CAED101 SAN Lorenzo ACN1 Sensitivity Analysis PDF

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sensitivity analysis...

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MARY MELLENE F. SAN LORENZO

ACN1

P(S1) = 0.2 P(S2) = 0.8 EV (di) = ∑ 𝑁 𝑗=1 𝑃(𝑆𝑗 )𝑉𝑖𝑗 EV(d1) = 0.2(10) + 0.8(1) = 2 + 0.8 = 2.8 EV(d2) = 0.2(4) + 0.8(3) = 0.8 + 2.4 = 3.2 Using the expected value approach, decision alternative d2 is recommended with an expected value of 3.2 Sensitivity Analysis P(S1) = p P(S2) = 1 – P(S1) = 1 – p

EV(d1) = P(S1) (10) + P(S2) (1) EV(d1) = p (10) + (1-p) (1) EV(d1) = 10p +1 – p EV(d1) = 9p + 1

EV(d2) = P(S1) (4) + P(S2) (3) EV(d2) = p (4) + (1-p) (3) EV(d2) = 4p +3 –3 p EV(d2) = p + 3

Set EV(d1) = EV(d2) 9p + 1 = p + 3

9p – p = 3 – 1 8p = 2;

8𝑝 8

=

2 8

P = 0.25 In the original problem, the expected values for the two decision alternatives were as follows: EV(d1) = 2.8 EV(d2) = 3.2 Decision alternative (d2) is recommended. Decision alternative d2 will remain the optimal decision alternative as long as EV(d2) is greater than or equal to the expected value of the second-best decision alternative, in this case, no other decision alternative, but d1. Thus, decision alternative d2 will remain the optimal decision alternative as long as: EV(d2) ≥ 2.8 Using P(S1) = 0.2 and P(S2) = 0.8, the general expression for EV(d2) is: S = strong demand/ S1 W = weak demand/ S2 EV(d2) = 0.2S + 0.8W EV(d2) = 0.2S + 0.8(3) ≥ 2.8 0.2S +2.4 ≥ 2.8 0.2S ≥ 2.8 – 2.4 0.2S ≥ 0.4 S≥2

EV(d2) = 0.2S + 0.8W EV(d2) = 0.2(4) + 0.8W ≥ 2.8 0.8 + 0.8W ≥ 2.8 0.8W ≥ 2.8 – 0.8 0.8W ≥ 2 W ≥ 2.5...