1. 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…

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: http://www.niceprof.nethttp://www.niceprof.net Lindo Co.: http://www.lindo.comhttp://www.lindo.com 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 >=