Applied mathematical programming using algebraic systems by McCarl B.A., Spreen T.H.

By McCarl B.A., Spreen T.H.

Show description

Read Online or Download Applied mathematical programming using algebraic systems PDF

Similar mathematics books

Topics in mathematical physics, general relativity, and cosmology in honor of Jerzy Plebański: proceedings of 2002 international conference, Cinvestav, Mexico City, 17-20 September 2002

Considered one of glossy science's most famed and debatable figures, Jerzy Pleba ski was once a very good theoretical physicist and an writer of many interesting discoveries typically relativity and quantum thought. identified for his remarkable analytic abilities, explosive personality, inexhaustible power, and bohemian nights with brandy, espresso, and massive quantities of cigarettes, he used to be devoted to either technology and paintings, generating innumerable handwritten articles - akin to monk's calligraphy - in addition to a suite of oil work.

Symmetries, Integrable Systems and Representations

This quantity is the results of overseas workshops; limitless research eleven – Frontier of Integrability – held at college of Tokyo, Japan in July twenty fifth to twenty ninth, 2011, and Symmetries, Integrable platforms and Representations held at Université Claude Bernard Lyon 1, France in December thirteenth to sixteenth, 2011.

Extra info for Applied mathematical programming using algebraic systems

Example text

Furthermore, since the basic variables must remain nonnegative the solution must satisfy XB ' B & 1 b & B & 1 a0 x0 $ 0. This equation permits the derivation of a bound on the maximum amount the nonbasic variable x0 can be changed while the basic variables remain non-negative. Namely, x0 may increase until one of the basic variables becomes zero. Suppose that the first element of XB to become zero is xBi*. Solving for xBi* gives xBi ( ' (B & 1 b)i ( & (B & 1 a0)i ( x0 ' 0 where ( )I denotes the ith element of the vector.

Thus, we add an 1xM vector of zero's to the objective function and conditions constraining the slack variables to be nonnegative. t. AX % X, copyright Bruce A. McCarl and Thomas H. Spreen 3-2 IS ' b S $ 0. Throughout the rest of this section we redefine the X vector to contain both the original X's and the slacks. Similarly, the new C vector will contain the original C along with the zeros for the slacks, and the new A matrix will contain the original A matrix along with the identity matrix for the slacks.

In fact, they are usually estimated by statistical techniques. Thus, after developing a LP model, it is often useful to conduct sensitivity analysis by varying one of the exogenous parameters and observing the sensitivity of the optimal solution to that variation. For example, in the van shop problem the net return per fancy van is $2,000, but this value depends upon the van cost, the cost of materials and the sale price all of which could be random variables. Considerable research has been directed toward incorporating uncertainty into programming models.

Download PDF sample

Rated 4.36 of 5 – based on 4 votes