1 Chapter 4 Decision Making. 2 Advanced Organizer.

1

Chapter 4Decision Making

2

Advanced Organizer

D ecision Mak ing

P lanning

O rganizing

Leading

C ontro lling

Managem ent Functions

R esearch

D esign

Production

Q uality

Marketing

Project Managem ent

Managing Technology

Tim e Managem ent

E thics

C areer

Personal Technology

Managing Engineering and Technology

3

Chapter Objectives

• Discuss how decision making relates to planning• Explain the process of engineering problem

solving• Be able to solve problems using three types of

decision making tools• Discuss the differences between decision

making under certainty, risk, and uncertainty• Describe the basics of other decision making

techniques

4

Relation to Planning

Managerial decision making is the process of making a conscious choice between two or more rational alternatives

5

Types of Decisions

• Routine and Non-Routine Decisions

• Objective vs. Bounded Rationality

• Level of Certainty

6

Management ScienceCharacteristics

• Systems view of the problem

• Team approach

• Emphasis on use of formal mathematical models and statistical and quantitative techniques

7

Models & Analysis

• Formulate the problem

• Construct a mathematical model

• Test the model’s ability

• Derive a solution from the model

• Apply model’s solution to real system

8

Categories of Decision Making

• Decision Making under Certainty (Only one state of nature exists.)

• Decision Making under Risk (Probabilities for states of natures are known.)

• Decision Making under Uncertainty (Probabilities for states of natures are unknown.)

9

Payoff Table

Omn....Omj....

................

Oin....Oij....

................

O2n....O2j....

O1n....O1j....

Om2

....

Oi2

....

O22

O12

Om1

....

Oi1

....

O21

O11

(Pn)....(Pj)....(P2)(P1)

Nn....Nj....N2N1

Am

....

Ai

....

A2

A1

Alt.

10

Payoff Tablefor Decision Making under Certainty

Omn....Omj....

................

Oin....Oij....

................

O2n....O2j....

O1n....O1j....

Om2

....

Oi2

....

O22

O12

Om1

....

Oi1

....

O21

O11

(Pn)....(Pj)....(P2)(P1)

Nn....Nj....N2N1

Am

....

Ai

....

A2

A1

Alt. 1.0

11

Tools for Decision Making under Certainty

• Linear programming– Graphical solution– Simplex method– Computer software

• Non-linear programming

• Engineering Economic Analysis

12

Linear Programming

• Decision Variables

• Objective Function (Maximizing or Minimizing)– Example:

• A factory produces two products, product X and product Y. If we can realize $10 profit per unit of product X and $14 per unit of Y, what should be the production level for product X and product Y?

– Maximize P = 10x + 14y

13

Linear Programming

• Constrains– Example:

• 3 machinists• 2 assemblers• Each works 40 hours/week• Product X requires 3 hours of machining and 1

hour of assembly per unit• Product Y requires 2 hours of machining and 2

hours of assembly per unit– For machining time: 3x + 2y 3(40)– For assembly time: 1x + 2y 2(40)

14

Linear programming Graphical solution (Constraints)

3x+2y≤120

(40,0)

(0,60)

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

Y

X

x+2y≤80

(80,0)

(0,40)

Feasible Region

Corner Solutions

15

Linear programming Graphical solution (Objective Function)

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

Y

X

P=10x+14y

P=1050

P=700

P=350

16

Linear programming Graphical solution (Objective Function)

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

Y

X

P=10x+14y

P=1050

P=700

P=350

17

Linear programming Graphical solution

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

Y

X

Optimal Solution(20, 30)

18

Linear programming Simplex method

 BV

Coefficient ofRS

Ratio

P X Y S1 S2 

P 1 -10 -14 0 0 0  

S1 0 3 2 1 0 120 60

S2 0 1 2 0 1 80 40P 1 -3 0 0 7 560  

S1 0 2 0 1 -1 40 20

Y 0 1/2 1 0 1/2 40 80P 1 0 0 3/2 11/2 620  

X 0 1 0 1/2 -1/2 20  

Y 0 0 1 -1/4 3/4 30  

19

Linear programming Computer Software

• Excel: Solver

• LINDO: www.lindo.com

max 10x + 14 y

subject to

M) 3x + 2y <= 120

A) x + 2y <= 80

end

20

Engineering Economic Analysis

• Time Value of Money

• Minimum Acceptable Rate of Return

• Decision Criteria– Net Present Worth– Equivalent Annual Worth– Internal Rate of Return– Benefit / Cost Ratio

21

Payoff Tablefor Decision Making under Risk

Omn....Omj....

