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sensitivity handout

# sensitivity handout - STOR 415 Handout Sensitivity analysis...

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STOR 415 Handout Sensitivity analysis: an example Consider the problem max z = 41 x 1 +25 x 2 s.t. 3 x 1 +2 x 2 + x 3 = 10 5 x 1 +3 x 2 + x 4 = 16 x 1 , ··· , x 4 0 . The initial tableau (called tableau 1): z x 1 x 2 x 3 x 4 rhs Basic var 1 -41 -25 0 0 0 z = 0 0 3 2 1 0 10 x 3 = 10 0 5 3 0 1 16 x 4 = 16 After several iterations, we arrive at the tableau below (called tableau 2), which shows the optimal BFS in which x 1 and x 2 are basic variables: z x 1 x 2 x 3 x 4 rhs Basic var 1 0 0 2 7 132 z = 132 0 1 0 -3 2 2 x 1 = 2 0 0 1 5 -3 2 x 2 = 2 Change the objective eﬃcient for x 3 Note that x 3 is a nonbasic variable in tableau 2. Let us consider changing its eﬃcient in the objective function from 0 to δ . The initial tableau (note that it is not a valid simplex tableau, because x 3 is a basic variable in this tableau, and its coeﬃcient in row 0 needs to be 0): z x 1 x 2 x 3 x 4 rhs Basic var 1 -41 -25 - δ 0 0 z = 0 0 3 2 1 0 10 x 3 = 10 0 5 3 0 1 16 x 4 = 16 After conducting the same EROs that bring tableau 1 to tableau 2, we

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sensitivity handout - STOR 415 Handout Sensitivity analysis...

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