Simple alogrithm
7 important questions on Simple alogrithm
When using the simplex algorithm when is a solution considered optimal?
- All NBV have a nonnegative value in row 0 (NBV >= 0)
- Right hand side >= 0
What if there is a NBV (Non Basic Variable) with a 0 coëfficient in row 0?
Considering the simplex algorithm when is an LP unbounded?
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When is an LP considered non-degenerate?
What does an degenerate LP result in?
In applying the 2 phase simplex method (minimization problem) what are the steps of phase I?
- Modify the constraints such that the right hand side of each constraint is non negative (multiplication by -1) ;
- Convert each inequality constraint to the standard/canonical form;
- Add a artificial variable a for all constraints that were bigger >= or in step 2;
- Solve the phase I LP through min w' = [all artificial variables] and force them into the basis;
- Solve the rest of the simplex;
In application of the 2 phase simplex method and the transition to phase II what are the 3 cases differentiated
w' > 0, no feasible solution for the original tableau;
Case 2
w'= 0 and no artificial variables in the BV, drop all columns corresponding to artificial variables and combine the original objective function with the constraints from the optimal phase I tableau;
Case 3
w'= 0 and at least 1 artificial variable is in the BV, drop all nonbasic artificial variables and any variable that has a negative coefficient in row 0 of the optimal phase I tableau;
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