Allowable decrease

Definition

Allowable decrease refers to the maximum amount by which an objective function coefficient can be reduced without changing the optimal solution of a linear programming problem. This concept is crucial in understanding how sensitive an optimal solution is to changes in the coefficients, and it plays a significant role in sensitivity analysis and parametric programming. By determining the allowable decrease, one can identify how robust the current solution is against fluctuations in input parameters.

5 Must Know Facts For Your Next Test

1. The allowable decrease helps in evaluating the stability of the optimal solution by indicating how much the coefficients can drop before a new solution is required.
2. It is derived from the dual prices associated with the constraints of a linear programming model.
3. If the allowable decrease is zero for a specific coefficient, it means that any reduction will immediately change the optimal solution.
4. This concept allows decision-makers to understand how sensitive their decisions are to changes in input data, helping in risk assessment.
5. The allowable decrease is often calculated during sensitivity analysis, which examines how variations in parameters affect the outcomes.

Review Questions

• How does allowable decrease impact decision-making in linear programming?
  • Allowable decrease significantly impacts decision-making by indicating how much flexibility there is in adjusting objective function coefficients without altering the optimal solution. By understanding this limit, decision-makers can assess potential risks associated with changes in input data. If they know that a coefficient can be decreased by a certain amount while maintaining optimality, they can make informed decisions about resource allocation and budgeting.
• Discuss the relationship between allowable decrease and sensitivity analysis in linear programming.
  • Allowable decrease is a key component of sensitivity analysis, which evaluates how changes in input parameters affect the optimal solution. Sensitivity analysis utilizes allowable decrease values to show how stable an optimal solution is when faced with variations in objective function coefficients. By analyzing these values, one can determine which coefficients have more influence on the outcome, guiding more effective decision-making and strategic planning.
• Evaluate the implications of an allowable decrease of zero on an optimal solution and its significance in practical applications.
  • An allowable decrease of zero indicates that any reduction in that coefficient will lead to a change in the optimal solution, highlighting a critical sensitivity point. In practical applications, this signifies that stakeholders must be particularly cautious with any alterations to that specific parameter, as even minor changes could result in suboptimal outcomes. Understanding this limitation allows organizations to prepare for various scenarios and make strategic adjustments while maintaining effectiveness in operations.

Related terms

sensitivity analysis: A method used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions.

objective function: A mathematical expression that defines the goal of a linear programming problem, typically to maximize or minimize some quantity.

shadow price: The value that represents the change in the objective function's value resulting from a one-unit increase in the right-hand side of a constraint.