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Unformatted text preview: Nonlinear Objectives Absolute Value Multiperiod Planning IE426: Optimization Models and Applications: Lecture 7 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University September 17, 2006 Jeff Linderoth IE426:Lecture 7 Nonlinear Objectives Absolute Value Multiperiod Planning Homework Helper Important Homework Tips From now on, please print out and attach sufficient information for me to grade your homeworks In addition, email me Mosel model and data files you used to get the answers you printed out and attached in Jeff Linderoth IE426:Lecture 7 Nonlinear Objectives Absolute Value Multiperiod Planning Homework Comments Problem 1: You should show the work necessary to draw the conclusions Problem 2.7: Trick Question! Only one person really got it right. :-) Graphing LP: A “trick” to know which side of inequality you are on. Problems 4-6. A mosel model is not a mathematical program. You should write (using appropriate notation) the models and instances you create. Some of you are having trouble getting the “general” case for various models. You need to figure out how to do this! You will get more practice. Jeff Linderoth IE426:Lecture 7 Nonlinear Objectives Absolute Value Multiperiod Planning Example Changing the Model Stupid Management! Management wants to be sure to turn a decent profit even if these numbers aren’t accurate. You have been tasked to find a production schedule that will maximize the minimum profit that the company would make in any of the following net-profit scenarios. Net Profit Net Profit N Product 1 Product 2 1 $1 $2 2 $1.20 $1.50 3 $1.50 $1.50 4 $0.50 $2.50 Jeff Linderoth IE426:Lecture 7 Nonlinear Objectives Absolute Value Multiperiod Planning Example Changing the Model World Light – Hedging max min { x 1 + 2 x 2 , 1 . 2 x 1 + 1 . 5 x 2 , 1 . 5 x 1 + 1 . 5 x 2 , . 5 x 1 + 2 . 5 x 2 } subject to x 1 + 3 x 2 ≤ 200 Frame Part Units 2 x 1 + 2 x 2 ≤ 300 Electrical Components x 2 ≤ 60 Rule out production over 60 units x 1 ≥ The immutable laws of physics x 2 ≥ The immutable laws of physics Does this do what management wants? Is this a linear program? Jeff Linderoth IE426:Lecture 7 Nonlinear Objectives Absolute Value Multiperiod Planning Example Changing the Model Linear (non)Linear Objectives Minimax. minimize f ( x ) def = ( maximum i X j ∈ N a ij x j ) Is this easy or hard? Is f ( x ) convex, concave, or nonconvex? If f ( x ) is convex, we would expect the problem to be easy! Jeff Linderoth IE426:Lecture 7 Nonlinear Objectives Absolute Value Multiperiod Planning Example Changing the Model Minimax a_2 x a_3 x a_4 x Jeff Linderoth IE426:Lecture 7 Nonlinear Objectives Absolute Value Multiperiod Planning Example Changing the Model Modeling Minimax Did you read first portion of “Beyond Linear Optimization” on course web site? Questions?...
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This note was uploaded on 02/29/2008 for the course IE 426 taught by Professor Linderoth during the Spring '08 term at Lehigh University .

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lecture7-markup - Nonlinear Objectives Absolute Value...

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