................

Oin....Oij....

................

O2n....O2j....

O1n....O1j....

Om2

....

Oi2

....

O22

O12

Om1

....

Oi1

....

O21

O11

(Pn)....(Pj)....(P2)(P1)

Nn....Nj....N2N1

Am

....

Ai

....

A2

A1

Alt.

22

• Expected value

Tools for Decision Making under

Risk

n

1jijji OpE

• Decision treesDecision NodeChance Node

• Queuing theory• Simulation

23

Payoff Table & Expected Value(Fire Insurance)

-$100

-$200

-$100,0000

-$200-$200

Expected

Value

A2=Self-Ins.

A1=Buy Ins.

(Fire)(No Accident)P2=0.001P1=0.999

N2N1

24

Decision Trees

• Decision tree graphically displays all decisions in a complex project and all the possible outcomes with their probabilities.

Decision Node

D1

D2

DX

Chance Node

C1

C2

CY

p1

p2

py

Outcome Node

Pruned Branch

25

Decision Tree(Fire Insurance)

-$200

-$200FireP=0.001

$0

-$100,000

No accidentP=0.999

FireP=0.001

Buy Insurance$200

Self-Insure$0

EV=-$200

EV=-$100

No accidentP=0.9No accidentP=0.999

26

Payoff Table & Expected Value(Car Insurance)

$36$500$300$0

$411$13,000$300$0

A1=Buy Ins. ($800)

A2=Self-Ins.

($500 Deduc.)

Expected

Value

(Totaled)(Small Accident)

(No Accident)

P3=0.03P2=0.07P1=0.90

N3N2N1

27

Decision Tree(Car Insurance)

$0

$300 (<$500 deductible)

$500TotaledP=0.03

$0

$300

$13,000

No accidentP=0.9

Small accidentP=0.07

TotaledP=0.03

Buy Insurance$800

Self-Insure$0

EV=$36

EV=$411

No accidentP=0.9No accidentP=0.9

Small accidentP=0.07

Small accidentP=0.07

28

Payoff Table & Expected Value(Well Drilling)

Value

Expected

$162.5k$1,250k$125k$0

$720k$9,300k$300k-$500k

$0$0$0$0

A3:Farm out

A2:Drill alone

A1:Don’t drill

P3=0.1P2=0.3P1=0.6

BigSmallDry

N3N2N1

29

Decision Tree(Well Drilling)

$0

$0

$0Big well P=0.1Don’t drill $0

Farm out $0

EV=$0

EV=$162.5k

Dry P=0.6

Small well P=0.3

-$500k

$300k

$9,300kBig well P=0.1

Dry P=0.6

Small well P=0.3

$0

$125k

$1,250kBig well P=0.1

Dry P=0.6

Small well P=0.3

Drill alone $500k

EV=$720k

30

Decision Tree(New Product Development)

1. Build New Product

2. Volume forNew Product

3. $0No

YesFirst cost=$1M

4. Net Revenue Year 1=$100K

7. Revenue=$0

8.Revenue=$100K/yr

6. Net Revenue Year 1=$400K

9. Revenue=$600K/yr

10.Revenue=$400K/yr

5. Revenue Year 1, 2..8 =$200K

Low Volume P=0.3

Med. Volume P=0.6

High Volume P=0.1

Terminate

Continue

Continue

ExpandFirst cost=$800K

t=0 t=1 t=2, …,

31

Decision Tree (New Product Development)

1. Build New Product

2. Volume forNew Product

3. $0No

YesFirst cost=$1M

4. Net Revenue Year 1=$100K

7. Revenue=$0

8.Revenue=$100K/yr

6. Net Revenue Year 1=$400K

9. Revenue=$600K/yr

10.Revenue=$400K/yr

5. Revenue Year 1, 2..8 =$200K

Low Volume P=0.3

Med. Volume P=0.6

High Volume P=0.1

Terminate

Continue

Continue

ExpandFirst cost=$800K

t=0 t=1 t=2, …,

PW1=$550,000

PW1=$486,800PW=$590,915

PW=$1,067,000

PW1=$2,120,800

PW1=$1,947,200PW=$2,291,660

EV=$1,046,640

32

Queuing Theory

• Basics Goal: make an analytical model of customers needing service, and use that model to predict queue lengths and waiting times.

a9 a8 a7 a6 a5 a4 a3 a2 a1 Server

Queue

33

Queuing Theory - Terminology

• Customers — independent entities that arrive at random times to a Server and wait for service, then leave.

