1. Chapter 4 Decision Making

2. Advanced Organizer

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 Science Characteristics
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 Am .... Ai A2 A1 Alt. Nn .... Nj N2 N1 (Pn) .... (Pj)
Om1
....
Oi1
O21
O11
Om2
....
Oi2
O22
O12
Omn
....
Omj
Oin
Oij
O2n
O2j
O1n
O1j

10. Payoff Table for 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 N2 N1 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)Y 10 20 30 40 50 60
(0,60)
(0,40)
3x+2y≤120
Corner Solutions
x+2y≤80
Feasible Region
(40,0)
(80,0) X

15. Linear programming Graphical solution (Objective Function)Y 10 20 30 40 50 60
P=10x+14y
P=1050
P=700
P=350 X

16. Linear programming Graphical solution (Objective Function)Y 10 20 30 40 50 60
P=10x+14y
P=1050
P=700
P=350 X

17. Linear programming Graphical solutionY 10 20 30 40 50 60
Optimal Solution
(20, 30) X

18. Linear programming Simplex methodBV
Coefficient of RS
Ratio P X Y S1 S2 P 1
-10
-14 S1 3 2
120 60 S2 80 40 P 1 -3 7
560 S1 2 -1 40 20 Y
1/2 80 P 1
3/2
11/2
620 X
1/2
-1/2 20 Y
-1/4
3/4 30

19. Linear programming Computer Software
Excel: Solver
LINDO:
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 Table for 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 N2 N1 Am Ai A2 A1
Alt.

22. Tools for Decision Making under Risk
Expected value
Decision trees
Decision Node
Chance Node
Queuing theory
Simulation

23. Payoff Table & Expected Value (Fire Insurance)
(No Accident)
P2=0.001
P1=0.999 N2 N1
Expected
Value
A2=Self-Ins.
A1=Buy Ins.
-$100,000
-$200
-$200
-$100

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
Outcome Node
Chance Node C1 C2 CY p1 p2 py
Pruned Branch

25. Decision Tree (Fire Insurance)
No accident
P=0.9
P=0.999
-$200
EV=-$200
Buy Insurance
$200
Fire
P=0.001
-$200
No accident
P=0.999
Self-Insure $0 $0
EV=-$100
Fire
P=0.001
-$100,000

26. Payoff Table & Expected Value (Car Insurance)
(Totaled)
(Small Accident)
(No Accident)
P3=0.03
P2=0.07
P1=0.90 N3 N2 N1
Expected
Value
A1=Buy Ins. ($800)
A2=Self-Ins.
($500 Deduc.)
$500
$300 $0
$36
$13,000
$300 $0
$411

27. Decision Tree (Car Insurance)
No accident
P=0.9 $0
EV=$36
Small accident
P=0.07
$300
(<$500 deductible)
Buy Insurance
$800
Totaled
P=0.03
$500
No accident
P=0.9 $0
Self-Insure $0
EV=$411
Small accident
P=0.07
$300
Totaled
P=0.03
$13,000

28. Payoff Table & Expected Value (Well Drilling)
Big
Small
Dry N3 N2 N1
Value
Expected
A3:Farm out
A2:Drill alone
A1:Don’t drill $0 $0
$9,300k
$300k
-$500k
$720k
$1,250k
$125k $0
$162.5k

29. Decision Tree (Well Drilling)$0
EV=$0
Dry P=0.6 $0
Small well P=0.3
Don’t drill $0
Big well P=0.1 $0
EV=$720k
Dry P=0.6
-$500k
Small well P=0.3
$300k
Farm out $0
Drill alone $500k
Big well P=0.1
$9,300k
EV=$162.5k $0
Dry P=0.6
$125k
Small well P=0.3
Big well P=0.1
$1,250k

30. Decision Tree (New Product Development)
7. Revenue=$0
Terminate
4. Net Revenue
Year 1=$100K
Low Volume
P=0.3
Continue
8.Revenue=$100K/yr
2. Volume for
New Product
Med. Volume
P=0.6
5. Revenue Year 1, 2..8 =$200K
Yes
First cost=$1M
High Volume
P=0.1
9. Revenue=$600K/yr
Expand
First cost=$800K
6. Net Revenue
Year 1=$400K
Build New
Product No
Continue
10.Revenue=$400K/yr
3. $0
t=0
t=1
t=2, …,

31. Decision Tree (New Product Development)
Build New
Product
2. Volume for
New Product
3. $0 No
Yes
First 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
Expand
First cost=$800K
t=0
t=1
t=2, …,
PW1=$550,000
PW=$590,915
PW1=$486,800
EV=$1,046,640
PW=$1,067,000
PW1=$2,120,800
PW=$2,291,660
PW1=$1,947,200

