Lecture 5

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Unformatted text preview: on the same edge of the boundary of the feasible region. 4.2 – Preview of the Simplex Algorithm General descripWon of the simplex algorithm solving an LP in a maximizaCon problem: Step 1 Find a bfs to the LP. We will call this bfs the iniWal bfs. In general, the most recent bfs will be called the current bfs, so at the beginning of the problem, the iniWal bfs is the current bfs. Step 2 Determine if the current bfs is an opWmal soluWon to the LP. If it is not, find an adjacent bfs that has a larger z‐value. Step 3 Return to Step 2, using the new bfs as the current bfs. 4.3 – The Simplex Algorithm (max LPs) The Simplex Algorithm Procedure for maximizaCon LPs Step 1 Convert the LP to standard form Step 2 Obtain a bfs (if possible) from the standard form Step 3 Determine whether the current bfs is opWmal Step 4 If the current bfs is not opWmal, determine which nonbasic variable should be come a basic variable and which basic variable should become a nonbasic variable to find a bfs with a beaer objecWve funcWon value. Step 5 Use ero s to find a new bfs with a beaer objecWve funcWon value. Go back to Step 3. In performing the simplex algorithm, write the objecWve funcWon in the form: z – c1x1 – c2x2 ‐ … ‐ cnxn = 0 We call this format the row 0 version of the objecWve funcWon (row 0 for short). 4.3 – The Simplex Algorithm (max LPs): Example The Dakota Furniture company manufactures desk, tables, and chairs. The manufacturer of each type of furniture requires lumber and two types of skilled labor: ...
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This note was uploaded on 09/20/2011 for the course ENG 300 taught by Professor Albin during the Fall '11 term at Rutgers.

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