• Server — can only service one customer at a time; length of time to provide service depends on type of service; customers are served in FIFO order.

• Time — real, continuous, time.• Queue — customers that have arrived at server but are

waiting for their service to start are in the queue.• Queue Length at time t — number of customers in the

queue at time t.• Waiting Time — for a given customer, how long that

customer has to wait between arriving at the server and when the server actually starts the service (total time is waiting time plus service time).

34

Types of Queuing Models

• M/M/1 — exponential arrival rate and service times, with 1 server (like office hours).

• M/M/m — exponential arrival rate and service times, with m servers (like grocery store with many checkout lanes).

• M/M/m/m — exponential arrival rate and service times, with m servers, but nobody waits in queue (if all m servers are busy when a customer arrives, that customer gives up and leaves).

• M/M/ — exponential arrival rate and service times, with unlimited number of servers (customers never wait in queue).

35

Types of Queuing Models

• M/D/1 —service times are deterministic (e.g. a constant, fixed service time regardless of customer).

• M/G/1 — exponential arrival rate, but service rate has a “general” (arbitrary) probability distribution, and a single server.

• M/G/m —same as above, but with m servers.

36

Simulation

To study a system

Experiment with actual system – Live Simulation

Experiment with a model of system

Physical model —Virtual

Simulation

Mathematical model

Analytical Solution

Computer Simulatio

n

37

Simulation

Simulation modeling seeks to:• Describe the behavior of a system• Use the model to predict future behavior,

i.e. the effects that will be produced by changes in the system or in its method of operation.

38

Simulation

Types of Simulation Modes:• Continuous Simulation

– For systems vary continually with time

• Discrete Simulation– For systems change only at discrete set of points in

time (state changes)

• Hybrid

39

Applications of Simulation

• Testing new designs, layouts without committing resources to their implementation

• Exploring new policies, procedures, rules, structures, information flows, without disrupting the ongoing operations.

• Identifying bottlenecks in information, material and product flows and test options for increasing the flow rates.

• Testing hypothesis about how or why certain phenomena occur in the system.

• Gaining insights into how a system works and which variables are most important to performance.

• Experimenting with new and unfamiliar situations and to answer "what if" questions.

40

Advantages and Limitations of Simulation

+ Easy to comprehend + Credible because the behavior can be validated + Fewer simplifying assumptions

- Requires specialized training and skills - Utility of the study depends upon the quality of the model - Data Gathering reliable input data can be time consuming- “Run" rather than solved. - Do not yield an optimal solution, rather they serve as a

tool for analysis

41

Simulation Tools

• General purpose language– C, C++, Java, Visual BASIC

• General simulation language– Discrete simulation: AutoMod, Arena, GASP, GPSS,

SIMAN, SimPy, SIMSCRIPT II.5– Continuous simulation: ACSL, Dynamo, SLAM ,VisSim– Hybrid: EcosimPro Language (EL), Saber-Simulator,

Simulink, Z simulation language, Flexsim 4.0 • Special purpose simulation package

– Chemical process, electrical circuits, transportation

42

Risk as Variance

$4000$4000Mean

$1140$548Std. Deviation

$60000.10

$30000.25

$40000.30

Cash F. Prob.

$50000.25

$20000.10

Project Y

$50000.10

$35000.20

$40000.40

Cash F.Prob.

$45000.20

$30000.10

Project X

43

Risk as Variance

Probability

Cash Flow

X

Y

44

Payoff Table for Decision Making under Uncertainty

Omn....Omj....

................

Oin....Oij....

................

O2n....O2j....

O1n....O1j....

Om2

....

Oi2

....

O22

O12

Om1

....

Oi1

....

O21

O11

(Pn)....(Pj)....(P2)(P1)

Nn....Nj....N2N1

Am

....

Ai

....

A2

A1

Alt.

45

Tools for Decision Making under Uncertainty

• Laplace criteria (Equally likely)

• Maximax criteria

• Maximin criteria

• Hurwicz criteria

• Minimax regret criteria

• Game theory

46

Laplace criteria (Equally likely)

N1 N2 .... Nj .... Nn Max

Alt. (P1) (P2) .... (Pj) .... (Pn)

A1 O11 O12 .... O1j .... O1n EV1

A2 O21 O22 .... O2j .... O2n EV2

.... .... .... .... .... .... .... ....

Ai Oi1 Oi2 .... Oij .... Oin EVi

.... .... .... .... .... .... .... ....

