2007-09-24_Presentation

2007-09-24_Presentation - Representing Non-linear functions...

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IEOR160 © 2007 1 More on Integer Programming models IEOR160 © 2007 2 Representing Non-linear functions z Suppose we are to buy laptops and desktop computers, subject to some demand requirements. Suppose that the cost of computers is as follows: $2,000 each if you buy 1 to 10 $1,800 for each computer from 11 to 25 $1,700 for each computer from 26 to 50 No more than 50 may be purchased. Let x = number of computers bought x 1 = number bought at $2,000 x 2 = number bought at $1,800 x 3 = number bought at $1,700 s.t. 0 x 1 10 0 x 2 15 0 x 3 25 If x 1 < 10, then x 2 = 0. If x 2 < 15, then x 3 = 0. The cost function includes the term: Minimize 2,000 x 1 +1,800 x 2 + 1,700 x 3 IEOR160 © 2007 Representing Non-linear functions s.t. Minimize 2,000 x 1 +1,800 x 2 + 1,700 x 3 + other terms Let w 1 = 1 if x 1 = 10 w 1 = 0 if x 1 < 10 Let w 2 = 1 if x 2 = 15 w 2 = 0 if x 2 < 15 0 x 1 10 and other constraints 0 x 2 15 w 1 0 x 3 25 w 2 0 w 1 x 1 /10 0 w 2 x 2 /15 If x 1 < 10, then x 2 = 0.
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2007-09-24_Presentation - Representing Non-linear functions...

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