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simplex_method_lecture_1-1

simplex_method_lecture_1-1 - THE SIMPLEX ALGORITHM I Step 1...

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THE SIMPLEX ALGORITHM I Step 1 Convert LP into standard form. Step 2 Obtain a bfs (if possible) from standard form. Step 3 Determine if the bfs is optimal. Step 4 If non-optimal, determine: a nonbasic variable that should become basic. A basic variable that should become nonbasic. Step 5 Use ero’s to find new bfs with better obj val. Go to step 3. Saigal (U of M) IOE 310 1 / 9
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FLOW CHART - SIMPLEX ALGORITHM start with a bfs is it optimum ? stop yes no is there a leaving variable? stop no yes find new bfs unbounded solution optimum solution Saigal (U of M) IOE 310 2 / 9
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AN EXAMPLE I A furniture manufacturer has the following data: Desk Table Chair Available Lumber in Board ft 8 6 1 48 Finishing Hours 4 2 1.5 20 Carpentry Hours 2 1.5 0.5 8 Selling Price $60 $30 $20 Decision variables x 1 x 2 x 3 number produced Saigal (U of M) IOE 310 3 / 9
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AN EXAMPLE II The LP Model: max z = 60 x 1 + 30 x 2 + 20 x 3 8 x 1 + 6 x 2 + x 3 48 4 x 1 + 2 x 2 + 1 . 5 x 3 20 2 x 1 + 1 . 5 x 2 + 0 . 5 x 3 8 x 2 5 with x j 0 for each j = 1 , · · · , 3.
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