Am Om1 Om2 .... Omj .... Omn EVm

1/n 1/n 1/n 1/n

47

Payoff Table(Well Drilling – Equally likely)

$458k$1,250k$125k$0

$3033k

$0$0$0$0

A3:Farm out

A2:Drill alone

A1:Don’t drill

Value

Expected

BigSmallDry

N3N2N1

$9,300k$300k-$500k

48

Maximax Criteria

MAXmOmn....Omj....Om2Om1

............................

MAXiOin....Oij....Oi2Oi1

............................

MAX2

MAX1

Max.

Am

....

Ai

....

A2

A1

Alt.

Nn....Nj....N2N1

O1n....O1j....O12O11

O2n....O2j....O22O21

49

Payoff Table(Well Drilling - Maximax)

Max.

$1,250k$1,250k$125k$0

$9,300k$9,300k$300k-$500k

$0$0$0$0

A3:Farm out

A2:Drill alone

A1:Don’t drill

BigSmallDry

N3N2N1

50

Maximin Criteria

MINmOmn....Omj....Om2Om1

............................

MINiOin....Oij....Oi2Oi1

............................

MIN2

MIN1

Max.

Am

....

Ai

....

A2

A1

Alt.

Nn....Nj....N2N1

O1n....O1j....O12O11

O2n....O2j....O22O21

51

Payoff Table(Well Drilling - Maximin)

Min.

$0$1,250k$125k$0

-$500k$9,300k$300k-$500k

$0$0$0$0

A3:Farm out

A2:Drill alone

A1:Don’t drill

BigSmallDry

N3N2N1

52

Hurwicz Criteria

MAXm MINm

MAX2 MIN2

MAX1 MIN1

(1-)

Im.... Omn....OmjOm2Om1

.... ........ .... ....................

Ii.... Oin....OijOi2Oi1

.... ........ .... ....................

I2.... O2n....O2jO22O21

I1.... O1n....O1jO12O11

Max

Am

....

Ai

....

A2

A1

Alt.

Index.... Nn....NjN2N1

MAXi MINi

Index = (MAX) + (1 - )(MIN)

53

Payoff Table(Well Drilling - Hurwicz)

$1,250k $0

$9,300k -$500k

$0 $0

Max. Min.

$250k$1,250k$125k$0

$1460k$9,300k$300k-$500k

$0$0$0$0

A3:Farm out

A2:Drill alone

A1:Don’t drill

Index

(=0.2)

BigSmallDry

N3N2N1

54

Minimax Regret Criteria

• First convert payoff table to regret table

Omn....Omj....

................

Oin....Oij....

................

O2n....O2j....

O1n....O1j....

Om2

....

Oi2

....

O22

O12

Om1

....

Oi1

....

O21

O11

Nn....Nj....N2N1

Am

....

Ai

....

A2

A1

Alt.

• Work on one state of nature at a time

• Identify the maximum output in that state

• Regret = Max. output - output

• Repeat for all states of nature

55

Minimax Regret Criteria

Rmn

....

Rin

....

R2n

R1n

Nn

MAXm

....

MAXi

....

MAX2

MAX1

Am

....

Ai

....

A2

A1

Alt.

Min.

....

....

....

....

....

....

....

Rmj

....

Rij

....

R2j

R1j

Nj

....

....

....

....

....

....

....

Rm2

....

Ri2

....

R22

R12

N2

Rm1

....

Ri1

....

R21

R11

N1

56

Payoff Table & Regret Table(Well Drilling – Minimax Regret)

Payoff

$1,250k$125k$0$9,300k$300k-$500k

$0$0$0

A3:Farm out

A2:Drill alone

A1:Don’t drillBigSmallDry

N3N2N1

MaxRegret

$8,050k

$500k$9,300k

$8,050k

$0$9,300k

$175k

$0$300k

$0

$500k$0

A3:Farm out

A2:Drill alone

A1:Don’t drillBigSmallDry

N3N2N1

57

Game theory

• Game theory attempts to mathematically capture behavior in strategic situations, where an individual’s success in making choices depends on the choices of others.

• Traditional applications of game theory attempt to find equilibria in these games—sets of strategies where individuals are unlikely to change their behavior.

58

Game theory (Example)

2nd-best for U.S.S.R.

2nd-best for U.S.

Best for U.S.S.R.

Worst for U.S.

Worst for U.S.S.R.

Best for U.S.

3rd-best for U.S.S.R.

3rd-best for U.S.

Disarm

Arm

U.S. Strategy DisarmArm

Soviet Strategy

59

Computer-Based Information Systems

• Integrated Database

• CAD/CAM

• Management Information Systems (MIS)

• Decision Support Systems (DSS)• Expert Systems