Continues in the back
DECISION ANALYSIS. JANUARY 2020
Name and surname ________________________________________________________ Group ________
Time for exam: 2 hours and 30 minutes. Remark: use 4 decimals on calculations
QUESTION 1 (3 points). Consider a linear business decision problem in which we want to maximize three
criteria, whose value is subject to a feasible set K. Once calculations are made, value of criteria (attributes) in
vertexes of the image of K in the space of objectives is:
Vertex
A’
B’
C’
D’
E’
F’
f1(x)
50
100
50
60
60
110
f2(x)
50
50
100
150
200
150
f3(x)
46
47
30
30
14
31
Working always in the space of objectives:
a) Determine the payoff matrix. Ideal and Nadir (anti-ideal) points.
b) Calculate compromise solutions using Manhattan metric (L1)
i. if all three criteria are considered equally important.
ii. if the second criterion, f2, is considered twice more important that any of the other two.
c) If any solution which makes f1 ≥ 60, f2 ≥ 60 and f3 ≥ 40 is considered acceptable,
i. analyze if the solution whose image is point F’ is a satisfactory and/or efficient solution.
ii. Propose the weighted goal programming program to be solved if first criterion is two times more
important than the second, which is two times more important than the third.
QUESTION 2 (3 points). A corporation, with the purpose of offering a new product line to its customers, is
analyzing the possibility to rebuild its current factory layout. Demand on the new product line may be favorable
or unfavorable. If the Company chooses to perform a deep rebuild of the existing factory layout, then estimated
profit in case demand on the new line is favorable is 500 000 euro, whereas if demand is unfavorable
estimated profit is only 100 000 euro. If the corporation performs a moderate rebuild on the factory layout, if
demand is favorable estimated profit is 400 000 euro, and if unfavorable estimated profit is 250 000 euro.
a) It’s not clear if people in charge of the corporation are optimistic or pessimistic. Using given information
establish, therefore, the optimal behavior rule of the corporation depending on the value of the relative
pessimism coefficient.
Later, based on self-estimations, the corporation a priori considers that the probability of demand being
favorable is 0.4.
b) Determine the optimal alternative and the decision maker attitude towards risk, in this case, if the Company
utility function is:
xi (Thousands of euro)
100
250
290
310
400
500
u(xi)
0
0.35
0.4
0.53
0.8
1
c) Determine the optimal alternative using the expected monetary value criterion. Before taking the decision,
the corporation could obtain perfect information indicating is the demand is going to be favorable or
unfavorable, hiring a market investigation firm to carry out a demand survey. How much is the maximum
the corporation would pay for such perfect information?
