Linear Programming (1)

The linear programming is a kind of mathematical modeling problems that we try to find out an extreme value of the objective function and satisfy a set of constraints which are linear. Normally, we can write down as following format:


Under the advent of modern computing technology, the requirement of the resulting analytic methods translates to the efficient algorithmic procedures witch able to provide a systematic and fast solution to the models of many managerial and/or technological decisions.

The Simplex algorithm provides a powerful computational procedure to solve very large scale applications including hundreds even thousands of variables, i.e. the decision factors and its significant contribution is the applications of operations research as a scientific decision making.

AHP Analytic Hierarchy Process

Analytic Hierarchy Process, AHP is good to provide information for decision.
Here is a case that estimates the ratio of score by AHP and uses the ratio as a certificate standard for suppliers.
What follows is six steps and simply explanations.

Step 1:

List these items that are inportant for your concerns.

• company ages and history cases
• number of professionals and education background
• number of friendship companies
• average response time for new questions
• average project close time
• charge
• service

Step 2:

Define factors by comparing importance of item with another one, then create a comparative coefficient matrix.

The factors table

The comparative coefficient matrix

Step 3:

Estimate the eigenvector.

(1) Uniform each column.

(2) Sum up by each row then uniform.

Step 4:

Estimate the maximun eigenvalue.

Step 5:

Do the test for uniform.

Step 6:

Make out the ratio.