1 / 8

Linear programming

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

evers
Download Presentation

Linear programming

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. 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

  3. Possible solutions to a linear programming problem • Unique solution • Nonunique solution • Unbounded solution • No feasible solution

  4. 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

  5. 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

  6. Tableau: canonical form Basic variables Nonbasic variables

  7. x2 leave Tableau: swapping variables Pivot element xm+1 enter

  8. Example A, B, C: BS

More Related