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

Dynamic Stochastic PERT

Activities, Resources, Random durations

Multiple projects

FS

A

C

Depart ArriveB

Queues due to

Scarce Resources

Queues due to

Synchronization Gaps

5

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

Electrical Eng.

Purchasing

Civil Eng. Research EConstruction

Assets

Conceptual

Design Conceptual

Schema

Equipment

Mechanical Eng.

Electro Mechanic

Design

Electric

Design

Build Permit

Repartition

General

Layout Conceptual

Design

Conceptual

Design

S

Specifications

Civil

Programs Area

Location

Resource

Synchronization Queue

Service Queue

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