1 Chapter 4 Decision Making
Jan 21, 2016
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Chapter 4Decision Making
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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
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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
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Relation to Planning
Managerial decision making is the process of making a conscious choice between two or more rational alternatives
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Types of Decisions
• Routine and Non-Routine Decisions
• Objective vs. Bounded Rationality
• Level of Certainty
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Management ScienceCharacteristics
• Systems view of the problem
• Team approach
• Emphasis on use of formal mathematical models and statistical and quantitative techniques
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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
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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.)
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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.
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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
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Tools for Decision Making under Certainty
• Linear programming– Graphical solution– Simplex method– Computer software
• Non-linear programming
• Engineering Economic Analysis
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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
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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)
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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
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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
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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
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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)
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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
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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
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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
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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.
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• Expected value
Tools for Decision Making under
Risk
n
1jijji OpE
• Decision treesDecision NodeChance Node
• Queuing theory• Simulation
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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
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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
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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
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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
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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
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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
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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
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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, …,
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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
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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
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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).
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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).
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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.
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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
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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.
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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
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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.
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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
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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
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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
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Risk as Variance
Probability
Cash Flow
X
Y
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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.
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Tools for Decision Making under Uncertainty
• Laplace criteria (Equally likely)
• Maximax criteria
• Maximin criteria
• Hurwicz criteria
• Minimax regret criteria
• Game theory
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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.
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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
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Computer-Based Information Systems
• Integrated Database
• CAD/CAM
• Management Information Systems (MIS)
• Decision Support Systems (DSS)• Expert Systems