Zahra_Mohaghegh_April%201th

Zahra_Mohaghegh_April%201th - Engineering Management &...

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1 Engineering Management & Systems Engineering The George Washington University EMSE 102 EMSE 102 - - 202 202 Survey of Operations Research Methods Survey of Operations Research Methods Zahra Mohaghegh mohagheg@umd.edu Post-Doctoral Research Associate Center For Risk and Reliability University of Maryland April 01, 2008
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2 Engineering Management & Systems Engineering The George Washington University Integer Programming Integer Programming
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3 Engineering Management & Systems Engineering The George Washington University Outline Outline ± Integer Programming Concept ± Geometrical Interpretation of IPs ± Formulating IP problems ± Personnel scheduling (solving with LINDO) ± The Knapsack Problem ± One-time Decision problems ± Set-covering Problems ± Fixed Charge problems: ± Modeling Gandhi Clothing Fixed Costs ± Lockbox problem ± Either-or logic ± If-then Logic ± Techniques for solving Integer Programs ( Branch and Bound Method)
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4 Engineering Management & Systems Engineering The George Washington University Introduction Introduction ± An integer program is a linear program that requires some decision variables to take integer values. ± Example: assignment problems seen earlier, (fractional values have no useful meaning). ± Dramatically improves the modeling capability. Examples: ± Economic indivisibilities ± Logical constraints ± classical problems in capital budgeting and in supply chain management ± Disadvantages! ± More difficult to model ± Can be much more difficult to solve ± Integer programming is an active area of research
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5 Engineering Management & Systems Engineering The George Washington University Types of Types of IPs IPs ± IP : A pure integer program is one where all decisions variables are required to take integer values. ± MIP : A mixed integer program is one where some, but not all, decision variables are required to take integer values. ± BIP : A binary integer program or 0-1 integer program requires decision variables to take values in the set {0,1}. ± The LP relaxation of an IP is the LP that results when the integer or 0-1 constraints are removed.
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6 Engineering Management & Systems Engineering The George Washington University max z = 3 x 1 + 2 x 2 s . t . x 1 + x 2 6, x 1 , x 2 0, x 1 , x 2 integer max z = 3 x 1 + 2 x 2 s . t x 1 + x 2 x 1 , x 2 0, x 1 integer max z = x 1 x 2 s . t x 1 + 2 x 2 2, 2 x 1 x 2 1, x 1 , x 2 = 0 or 1 A pure integer program (IP): A mixed integer program (MIP): A 0-1 Integer program (BIP): Examples Examples
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7 Engineering Management & Systems Engineering The George Washington University Outline Outline ± Integer Programming Concept ± Geometrical Interpretation of IPs ± Formulating IP problems ± Personnel scheduling (solving with LINDO) ± The Knapsack Problem ± One-time Decision problems ± Set-covering Problems ± Fixed Charge problems: ± Modeling Gandhi Clothing Fixed Costs ± Lockbox problem ± Either-or logic ± If-then Logic ± Techniques for solving Integer Programs ( Branch and Bound Method)
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8 Engineering Management & Systems Engineering
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Zahra_Mohaghegh_April%201th - Engineering Management &...

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