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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.

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Presentation on theme: "Agenda of Week III. LP I LP Standardization Optimization LP intro Week 2 134 Definition Basic assumptions Example General form Standard form Objective."— Presentation transcript:

1 Agenda of Week III. LP I LP Standardization Optimization LP intro Week 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…

2 Review of Week 2 1 Objective : Understanding the optimization problems

3 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

4 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

5 LINGO o How to get… Lecture HP: Lindo Co.: Solving Optimization Problems

6 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

7 LP o Basic assumptions Proportionality Additivity Divisibility Certainty

8 LP o General from of LP

9 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:

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

11 LP General from of LP

12 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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