32. Queuing Theory
Basics Goal: make an analytical model of customers needing service, and use that model to predict queue lengths and waiting times.
Queue a9 a8 a7 a6 a5 a4 a3 a2 a1
Server

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. Physical model —Virtual 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 Simulation

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 General simulation 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 $5000 0.10 $3500 0.20 $4000 0.40 Cash F. Prob. $4500
$3000
Project X
$6000
0.10
$3000
0.25
$4000
0.30
Cash F.
Prob.
$5000
$2000
Project Y
$4000
Mean
$1140
$548
Std. Deviation

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 N2 N1 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)
Big
Small
Dry N3 N2 N1
Value
Expected
A3:Farm out
A2:Drill alone
A1:Don’t drill $0 $0
$9,300k
$300k
-$500k
$3033k
$1,250k
$125k $0
$458k

48. Maximax Criteria Nn .... Nj N2 N1 Max. Am .... Ai A2 A1 Alt. O1n ....
O1j
O12
O11
MAX1
O2n
....
O2j
O22
O21
MAX2
....
....
Oin
....
Oij
Oi2
Oi1
MAXi
....
....
Omn
....
Omj
Om2
Om1
MAXm

49. Payoff Table (Well Drilling - Maximax)
Big
Small
Dry N3 N2 N1
Max.
A3:Farm out
A2:Drill alone
A1:Don’t drill $0 $0
$9,300k
$300k
-$500k
$9,300k
$1,250k
$125k $0
$1,250k

50. Maximin Criteria Nn .... Nj N2 N1 Max. Am .... Ai A2 A1 Alt. O1n ....
O1j
O12
O11
MIN1
O2n
....
O2j
O22
O21
MIN2
....
....
Oin
....
Oij
Oi2
Oi1
MINi
....
....
Omn
....
Omj
Om2
Om1
MINm

51. Payoff Table (Well Drilling - Maximin)
Big
Small
Dry N3 N2 N1
Min.
A3:Farm out
A2:Drill alone
A1:Don’t drill $0 $0
$9,300k
$300k
-$500k
-$500k
$1,250k
$125k $0 $0

52. Hurwicz Criteria .... Nn Nj N2 N1  (1-) Index Am .... Ai A2 A1 Alt.
Max
....
O1n
O1j
O12
O11
MAX1
MIN1 I1
....
O2n
O2j
O22
O21
MAX2
MIN2 I2
....
....
Oin
Oij
Oi2
Oi1
MAXi
MINi Ii
....
....
Omn
Omj
Om2
Om1
MAXm
MINm Im
Index =  (MAX) + (1 - )(MIN)

53. Payoff Table (Well Drilling - Hurwicz)
Big
Small
Dry N3 N2 N1
Index
(=0.2)
Max.
Min.
A3:Farm out
A2:Drill alone
A1:Don’t drill $0 $0 $0
$9,300k
$300k
-$500k
$9,300k
-$500k
$1460k
$1,250k
$125k $0
$1,250k $0
$250k

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 N2 N1 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
Rm1
....
Ri1
R21
R11 N1
Rm2
....
Ri2
R22
R12 N2
....
Rmj
....
Rij
R2j
R1j Nj
....
Rmn
....
Rin
R2n
R1n Nn
Min. Am
.... Ai A2 A1
Alt.
MAX1
MAX2
....
MAXi
....
MAXm

56. Payoff Table & Regret Table (Well Drilling – Minimax Regret)
Big
Small
Dry N3 N2 N1
Payoff
A3:Farm out
A2:Drill alone
A1:Don’t drill $0
$9,300k
$300k
-$500k
$1,250k
$125k $0
Big
Small
Dry N3 N2 N1
Regret
Max
A3:Farm out
A2:Drill alone
A1:Don’t drill $0
$500k
$175k $0
$300k
$8,050k $0
$9,300k
$9,300k
$500k
$8,050k

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) Disarm Arm Soviet Strategy Disarm Arm
U.S. Strategy
3rd-best for U.S.S.R.
3rd-best for U.S.
Worst for U.S.S.R.
Best for U.S.
Best for U.S.S.R.
Worst for U.S.
2nd-best for U.S.S.R.
2nd-best for U.S.

59. Computer-Based Information Systems
Integrated Database
CAD/CAM
Management Information Systems (MIS)
Decision Support Systems (DSS)
Expert Systems