decision making under uncertainty - vtk gent · 2016-02-01 · decision making under uncertainty...
TRANSCRIPT
Introduction to Operations Research
ANSWERS
Decision Making Under Uncertainty
Prof. dr. E-H. Aghezzafir. Rodrigo Rezende Amaral
Exercise 1
Maximin:
Pizza King chooses small
Maximax:
Pizza King chooses large
9k – 6k = 3,000 6k – 5k = 1,000 2k – 2k = 09k – 5k = 4,000 6k – 6k = 0 2k – 1k = 1,0009k – 9k = 0 6k – 6k = 0 2k – 0k = 2,000
Minimax regret:
Pizza King chooses large
Regret matrix:
Exercise 2
(i.e., Maximin, Maximax, Minimax Regret, and Expected Value)
Exercise 2
Noble Greek (p2)
$6 $8 $10
Piz
za K
ing
(p1) $5 125 175 225
$6 200 300 400
$7 225 375 525
$8 200 400 600
$9 125 375 625
profit = (p1 – 4) x [100 + 25(p2-p1)]
Exercise 2
Noble Greek (p2)
$6 $8 $10
Piz
za K
ing
(p1) $5 125 175 225
$6 200 300 400
$7 225 375 525
$8 200 400 600
$9 125 375 625
Maximin: Pizza King chooses $7
Exercise 2
Noble Greek (p2)
$6 $8 $10
Piz
za K
ing
(p1) $5 125 175 225
$6 200 300 400
$7 225 375 525
$8 200 400 600
$9 125 375 625
Maximax: Pizza King chooses $9
Exercise 2
Noble Greek (p2)
$6 $8 $10
Piz
za K
ing
(p1) $5 225-125 = 100 400-175 = 225 625-225 = 400
$6 225-200 = 25 400-300 = 100 625-400 = 225
$7 225-225 = 0 400-375 = 25 625-525 = 100
$8 225-200 = 25 400-400 = 0 625-600 = 25
$9 225-125 = 100 400-375 = 25 625-625 = 0
Minimax Regret: Pizza King chooses $8
Exercise 2
Noble Greek (p2)
$6 $8 $10 ∑
Piz
za K
ing
(p1) $5 31.25 87.50 56.25 175
$6 50.00 150.00 100.00 300
$7 56.25 187.50 131.25 375
$8 50.00 200.00 150.00 400
$9 31.25 187.50 156.25 375
Expected Value: Pizza King chooses $8
Exercise 4
…
Exercise 4
…
Exercise 4
Exercise 5
…
Exercise 5…
.9991
.0009
.9996
.0004
Observe for 12 hours
.9991
.0009
.9996
.0004
.9936
.0064
1
1
1
1
1
0
0
0
0
0
.9991
.9996
.9936
.9991
.9996
.28
.72
.06
.22
.72
.99946
.99913
Operate now
.99946
Exercise 6
EVSI = EVWSI – EVWOI = $1,020EVPI = EVWPI – EVWOI = $2,120
Invest in bonds
6,000
3,000
.96
.045,880
Grant loan
Grant loan without
investigation
6,000
-50,000
.96
.043,7603,760
Investigate 4,280+5004,780
Without information
(EVWOI)
With sample information
(EVWSI)
With perfect information
(EVWPI)
Exercise 10
Exercise 10
Test
Don’t test
c1
c2
c3
0
c2
0
.05
.95
.14
.86
45/14095/140c1
5/860
855/860
(5/860)c2 +(855/860)c3
0.14 *(95/140)c1 +0.86 * [(5/860)c2 +
855/860)c3]
0.05c2
95/140
Exercise 10
Total cost when testing:
0.095c1 + 0.005c2+ 0.855c3
Total cost without testing:
0.05c2
(Remark: we consider that c1 includes the cost due to invasion of privacy)
Utility Theory - Exercise 1
Utility Theory - Exercise 1: solution
Utility Theory - Exercise 1: extra questions
Is Joan risk averse? Compute the risk premium for L2.
Utility Theory - Exercise 1: extra questions
Is Joan risk averse? Compute the risk premium for L2.
Utility Theory - Exercise 1: extra questions
Is Joan risk averse? Compute the risk premium for L2.