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…

Review of Week 2 1 Objective : Understanding the optimization problems

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

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

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

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

LP o Basic assumptions Proportionality Additivity Divisibility Certainty

LP o General from of LP

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:

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

LP General from of LP

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 >=