{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

4120_lecture11-F10

4120_lecture11-F10 - Computational Methods for Management...

This preview shows pages 1–8. Sign up to view the full content.

Computational Methods for Management and Economics Carla Gomes Lecture 10 Reading: 4.1-4.3 of textbook

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

View Full Document
Outline Simplex: algebraic procedure By hand Using IOR Java applet (CD textbook)
Simplex as an algebraic procedure System of functional constraints n (5) variables (5) and m (3) equations 2 degrees of freedom, (i.e., we can set those two variables to any arbitrary values); they are the nonbasic variables; the other variables are the basic variables; Simplex chooses to set the non-basic variables to ZERO. Simplex solves the simultaneous equations to set the values of the basic variables;

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

View Full Document
Properties of Basic Solutions A basic solution is composed of: 1. Basic variables – 1. number of basic variables equals number of functional constraints 2. Their values results from solving the system of functional constraints (non-basic variables set to 0) 3. They form the basis 1. Non-basic variables – 1. number of non-basic variables equals (total number of variables - number of functional constraints) 2. They are set to ZERO Basic Feasible solution – it is a basic solution that satisfies the non- negativity constraints Adjacent basic feasible solutions – all but one of their basic (non-basic) variables are the same moving from one basic feasible solution to an adjacent one involves switching one variable from non-basic to basic and one variable from basic to non-basic (check graph)

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

View Full Document
Simplex Procedure Initialization – origin whenever possible (decision variables 0) (okay if standard form with positive RHS’s; basic feasible solution (BFS): each equation has a basic variable with coefficient 1 (slack variable = RHS) and the variable does not appear in any other eq; the decision variables are the non-basic variables set to 0) Optimality test – is current BFS optimal? ( the coefficients of the objective function of the non-basic variables gives the rate of improvement in Z )
Iteration – move to a better adjacent BFS a)Variable entering the basis Consider non-basic variables (Graphically - Consider edges emanating from current CPF solution) Pick

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