
+1
101+
2
PA
2
•
Not Interqueued:
1503(84.9)
74
+7
508
+2
External arrivals: 1694
1687(99.6%
Served)+7( 0.4% Aban)
•
RI
3
8+
1
20
External arrivals: 1770
1755(99.2
Served)+15(0.8 Aban)
Internal arrivals:
81
Served at 1:
41(6.7)
Served at 2:
513(83.7)
Served at 3:
55(9.0)
Aban at 1:
2(0.3)
•
•
•
38
Served at 1:
17(21)
Served at 3:
42(51.9)
Served at 4:
15(18 5)
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
Balancing Protocols and Performance Level
U.S. Bank: Histograms of Waiting Times
Retail
Business
Chart1
Sheet3 Chart 1
12
20
10
16
Relative frequencies, %
Relative frequencies, %
18
14
12
10
8
6
4
8
6
4
2
2
0
0
2
5
8
11
14
17
20
23
26
29
32
35
2
Time
8
14
20
26
32
38
44
50
56
62
68
74
80
86
Time
Page 1
Page 1
Peak for Retail service at 10 seconds – Why?
After 10 seconds of wait, Retail customers sent into the inter-queue.
Business customers – peak at 5 seconds, for the same reason.
Second peak – unclear, maybe priority-upgrade.
39
92
Data-Based Service-Research
(with DataMOCCA, even before tenure)
I
I
I
Contrast with EmpOM: Industry / Company / Survey Data
(Social Sciences)
Converge to: Measure, Model, Validate, Experiment, Refine
(Physics, Biology, . . .).
Prerequisites:
I
I
I
OR, OM, IE, (Mktg.) - for Design
CS, IS, Stat. - for Implementation.
Outcomes: Relevance, Credibility; Interest, Fun;
Call Centers as a Pilot (eg. for Healthcare). Moreover,
I
I
I
Teaching: Class, Homework (Experimental Data Analysis); Cases.
Research: Validate Existing (Queueing) Theory/Laws and Suggest
New Models/Research.
Practice: OM Tools (Scenario Analysis), Mktg. (Trends,
Benchmarking).
40
Live Demonstration of DataMOCCA
5-7 minutes, to emphasize “online" capabilities.
U.S. Bank
I
I
I
Daily Reports: October 2003, weekdays; typically takes 10-20
sec till a first output, but this is because of PowerPoint/Windows.
Then do few additional Daily Reports, say Monday, Tuesday,...
(starting with STATCCA, as opposed to by minimizing the
powerpoint screnn) - this will be now happening very fast.
Time-Series: Number of agents, for ALL classes, all months,
weekdays. (Including total). Shows scale, trends. Then do
Service Durations, indicating that 1 second of 1000 agents could
cost $500M per year. Could also do Unhandled (lower middle
entry in list), for only Retail and Premium - Premium is worse,
and deteriorating,
Daily Summaries:
I
I
I
Tuesdays in September 2001; September 11th; shown during
lecture under the heading “Predictable or Random";
30 sec scale - stoch. variability, 1 hour scale - the “right" scale;
% to mean, to show very similar shape over 3 Tuesdays. Suggests
the model λ(t) = λ0 (t) · Z , for 0 ≤ t ≤ T .
41