Simpleks |
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funkcja celu: |
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Monte carlo |
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f(x1,x2) = 5x1 + 10x2 -> max |
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A |
B |
Zapas |
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Kryteria optymalności: |
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L. awarii |
1 |
2 |
3 |
4 |
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S1 |
0.2 |
0.5 |
2000 |
1) |
0,2x1 + 0,5x2 <= 2000 |
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P(x) |
0.7 |
0.1 |
0.1 |
0.1 |
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S2 |
0.3 |
0.1 |
2100 |
2) |
0,3x1 + 0,1x2 <= 2100 |
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S3 |
0.2 |
0.3 |
2500 |
3) |
0,2x1 + 0,3x2 <= 2500 |
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Czas usuw. Awarii |
1 |
2 |
3 |
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S4 |
0.1 |
0.1 |
1000 |
4) |
0,1x1 + 0,1x1 <= 1000 |
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P(x) |
0.1 |
0.2 |
0.7 |
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Zysk |
5 |
10 |
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Liczba awarii |
Awarie |
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Suma awarii |
Czas usuwania awarii |
Sumy: |
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0.6 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
Iteracja I |
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0.4 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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cj |
5 |
10 |
0 |
0 |
0 |
0 |
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0.0 |
4 |
0 |
1 |
1 |
1 |
0 |
0 |
cb |
baza |
xi |
x1 |
x2 |
xd3 |
xd4 |
xd5 |
xd6 |
xi/aik |
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Macierz bazowa |
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0.6 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
0 |
xd3 |
0 |
0.2 |
0.5 |
1 |
0 |
0 |
0 |
2000 |
4000 |
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0.5 |
0 |
0 |
0 |
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0.6 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
0 |
xd4 |
0 |
0.3 |
0.1 |
0 |
1 |
0 |
0 |
2100 |
21000 |
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0.1 |
1 |
0 |
0 |
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0.3 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
0 |
xd5 |
0 |
0.2 |
0.3 |
0 |
0 |
1 |
0 |
2500 |
8333.33333333333 |
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0.3 |
0 |
1 |
0 |
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0.3 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
0 |
xd6 |
0 |
0.1 |
0.1 |
0 |
0 |
0 |
1 |
1000 |
10000 |
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0.1 |
0 |
0 |
1 |
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0.2 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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zj |
0 |
0 |
0 |
0 |
0 |
0 |
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0.1 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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zj-cj |
5 |
10 |
0 |
0 |
0 |
0 |
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0.6 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
Iteracja II |
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1.0 |
1 |
0.1 |
0.7 |
0.1 |
0 |
1 |
0 |
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cj |
5 |
10 |
0 |
0 |
0 |
0 |
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0.8 |
1 |
0.1 |
0.7 |
0.1 |
0 |
1 |
0 |
cb |
baza |
xi |
x1 |
x2 |
xd3 |
xd4 |
xd5 |
xd6 |
xi/aik |
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0.5 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
0 |
x2 |
10 |
0.4 |
1 |
2 |
0 |
0 |
0 |
4000 |
10000 |
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0.4 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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0 |
xd4 |
0 |
0.26 |
0 |
-0.2 |
1 |
0 |
0 |
1700 |
6538.46153846154 |
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1.0 |
1 |
0.1 |
0.7 |
0.1 |
0 |
1 |
0 |
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Na podstawie danych z tabeli (wyników z symulacji monte carlo) należy zatrudnić przynajmniej 1 pracownika do napraw urządzeń wytwórczych. Jest to związane z tym, iż najwyższe prawdopodobieństwo ma wystąpienie dwu lub 1 awarii,co zajmuje około godziny do kilku godzin naprawy |
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xd5 |
0 |
0.08 |
0 |
-0.6 |
0 |
1 |
0 |
1300 |
16250 |
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0.7 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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0 |
xd6 |
0 |
0.06 |
0 |
-0.2 |
0 |
0 |
1 |
600 |
10000 |
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0.8 |
1 |
0.1 |
0.7 |
0.1 |
0 |
1 |
0 |
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zj |
4 |
10 |
20 |
0 |
0 |
0 |
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0.4 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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zj-cj |
1 |
0 |
-20 |
0 |
0 |
0 |
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Macierz bazowa |
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0.2 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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Iteracja III |
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0.5 |
0.2 |
0 |
0 |
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0.9 |
1 |
0.1 |
0.7 |
0.1 |
0 |
1 |
0 |
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cj |
5 |
10 |
0 |
0 |
0 |
0 |
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0.1 |
0.3 |
0 |
0 |
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0.6 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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cb |
baza |
xi |
x1 |
x2 |
xd3 |
xd4 |
xd5 |
xd6 |
xi/aik |
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0.3 |
0.2 |
1 |
0 |
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0.4 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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0 |
x2 |
10 |
-5.55111512312578E-17 |
1 |
2.30769230769231 |
-1.53846153846154 |
0 |
0 |
1384.61538461538 |
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0.1 |
0.1 |
0 |
1 |
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0.8 |
1 |
0.1 |
0.7 |
0.1 |
0 |
1 |
0 |
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0 |
x1 |
5 |
1 |
-5.55111512312578E-17 |
-0.769230769230769 |
3.84615384615385 |
0 |
0 |
6538.46153846154 |
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0.9 |
1 |
0.1 |
0.7 |
0.1 |
0 |
1 |
0 |
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0 |
xd5 |
0 |
0 |
0 |
-0.538461538461539 |
-0.307692307692308 |
1 |
0 |
776.923076923077 |
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0.6 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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0 |
xd6 |
0 |
0 |
0 |
-0.153846153846154 |
-0.230769230769231 |
0 |
1 |
207.692307692308 |
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0.5 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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zj |
5 |
10 |
19.2307692307692 |
3.84615384615385 |
0 |
0 |
46538.4615384615 |
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0.7 |
1 |
0.1 |
0.7 |
0.1 |
0 |
1 |
0 |
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zj-cj |
0 |
0 |
-19.2307692307692 |
-3.84615384615385 |
0 |
0 |
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0.2 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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0.6 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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Rozwiązanie: |
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Zysk: |
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0.6 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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x2 = |
1384.6 |
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46538.5 |
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0.4 |
2 |
0.2 |
0.8 |
0.3 |
0 |
0 |
1 |
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x1 = |
6538.5 |
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∑= |
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56 |
5.2 |
24.2 |
8.4 |
1 |
8 |
22 |
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xd5 = |
776.9 |
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Czas usuwania awarii: |
Doba |
Godzina |
Kilka godzin |
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Na podstawie średniej czasu usuwania awarii wynika, iż usuwanie tychże zabiera około 1/3 doby co oznacza, iż optymalnym byłoby zatrudnienie co najmniej dwóch pracowników, odpowiedzialnych za naprawy urządzeń |
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xd6 = |
207.7 |
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Średni czas usuwania awarii: |
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