Lecture 20110415 no sol

# Lecture 20110415 no sol - IMSE2008 Operational Research...

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Unformatted text preview: IMSE2008 Operational Research Techniques Lecture 04/15 Integer Programming inal Review Final Review Miao Song Dept of Industrial & Manufacturing Systems Engineering genda Agenda  Introduction to Integer Programming teger Programming Formulation  Integer Programming Formulation  Knapsack and Logical Constraints  Fixed Charge Problems  “Or-constraints”  Piecewise Linear Functions ow to Solve IP  How to Solve IP 4/14/2011 2 and Piecewise Linear Functions IP and Piecewise Linear Functions 6 f(x) Can we formulate f(x) as an MIP model? g f(x) is part of the E.g., f(x) is part of the objective function, which we want to maximize. y = 9 – x y = –5 + x 3 x) = 2x ≤ x ≤ 3 y = 2x 3 6 9 x f(x) = 2x if 0 ≤ x ≤ 3 f(x) = 9 – x if 3 ≤ x ≤ 7 x) = + x 8 ≤ x ≤ 9 4/14/2011 3 f(x) 5 x if 8 ≤ x ≤ 9 tep 1: Create Binary Variables Step 1: Create Binary Variables 6 f(x) If 0 ≤ x ≤ 3 then w 1 = 1 If 3 < x ≤ 7 then w 2 = 1 7 < x ≤ 9 then w 1 If 7 < x ≤ 9 then w...
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## This note was uploaded on 12/09/2011 for the course IMSE 0301 taught by Professor Song during the Spring '11 term at HKU.

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Lecture 20110415 no sol - IMSE2008 Operational Research...

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