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