Mini-course 1 Decision Analysis (Dr. Mariya Sodenkamp) / Class 3 / ITB_L3_ 2015_04_20
.pdf
Weighed addi+ve value
Criteria importance scores:
S → 100; DH → 18; VD → 34
Criteria
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Alternatives |
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Job A |
Job B |
Job C |
Salary (S) |
0.281 |
0.404 |
0.316 |
Distance from home(DH) |
-0.043 |
-0.652 |
-0.304 |
Vacation Days (VD) |
0.328 |
0.246 |
0.426 |
Trade-o the information above and define the best job using weighed
sum approach |
21 |
IT in Business: Decision Analysis| © Sodenkamp
Method of the Ideal Point
Decision |
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Decision criteria |
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Alternatives |
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Employment Rate |
Number of |
Bank Deposit Per |
Population |
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Competitors |
Capita |
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A |
0.4*0.37=0.15 |
0.15*(- 0.42)=-0.06 |
0.3*0.38=0.12 |
0.15*0.20=0.03 |
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B |
0.4*0.34=0.14 |
0.15*(- 0.33)=-0.05 |
0.3*0.33=0.10 |
0.15*0.34=0.05 |
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C |
0.4*0.29=0.11 |
0.15*(- 0.25)=-0.04 |
0.3*0.29=0.09 |
0.15*0.45=0.07 |
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IT in Business: Decision Analysis| © Sodenkamp
Matrix of deviations:
Decision |
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Decision criteria |
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Alternatives |
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Employment |
Number of |
Bank Deposit |
Population |
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Rate |
Competitors |
Per Capita |
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A |
0 |
0.024 |
0 |
0.037 |
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C |
0.031 |
0 |
0.027 |
0 |
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B is the best location
IT in Business: Decision Analysis| © Sodenkamp
Working place selec+on (The Ideal Point)
Criteria importance scores:
S → 100; DH → 18; VD → 34
Criteria
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Alternatives |
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Job A |
Job B |
Job C |
Salary (S) |
1,600 € |
2,300 € |
1,800 € |
Distance from home(DH) |
4 km |
60 km |
28 km |
Vacation Days (VD) |
20 |
15 |
26 |
Trade-o the information above and define the best job using the Main Criterion approach
24
IT in Business: Decision Analysis| © Sodenkamp
Decision |
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Decision criteria |
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Alternatives |
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Employment Rate, % |
Number of Competitors |
Bank Deposit Per Capita, $ |
Population |
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B |
65 |
4 |
27,600 |
7,283,682 |
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C |
55 |
3 |
24,200 |
9,590,715 |
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IT in Business: Decision Analysis| © Sodenkamp
Working place selec+on (Method of the Main Criterion)
S – the main criterion; DH<30 (km); VD>15
Criteria
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Alternatives |
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Job A |
Job B |
Job C |
Salary (S) |
1,600 € |
2,300 € |
1,800 € |
Distance from home(DH) |
4 km |
60 km |
28 km |
Vacation Days (VD) |
20 |
15 |
26 |
Trade-o the information above and define the best job using the Main Criterion approach
26
IT in Business: Decision Analysis| © Sodenkamp
Method of Successive Concessions (extended Lexicographic method) (1)
f (xk ) → max |
or f (xk ) → min; |
f j (x) ≥ Fj *−hj , or |
f j (x) ≤ Fj *+hj j =1,2,..., k −1, k +1,...J |
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hj − concession |
on the j −th |
criterion |
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Decision |
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Decision criteria |
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Alternatives |
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Employment Rate |
Number of Competitors |
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Bank Deposit Per Capita |
Population |
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α'j |
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0.4 |
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0.15 |
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0.3 |
0.15 |
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All criteria are numbered according to their importance (No. 1 is the most important, No. 2 is second most important etc.) On the second step the most important criterion must be maximized (or minimized), depending on its impact direction, and its best available value F* is found. Then a „concession“ must be set on this criterion. A concession is a performance reduction, compared with the best available value on that criterion, that DMs are agree to tolerate.
This method is applicable when all criteria are naturally ordered based on their importance.
1. Order criteria from the most important to the least important:
I - Employment Rate; II - Bank deposit per capita,
III - Number of Competitors, IV - Population
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Method of Successive Concessions (2)
2. Specify what criteria are negative / positive (must be minimized / must be maximized).
I - Employment Rate -> max; II - Bank deposit per capita -> max,
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3.
4.
III - Number of Competitors -> min, IV - Population -> max
Find the best value F* (maximal) for the most important criterion: F *(Employment Rate ) = max {70%; 65%; 55} = 70%
Define a “concession” for the employment rate
Concession for the Price: h(Employment Rate) = 20% means that the bank is agree to establish a new branch in the region with 20% less employment rate than the best available rate
Calculate a new restriction: F*(Employment Rate) - h(Employment Rate ): 70% - 20% = 50% - the minimal acceptable Employment Rate
Employment Rate(A) = 70%>50%; Employment Rate (B)=65%>50%; Employment Rate (C)=55% > 50%
=> A, B and C satisfy the restriction, none drops out of consideration
Method of Successive Concessions (3)
Decision |
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Decision criteria |
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Alternatives |
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Employment Rate, % |
Number of Competitors |
Bank Deposit Per Capita, $ |
Population |
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A |
70 |
5 |
31,500 |
4,260,351 |
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B |
65 |
4 |
27,600 |
7,283,682 |
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C |
55 |
3 |
24,200 |
9,590,715 |
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5. Find the best value F* (maximal) for the second important criterion: F *(Deposit) = max {31,500$; 27,600$; 24,200$} = 31,500$
6. Set a concession for the Bank deposit per capita:
h(Deposit) = 5,000$ - it means that the bank is agree to open a new branch in the region with average deposit per capita 5,000$ less than the best actual index on this criterion.
Calculate restriction for Deposit F*(Si) - h(Deposit):
31,500 $ - 5,000 $ = 26,500 $ - the minimal deposit per capita that the bank is accepting now Deposit(A) = 31,500 >26,500; Deposit(B)= 27,600 > 26,500;
Deposit(C)= 24,200 <26,500
=> A and B satisfy the restriction, C drops out
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Method of Successive Concessions (4)
Decision |
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Decision criteria |
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Alternatives |
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Employment Rate, % |
Number of Competitors |
Bank Deposit Per Capita, $ |
Population |
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A |
70 |
5 |
31,500 |
4,260,351 |
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B |
65 |
4 |
27,600 |
7,283,682 |
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7. Find the best value F* (minimal) for the third important criterion: F *(Competitors) = min {5, 4} = 4
8. Set a concession for the Number of Competitors:
h(Competitors) = 0 - this means that the bank is not agree to accept more than four competitors.
Calculate restriction for the Number of Competitors F*(Competitors) – h(Competitors):
4-0 = 4
Competitors(A) = 5 > 4; Competitors(B)= 4; => only B satisfy this restriction
30
B is the best location