HW4_solution

HW4_solution - solution of homework 4 Problem 1 a It fits...

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Unformatted text preview: solution of homework 4 Problem 1 a. It fits the convex case. b. Let f ( n,I n ) denote the minimum cost from period i to the end given the inventory level at the beginning of period i is I n . f (5 , 0) = 21 * (3- 0) = 63 f (5 , 1) = 1 + 21 * (3- 1) = 43 f (5 , 2) = 1 * 2 + 21 * (3- 2) = 23 f (4 , 0) = min 20 * 2 + f (5 , 0) 20 * 3 + f (5 , 1) 20 * 4 + f (5 , 2) = min 103 103 103 = 103 f (4 , 1) = min 1 * 1 + 20 * 1 + f (5 , 0) 1 * 1 + 20 * 2 + f (5 , 1) 1 * 1 + 20 * 3 + f (5 , 2) = min 84 84 84 = 84 f (4 , 2) = min 1 * 2 + 20 * 0 + f (5 , 0) 1 * 2 + 20 * 1 + f (5 , 1) 1 * 2 + 20 * 2 + f (5 , 2) = min 65 65 65 = 65 f(3,0) is an impossible situation, because it is impossible to satisfy the demand of period 3. f (3 , 1) = 1 * 1 + 17 * 4 + f (4 , 0) = 172 f (3 , 2) = min ( 1 * 2 + 17 * 3 + f (4 , 0) 1 * 2 + 17 * 4 + f (4 , 1) = min ( 156 154 = 154 f (2 , 0) = 16 * 4 + f (3 , 1) = 236 f (2 , 1) = min ( 1 * 1 + 16 * 3 + f (3 , 1) 1 * 1 + 16 * 4 + f (3 , 2) = min...
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HW4_solution - solution of homework 4 Problem 1 a It fits...

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