Lecture 4: Incomplete Information

Question 1

Incomplete Information

Answer 1

So far we have assumed that we can obtain the point estimates for weights by conducting an interview with the DM.

• Tradeoff method: System of equations is under-determined
• Swing method: DM is not willing or capable to allocate exact points to all alternatives

-> Sensitivity Analysis

Question 2

Sensitivity Analysis (Steps)

Answer 2

1. Determine the relationship between the attribute weights (express each weight in terms of the weight you like to alter)
2. Rewrite the value of each alternative as a function of the attribute weight that you would like to alter
3. Vary the objective weight in order to see how sensitive the decision is
4. Draw the graph and determine the pints of intersection

Question 3

What is the sensitivity analysis good for?

Answer 3

• Does the decision change if the weights are slightly altered?
• How robust is the decision?

Question 4

Dominance Test

Answer 4

Dominance checks allow for narrowing down the number of relevant alternatives on the basis of a low level information

Question 5

Dominance

Answer 5

If a dominates b then for any set of weights that is consistent with the incomplete information, V(a) >= V(b) holds and at least for one weight combination V(a) > V(b)

Question 6

Dominance Check (Steps)

Answer 6

1. Pick any set of weights that satisfies the boundary conditions
2. Calculate the value of each alternative for the chosen set of weights
3. Eliminate on of the possible dominance relationships
4. Check for the opposite direction by investigating the sign of max[V(a) - V(b)]

Question 7

Dominance Check without random initial solution

Answer 7

1. Determine min[V(a) - V(b)]
   - > for <0: further analysis
   - > for >0: a dominates b
2. Determine max[V(a) - V(b)]
   - > for <0: b dominates a
   - > for >0: no statement possible

Question 8

Dominance Check Conclusion

Answer 8

L.4 - Slide 19
Depending on the results for min[V(a) - V(b)] & max[V(a) - V(b)] we get a dominance relationship (a > b or b > a), no statement (min <0 and max >0), impossible (=0 and <0; >0 and <0; >0 and =0) or indifference (=0 and =0)