Dynamic programming.pdf

If 2000 m 3 profit is 5000 if 3000 m 3 profit is 6000

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If 2000 m 3 , profit is 5000€. If 3000 m 3 , profit is 6000€. Next we investigate the stage 2. 5 4 5 2 4 1 2 1 6 7 6 3 f 3 (D 3 ) / k€ f 2 (D 2 ) / k€ f 1 (D 1 ) / k€ D i / 1000 m 3

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Exercise 1 – solution 2. stage: Form a table of the different possibilities. The idea is to investigate the optimal flow ratio between stations D 1 and D 2 with different S 2 values. 5 4 5 2 4 1 2 1 6 7 6 3 f 3 (D 3 ) / k€ f 2 (D 2 ) / k€ f 1 (D 1 ) / k€ D i / 1000 m 3
Exercise 1 – solution S 2 D 2 S 1 f 2 (D 2 ) f 1 * (S 1 ) f 2 * (S 2 )=f 2 (S 2 , D 2 )+f 1 * (S 1 ) 1 1 0 1 0 1 0 1 0 2 2 * 2 2 0 4 0 4 1 1 1 2 3 0 2 0 5 5 * 3 3 0 7 0 7 * 2 1 4 2 6 1 2 1 5 6 0 3 0 6 6 * Is maximum 5 4 5 2 4 1 2 1 6 7 6 3 f 3 (D 3 ) / k€ f 2 (D 2 ) / k€ f 1 (D 1 ) / k€ D i / 1000 m 3 2

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Exercise 1 – solution 3. Stage: For the stage 3 a similar table is formed: 5 4 5 2 4 1 2 1 6 7 6 3 f 3 (D 3 ) / k€ f 2 (D 2 ) / k€ f 1 (D 1 ) / k€ D i / 1000 m 3
Exercise 1 – solution S 3 D 3 S 2 f 3 (D 3 ) f 2 (S 2 ) * f 3 (S 3 )= f 3 (S 3 , D 3 )+f 2 * (S 2 ) 1 1 0 4 0 4 * 0 1 0 2 2 2 2 0 5 0 5 1 1 4 2 6 * 0 2 0 5 5 3 3 0 6 0 6 2 1 5 2 7 1 2 4 5 9 * 0 3 0 7 7 * represents the maximum 5 4 5 2 4 1 2 1 6 7 6 3 f 3 (D 3 ) / k€ f 2 (D 2 ) / k€ f 1 (D 1 ) / k€ D i / 1000 m 3 f

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