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Agenda of Week III. LP I LP Standardization Optimization LP intro Week 2 134 Definition Basic assumptions Example General form Standard form Objective : Understanding the solution of optimization problems Understanding the introduction of LP Solving 2 How to get…

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Review of Week 2 1 Objective : Understanding the optimization problems

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Solving Optimization Problems Theoretically Modeling with mathematical tools Theoretically solve model by employing calculus Always optimal solutions under some conditions Impossible for complex problems LINGO or Excel: Theory Algebra

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Heuristics Confirm current status Develop a specific logic/process improving current objective function and repeat it Not guarantee optimal solution E.g.: The blind climbing Solving Optimization Problems

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LINGO o How to get… Lecture HP: http://www.niceprof.nethttp://www.niceprof.net Lindo Co.: http://www.lindo.comhttp://www.lindo.com Solving Optimization Problems

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LP o Optimization problem with 1st order constraints and obj. func. General solution o Structure (Table 3-2) Obj. func. Constraints: LHE, RHS, Equality Decision variables, Parameters Nonnegativity

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LP o Basic assumptions Proportionality Additivity Divisibility Certainty

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LP o General from of LP

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LP o Decision variables n variables: o Contribution coefficients Coefficients in obj. func.: o Possible limits of resources (m resources) Right hand side constants: o Technology coefficients Coefficients in constraints:

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Modeling Examples of LP o Example 3-2 Server problem: p.113 Lingo program o Example 3-3 P.126 Lingo program

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LP General from of LP

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Transformation o Minimization Multiply -1 to obj. func. o Non nonnegativity Decompose variable x into 2 variables Give nonnegativity to both variables o Equality constraint Decompose it into 2 constraints with >= and <= Multiply -1 to constraint with >=

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Chapter 19 Linear Programming McGraw-Hill/Irwin

Chapter 19 Linear Programming McGraw-Hill/Irwin

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