Allowable range

Definition

The allowable range refers to the limits within which the coefficients of a mathematical model can vary without changing the optimal solution. This concept is particularly important when analyzing how sensitive an optimal solution is to changes in input values, helping to identify the robustness of the solution in a given situation.

5 Must Know Facts For Your Next Test

1. The allowable range helps determine how much a coefficient in an objective function can change before the optimal solution changes.
2. In sensitivity analysis, understanding the allowable range can help decision-makers assess risk and make informed adjustments to their models.
3. If a coefficient falls outside its allowable range, it may lead to a completely different optimal solution, prompting a reevaluation of the entire model.
4. The concept of allowable range applies not only to coefficients in objective functions but also to constraints in linear programming models.
5. Evaluating the allowable range is essential for identifying stable solutions in optimization problems, ensuring that decisions are robust against small fluctuations in data.

Review Questions

• How does the allowable range influence decision-making in optimization problems?
  • The allowable range directly impacts decision-making by indicating how much flexibility exists in the coefficients of a mathematical model without altering the optimal solution. If decision-makers understand this range, they can confidently make adjustments to input values while knowing their current solutions remain valid. This insight is crucial for effective planning and resource allocation in various business scenarios.
• Discuss the relationship between allowable range and sensitivity analysis in linear programming.
  • The allowable range is a key component of sensitivity analysis, which examines how variations in input values affect outcomes. When conducting sensitivity analysis, practitioners evaluate how changes in coefficients within their allowable ranges influence the optimal solution. By understanding these relationships, analysts can better prepare for potential changes in conditions and ensure robust solutions that withstand variability.
• Evaluate how exceeding the allowable range can impact optimization models and their solutions.
  • Exceeding the allowable range can lead to significant shifts in optimization models and may result in entirely different solutions. When coefficients move outside their predefined limits, it can invalidate previous decisions made based on the original model's outcomes. This necessitates a reassessment of the entire model, potentially leading to new strategies and operational adjustments that may not have been anticipated initially.

Related terms

Sensitivity Analysis: A method used to determine how different values of an independent variable affect a particular dependent variable under a given set of assumptions.

Objective Function: A function that defines the goal of a linear programming problem, typically representing the quantity to be maximized or minimized.

Constraints: Conditions or limitations placed on the variables in a mathematical model, defining the feasible region within which the solution must lie.