Analisis Sensitivitas : Penambahan Kendala Baru | Kelompok 10 Teknik Riset Operasi

Summary

This presentation focuses on sensitivity analysis in linear programming, particularly the impact of adding new constraints. The discussion explains how introducing new constraints can either be active (affecting the optimal solution) or passive (having no effect). Through a detailed example, the group demonstrates how the addition of new constraints, whether in a maximization or minimization problem, alters the optimal solution. The team also elaborates on the steps involved in using the Simplex method and Dual Simplex method to solve such problems, offering insights into both theory and practical applications of sensitivity analysis in linear programming.

The video is abnormal, and we are working hard to fix it.
Please replace the link and try again.

Q & A

What is the main focus of the presentation?

The main focus of the presentation is on sensitivity analysis in linear programming, specifically the impact of adding new constraints to the optimization process.

What are the two types of new constraints in linear programming?

The two types of new constraints are 'active' and 'passive'. Active constraints affect the optimal solution, while passive constraints do not.

How do you determine if a new constraint is active or passive?

You determine if a new constraint is active or passive by substituting the values from the optimal solution table into the new constraint. If the values violate the constraint, it is active; if they satisfy the constraint, it is passive.

What happens to the optimal value in a maximization problem when a new constraint is added?

In a maximization problem, adding a new constraint typically reduces the optimal value.

What happens to the optimal value in a minimization problem when a new constraint is added?

In a minimization problem, adding a new constraint typically increases the optimal value.

What is the role of the simplex method in sensitivity analysis?

The simplex method is used to solve linear programming problems by iterating through feasible solutions until the optimal one is found. It is applied to determine how the addition of new constraints affects the solution.

What is the dual simplex method, and when is it used?

The dual simplex method is used when a linear programming solution is feasible but not optimal after adding a new constraint. It adjusts the solution to find the optimal result while maintaining feasibility.

Can a new constraint in a linear programming problem sometimes not affect the optimal solution? If so, how?

Yes, a new constraint can sometimes be passive, meaning it does not affect the optimal solution. This occurs if the constraint is satisfied by the current optimal solution without violating any conditions.

What is the significance of substituting the values into the new constraint in the simplex method?

Substituting the values into the new constraint helps determine if the solution remains valid. If the substitution results in an incorrect or violated inequality, the new constraint is considered active and will affect the optimal solution.

What is the impact of adding administrative hours as a new constraint in a production problem?

Adding administrative hours as a new constraint may reduce the overall profit or optimal solution, as it limits the available resources for production, thereby affecting the ability to maximize profit.