Lecture 5 - Adapting the Simplex algorithm to other LP...

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Adapting the Simplex algorithm to other LP Models “=“ and “ ” type of constraints The Big-M Method Negative RHSs Minimization models No solution case
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“=“ type of constraints Recall that we have a basic variable (a slack variable for a “ ” constraint of the canonical model) in every constraint equation in the initial SM tableau. When we have a “=“ type of constraint we cannot insert a slack variable in it. Instead, we add an artificial variable to the LHS to serve as the initial basic variable and penalize it with a huge cost (big-M) in the objective function in order to guarantee that the artificial variable will become nonbasic and be set equal to zero as a result of optimization. Only then, the solution will become feasible for the original model.
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A modified LP model Consider a LP of the form max Z = 3 x 1 + 5 x 2 st: x 1 4 2 x 2 12 3 x 1 + 2 x 2 = 18 x 1 0, x 2 0 Set up this model now as follows: Z - 3 x 1 - 5 x 2 + M x 5 ’ =0 x 1 + x
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Lecture 5 - Adapting the Simplex algorithm to other LP...

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