05 Post Optimal Analysis
Deals with situation of finding new solution in efficient way when parameters are changed
Actions¶
| Existing Soln Feasible? | Existing Soln Optimal? | \(\implies\) | Action |
|---|---|---|---|
| ✅ | ✅ | No action | |
| ✅ | ❌ | Use primal simplex | |
| ❌ | ✅ | Use dual simplex | |
| ❌ | ❌ | Use generalized simplex method |
Change in Feasibility¶
| Change | Steps |
|---|---|
| RHS of constraint equation changes | 1. Check feasibility with inverse method 2. Calc new obj(), with values from step 1 3. Update table 4. Use dual simplex 5. Calc obj() when feasibility is maintained/obtained |
| Addition of new constraint(s) | 1. Check feasibility by substituting existing values into new constraint 2. Introduce slack/surplus into equation 3. Introduce slack/surplus row & column into table 4. Update introduced basic var row using below formula 5. Use dual simplex 6. Calc obj() when feasibility is maintained/obtained |
\[ \begin{aligned} & \text{Updated row of introduced basic var} \\ & = \text{Initial row of introduced basic var} - \left( \sum \text{coeff}_i \times x_i \right) \end{aligned} \]
where
- \(x_i =\) basic variables in new constraint
- coeff\(_i\) = coeff of \(x_i\) in new constraint
Change in Optimality¶
Caused due to change in obj()
Steps
- Find the dual var values, using new obj() coeff
- Check optimality
- If optimality is maintained, go to step 6
- Update obj() row using
- coeff found when checking optimality
- original obj() value, using above latest coeff
- Use primal simplex
- Calculate latest solution in new obj()
New Constraint¶
| Type | Meaning |
|---|---|
| Redundant | A new constraint that does not affect feasibility of an existing optimum solution. |
| Binding | - A new constraint that affects feasibility of an existing optimum solution. - Simplex table after incorporating the constraint |