HMWANSWERS - Homework III Answers 1) Stages (t): the coin...

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Unformatted text preview: Homework III Answers 1) Stages (t): the coin types (and a dummy last stage): 0, 1, 2, …, k States (it): the accumulated amount of money up to the stage t. for t = 0 and t = k we have single state “0” and “v” respectively, for 0 < t < k we have 0,1,2, … , Decisions (xt): the number of type t coins that we should take. , 0 constraints on the decision variable how the states are transformed the cost of the transformation 0 min initial cost the recursion the minimum total number of type , 2, … , of money 0 ?, 1 coins we should use if we have 1, amount ? 2) Stages (t): the months: 1, 2, 3, 4, 5. Note that we don’t need a dummy stage this time. (Why?) States (it): amount of the available total expert hours at the stage t. for t = 1 we have a single state “50*160”, for 1 < t < 6 we have 6000, … ,11000 . Don’t worry about the unnecessary states for they will be automatically eliminated due to the constraints. Decisions (xt): the number of new technicians that will be trained during month t. 50 160 2000 2000 , constraints on the decision variable is the necessary work hours for the month 0.95 160 how the states are transformed 1000 2000 min 160 the cost of the transformation initial cost 1000 0.95 160 the recursion the minimum total costs of the months , 1, 2, … ,5 if we have available work hours at month 8000 ?, ? 3) f6 = 0 f5 = 55 + f 6 = 55 ⎧20 + f5 = 77 f 4 = min ⎨ ⎩20 + 0.40 * 90 + f 6 = 56 ⎧45 + f 4 = 101 ⎪ f3 = min ⎨45 + 0.40 *140 + f 5 = 156 ⎪45 + 0.40 *140 + 2 * 0.40 * 90 + f = 173 6 ⎩ ⎧40 + f3 = 141 ⎪40 + 0.40 * 20 + f = 104 ⎪ 4 f 2 = min ⎨ 40 + 0.40 * 20 + 2 * 0.40 *140 + f 5 = 215 ⎪ ⎪40 + 0.40 * 20 + 2 * 0.40 *140 + 3* 0.40 * 90 + f 6 = 268 ⎩ ⎧50 + f 2 = 154 ⎪50 + 0.40 * 60 + f = 175 3 ⎪ ⎪ f1 = min ⎨50 + 0.40 * 60 + 2 * 0.40 * 20 + f 4 = 146 ⎪50 + 0.40 * 60 + 2 * 0.40 * 20 + 3* 0.40 *140 + f = 215 5 ⎪ ⎪50 + 0.40 * 60 + 2 * 0.40 * 20 + 3* 0.40 *140 + 4 * 0.40 * 90 + f 6 = 402 ⎩ ...
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This note was uploaded on 07/30/2011 for the course END 331 taught by Professor Ilkertopcu during the Spring '11 term at Istanbul Technical University.

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