handout03solutions

# handout03solutions - IEOR 162 Linear Programming Spring...

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IEOR 162 Linear Programming Spring 2007 Handout 3 Solutions 1. Variables: x t = amount to invest in the cash ﬂow starting in period t I t = balance at the end of period t Formulation: max I 5 s.t. I 0 = 200 I 1 = I 0 - x 1 I 2 = I 1 - 2 x 1 - x 2 I 3 = I 2 + 4 x 1 - 2 x 2 - x 3 I 4 = I 3 + 4 x 2 - 2 x 3 I 5 = I 4 + 4 x 3 x t , I t 0 2. Data: d t = demand in period t Variables: x t = production for period t I t = inventory left over at the end of period t Formulation: min 13 x 1 + 14 x 2 + 15 x 3 + 2( I 1 + I 2 + I 3 ) s.t. I 0 = 5 (1) I t + d t = x t + I t - 1 , t = 1 , 2 , 3 (2) 1 2 x t + I t - 1 d t , t = 1 , 2 , 3 (3) x t , I t 0 , t = 1 , 2 , 3 The objective minimizes the total of production costs plus inventory costs. Constraint 1 simply initializes the beginning inventory. Constraint 2 ensures the proper relation between inventory at
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## This note was uploaded on 04/02/2008 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at Berkeley.

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