Linear programming

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# Linear programming - PowerPoint PPT Presentation

Linear programming. Linear program: optimization problem, continuous variables, single, linear objective function, all constraints linear equalities or inequalities Applications Allocation models Operations planning models Limit load analysis in structues

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## PowerPoint Slideshow about 'Linear programming' - evers

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Presentation Transcript
Linear programming
• Linear program: optimization problem, continuous variables, single, linear objective function, all constraints linear equalities or inequalities
• Applications
• Allocation models
• Operations planning models
• Limit load analysis in structues
• Dynamic linear programming: time-phased decision making
Matrix form
• Basic solution (BS): solution of AX=b, n-m redundant variables zero (nonbasic variables), n constraints active. Remaining m variables non zero (basic variables)
• Each BS corresponds to a vertex
• BFS, non BFS
Possible solutions to a linear programming problem
• Unique solution
• Nonunique solution
• Unbounded solution
• No feasible solution
Simplex method

Idea: Start from a vertex. Move to adjacent vertex so that F decreaces. Continue until no further improvement can be made.

Facts

• Optimum is a vertex
• Vertex: BS
• Moving from a vertex to adjacent vertex: swap a basic variable with a non basic variable
Simplex method
• Variable with smallest negative cost coefficient will become basic
• Select variable to leave set of basic variables so that a BFS is obtained
• Design space convex
Tableau: canonical form

Basic variables

Nonbasic variables

Example

A, B, C: BS