Classes of Decision Problem:

1

• Classes of Decision Problem
• Under Certainty
• Under Risk - Known Probability
• Maximize E(return) method
• Minimize E(regret) method
• Maximize E(utility) method
• Under Uncertainty - Unknown Probability
• Laplace method
• Maximin of return method
• Maximax of return method
• Minmax of regret method

IE 417, Chap 13, Jan 99
2
Newsboy Problem Given Buy a paper for 10
c Sell a paper for 25 c Lost sale for each
paper 12 c Sell no paper P1 P(S1) P(d0)
1/10 Sell 1 paper P2 P(S2) P(d1)
3/10 Sell 2 papers P3 P(S3) P(d2)
4/10 Sell 3 papers P4 P(S4) P(d3) 2/10
Make a decision on number of papers to buy?
IE 417, Chap 13, Jan 99
3
Payoff (return) Table for the Newsboy
Problem Decision Criterion
. Deci- sion State of demand
0 1 2 3
0 0 -12 -24 -36 -20.4 -18 -36 0
1 -10 15 3 -9 2.9 -0.25 -10 15
2 -20 5 30 18 15.1 8.25 -20 30
3 -30 -5 20 45 12.5 7.5 -30 45
E(return)
Maximax
Laplace
Maximin
IE 417, Chap 13, Jan 99
4
Regret Table for the Newsboy Problem
Decision Criterion Deci- State of demand
sion 0 1 2 3 E(regret) minimax
0 0 27 54 81 45.9 81 1 10 0 27 54 22.6 54
2 20 10 0 27 10.4 27 3 30 20 10 0 13 30
IE 417, Chap 13, Jan 99
5
Creating a Utility Function 1) Select the end
points of the utility function U(smallest net
dollar return) U(sr) 0 U(largest net dollar
return) U(lr) 1 2) Utility of any other net
return, rij, is the probability, p, such
that p(lr) (1 - p )(sr) rij U(rij ) p
Uij
IE 417, Chap 13, Jan 99
6
Incorporating the Decision Makers
Personality If U(rij) gt p then he is
risk-averse If U(rij) p then he is
risk-indifferent If U(rij) lt p then he is
risk-seeking
IE 417, Chap 13, Jan 99
7
Using a Utility Function 1) Calculate the
expected utility for each decision i, using
probability of states EUi ? Uij Pj

j 2) Select the maximum EUi
IE 417, Chap 13, Jan 99
8
Utilities Table for the Newsboy Problem For a
risk neutral person Decision Criterion
Decision State of demand
0 1 2 3 E(utility) 0 0.44 0.3 0.15 0 0.194
1 0.32 0.63 0.48 0.33 0.479
2 0.2 0.51 0.81 0.67 0.631 3 0.07 0.38 0.69 1
0.597
IE 417, Chap 13, April 2003
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Utilities Table for the Newsboy Problem For a
risk neutral person Decision Criterion
Decision State of demand
0 1 2 3 E(utility) 0 0.44 0.3 0.15 0 0.194
1 0.32 0.63 0.48 0.33 0.479
2 0.2 0.51 0.81 0.67 0.631 3 0.07 0.38 0.69 1
0.597
IE 417, Chap 13, April 2003
10
Utilities Table for the Newsboy Problem For a
risk averse person Decision Criterion
Decision State of demand
0 1 2 3 E(utility) 0 0.67 0.54 0.34 0 0.38
1 1 0.57 0.79 0.69 0.58 0.686
2 0.44 0.71 0.90 0.82 0.781
3 0.27 0.62 0.83 1 0.745
IE 417, Chap 13, Jan 99
11

• Issues of concern
• Sensitivity analysis for subjective input data
• Expected Value of Perfect Information (EVPI)
• Analysis of the original data (drawback of some
• methods), after applying a method, for the
  final
• decision
• Motivation behind each method (personality aspect)

IE 417, Chap 13, Jan 2000
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Decision Tree Problem statement Create the
tree logical drawing input data
probabilities, terminal values Solve the
tree fold back expected value at nodes Derive
conclusion best decision EVSI,
EVPI sensitivity analysis New
information Testing change created
tree change probabilities (Bayes
rule) change terminal values
IE 417, Chap 13, Jan 99
13
Folding Back the Decision Tree (analyzing from
right to left) Expected value of
? (value of each branch)
(prob. of each
branch) Expected value of Best
branch
IE 417, Chap 13, Jan 99
14
Decision Tree for Protrac Problem
5
30 -8
Strong A
2
0.45
Weak A
6
0.55
Aggressive
1
7
20 7
Strong B
3
0.45
Weak B
8
0.55
Basic
Strong C
9
5 15
4
0.45
Weak C
10
Cautious
0.55