Service Engineering September, 2002 Last Revised: May, 2004 Why Queues ? via Dynamic Stochastic PERT/CPM Networks • Product/Service development • Project management Both "enjoy": - Stochastic environment - Multi-projects - Scarce resources 1
Service Engineering September, 2002
Last Revised: May, 2004
Why Queues ?
via Dynamic Stochastic PERT/CPM Networks
• Product/Service development
• Project management
Both "enjoy":
− Stochastic environment
− Multi-projects
− Scarce resources
1
History
• Product Development
− with Adler, P., Nguyen, V., Schwerer, E. (Management Science, HBR)
• Project Management
− Lamberg, Y. (M.Sc.) – Israeli Electric
− Baron, Y. (M.Sc.) – Conceptual Framework
− IE&M Projects – Software Development
− Cohen, I. (Ph.D.) – TOC vs. DS-PERT/CPM
3
• Teaching
− Static Deterministic Models
− Static Probabilistic
− Dynamic Stochastic
• Models: DS-PERTs (Fork-Join, Split-Match, ...).
− Important theoretically and practically.
− Intractable theoretically: simulation, approx.
3
4
Stochastic PERT / CPM
Activities A B C
Avg. Durat n 3 4 5
Distri tion 3 4 1 or 9
wp ½ and ½ A
Project time
io
bu
B
C
F S
max {3, 4, 1} = 4 wp ½
max {3, 4, 9} = 9 wp ½ =
4
5
Dyn c Stochastic PERT
Activities, Resources, Ra urations
Multiple projects
FS
A
C
Depart ArriveB
Queues due to
Scare Resources
Queues due to
Synchronization Gaps
5
ndom d
ami
6
Arrest - to – Arraignment (Lars
Arr.
Off.Arr.
Off.
Arrive at
Central
Booking
(5 hrs.)
Arrives at
Complaint
Room
(6 hrs.)
Complaint
Sworn
(14 hrs.)
A
C
(
Lodged at
Precinct
(12 hrs.)
Transmit-
-ted to
Albany
(10 hrs.)
Rap Sheet
Received
(15 hrs.)
P
C
(Fingerprint.
Off.
Arrive at
Precinct
(1 hr.)
Arrest
(0 hrs.)
Arr. Arr.
Off. = Arresting Officer.
Arr. = Arrestee Cards
Sourc
Impro
Larso
Interfa
3
1
e
v
n
on, ...)
rrives at
ourthouse
9 hrs.)
aperwork
ompleted
8 hrs.)
Arrestee
Arraigned
(48 hrs.)
:
ing the N.Y.C A-to-A system
, R. Cahn, M. Shell, M.
ces 23, 1993
6
Stochastic dynamic model:
Avg. 44.0 hoursStd. 16.2
Should be less than24 hours.
Arrest to Arraignment Time7
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
0-20
20-25
25-30
30-35
35-40
40-45
45-50
50-55
55-60
60-65
65-70
70-75
75-80
80-85
85-90
90-100
>100
Total Elapsed Arrest to Arraignment Time (in Hours)
Prob
abili
ty
7
8
Traditional PERT/CPM Representation
Project View
Specifications w50
Construction w110
General Layout w15
Locating Area w40
Conceptual Design w10
Build Permit w25
Electrical Design w40
Repartition
Start w0
Equipment w50
Electro- Mechanics Design w20
Conceptual Schema w15
Civil Eng. Programs w40
critical path End w0
80 activities 25 departments 500 projects
T = 250 weeks ? 8
w75
9
Processing Network Representation
Purchasing
Research
Assets
Conceptual
Design Conceptual
Schema
Equipment
Mechanical Eng.
Electro Mechanic
Design
General
Layout Conceptual
Design
Conceptual
Design
S
Specifications
Electrical Eng.
Civil Eng. EConstruction
Electric
Design
Civil
Programs Area
Locate
Resource
Synchronization Queue
Service Queue
Build Permit
Repartition
Workflow
9
Electrical Electro-Mechanic Electro-Mechanic Electro-Mechanic
Combined Outdoor IndoorEmployees Utilization Employees Utilization Employees Utilization Employees Utilization
6 129% 10 107% 4 79% 6 131%
7 117% 12 96% 5 67% 7 120%8 108% 14 88% 6 59% 8 112%9 101% 16 82% 7 54% 9 105%
10 95% 17 80% 7 54% 10 100%11 91% 18 78% 7 54% 11 96%12 87% 19 76% 7 54% 12 93%
Can We Do It ?10
of the number of employees:
Capacity Analysis -
Utilization as a function
[= Fluid-view (first moments)]
10
1214
16 17 18 194
56
7 7 7 7
121110
98
7
6
0.4
0.6
0.8
1
1.2
1.4
Employees
Util
izat
ion
ElectricalMech-CombinedMech-OutdoorMech-Indoor
10
Stochastic static model (single project):
Avg. 338 weeksStd. 10090% 475Det. 250
How long Will It Take ?11
0
0.05
0.1
0.15
0.2
0.25
0 150 300 450 600 750 900 1050
Completion Time in Weeks
Prob
abili
ty
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cum
ulat
ive
Dis
tribu
tion
11
Stochastic dynamic model:4 Types:TypeNew sub-station 3.27New switching stations 0.6Improvements 3.4Additional capacity 1.9
Avg. 485 weeksStd. 19990% 770Det. 250
Per year
How Long Will It Take ?12
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 150 300 450 600 750 900 1050
Completion Time in Weeks
Prob
abili
ty
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cum
ulat
ive
Dis
tribu
tion
12
Relieving bottlenecks:Unlimited resources:( = Stochastic static)Avg. 6 years.10% over 9 years.
6 years avg. too long.=> Resources NOT the
problem !
(Infinite-server modelsare important).
Can We Do Better ?13
0
0.05
0.1
0.15
0.2
0.25
0 150 300 450 600 750 900 1050
Completion Time in Weeks
Prob
abili
ty
Unlimited resources (static) - 338 weeks
Civil Eng. dept. - 458
Base case - 485 weeks
Electrical dept. - 394 weeks
13
New location management and standardization:Base New
New location mgt:40 weeks, 8 weeks0.5 prob. of repeat 0.8 prob.
Standardization:8000 hrs. planning, 2000repeats, nonelong execution times 25%
Avg. 485 weeks 189Std. 199 5590% 770 294
Can We Do Better ?14
0
0.1
0.2
0.3
0.4
0.5
0 100 200 300 400 500 600 700 800 900 1000 1100
Completion Time in Weeks
Prob
abili
ty
14
15
Summary
E σ 90%
Deterministic 251 weeks 0 251
Stochastic Static
Single-Project
338 100 475
Stochastic Dynamic
Multi-Projects
485 200 770 (14 years)
Infinite Resources 338 ... ...
Re-Engineering 189 55 294
15