I'm trying to understand how simplex algorithm works, and here are my questions:
1. Why we choose the entering variable as that with the most negative entry in the last row? My understanding is that this can increase the optimal value by the largest amount. Is this correct?
2. After determining the entering variable, why we calculate the θ-ratio just using the column corresponding to the entering variable?
3. After calculating the θ-ratio, why we ignore the negative value when deciding the exiting variable? Is this because the variable with negative θ-ratio will always increase no matter how we move? But then why we cannot set it as non-basic?
4. Do we choose the least positive θ-ratio in order to ensure all the variables are still non-negative?
5. I am taught that the simplex process can be translated as finding θ and d such that x'=x+θd where x is the current solution, x' is the new one, d is the moving direction, θ is the step size. But how this θ could equal to the θ-ratio and how d is related with anything in the tableau (the entries in the last row maybe?)?
I'm totally confused about the relation between x'=x+θd and the tableau calculation, could anyone just explain the logic behind the calculation (using the step size and direction approach) and how this can be shown on the diagram?
Best Answer
I'm assuming you're doing "Phase 2" of the simplex method, so your current tableau gives you a basic feasible solution.