{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 04 - Industrial Engineering 634 Integer Programming Fall...

This preview shows pages 1–2. Sign up to view the full content.

Industrial Engineering 634 Fall 2011 Integer Programming Lecturer: Nelson Uhan Scribe: Isaac Tetzloff August 29, 2011 Lecture 4. The Simplex Method and LP Duality Let J be a set of row indices. With J , we let A J be the submatrix of A with rows in J , and we let b J be the subvector of b with components in J . Algorithm 1 (The Simplex Algorithm) . The Simplex Algorithm for solving a linear program (LP) takes in the following as input: A R m × n , b R m , c R n , and a vertex x of P , { x R n : Ax b } . After the Simplex Algorithm terminates the following output is given: a vertex x of P attaining max { cx : x P } or a vector w R n with Aw 0 and cw > 0 (i.e., the LP is unbounded). The process for the Simplex Algorithm is given by the following steps: 1. Find an initial basis by choosing a set of n row indices J such that A J is nonsingular and A J x = b J . 2. Compute the reduced costs by computing cA - 1 J and add zeros in order to obtain a vector y with c = yA , and all entries of y outside of J are 0. If y

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern