Allowable Increase/Decrease

Definition

Allowable increase and decrease refer to the maximum amounts by which the coefficients of the objective function or the right-hand side constants in a linear programming problem can change without affecting the current optimal solution. These values provide crucial insights into how sensitive a solution is to changes in input parameters, allowing for informed decision-making in resource allocation and operational planning.

5 Must Know Facts For Your Next Test

1. Allowable increases and decreases help identify how robust an optimal solution is against changes in parameter values of the objective function.
2. If the allowable increase for a coefficient is exceeded, the current solution may no longer be optimal, and a new optimal solution will need to be identified.
3. The allowable decrease functions similarly, indicating how much a coefficient can reduce before necessitating a reevaluation of the current solution.
4. These ranges are typically calculated during sensitivity analysis as part of the revised simplex method, providing useful insights for decision-makers.
5. Understanding allowable increases and decreases can help in planning for resource management by indicating how flexible solutions are to changes in input values.

Review Questions

• How do allowable increases and decreases contribute to understanding the sensitivity of an optimal solution in linear programming?
  • Allowable increases and decreases directly relate to sensitivity analysis by highlighting how much change in coefficient values can occur without altering the optimal solution. This understanding is vital for assessing the stability of solutions when there are fluctuations in resources or costs. By analyzing these ranges, decision-makers can determine whether adjustments to parameters will require a new optimal solution or if they can operate within existing constraints.
• Discuss how the allowable increase/decrease concept is applied during the revised simplex method.
  • In the revised simplex method, allowable increases and decreases are calculated after identifying an optimal tableau. These values indicate how much each coefficient in the objective function can change while maintaining optimality. If changes exceed these limits, it signals that a pivot is needed to find a new optimal solution. Thus, this concept serves as a critical check during iterations of the revised simplex method, guiding adjustments and ensuring that optimality is preserved.
• Evaluate the implications of ignoring allowable increases and decreases when making decisions based on linear programming solutions.
  • Ignoring allowable increases and decreases can lead to significant consequences when implementing decisions based on linear programming solutions. For instance, if decision-makers proceed with plans that exceed these limits, they risk making inefficient choices that might not yield optimal outcomes or could require additional adjustments later on. This oversight could result in resource misallocation, increased costs, or suboptimal performance overall, ultimately undermining strategic objectives and operational efficiency.

Related terms

Sensitivity Analysis: A method used to determine how the variation in the output of a model can be attributed to changes in the inputs, often applied in linear programming to assess stability.

Shadow Price: The value associated with an additional unit of a resource in a linear programming problem, indicating how much the objective function would improve if the resource were increased.

Optimal Solution: The best feasible solution to a linear programming problem, maximizing or minimizing the objective function while satisfying all constraints.