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Sensitivity Analysis in LP
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Allowable Increase and Decrease
The maximum amount by which an objective function coefficient can increase (allowable increase) or decrease (allowable decrease) before the current set of basic variables changes.
Reduced Cost
The amount by which the coefficient of a non-basic variable must improve (increase for maximization, decrease for minimization) before that variable can enter the basis (become a basic variable).
Monte Carlo Simulation
Though not a traditional part of linear programming, Monte Carlo simulations can be used in sensitivity analysis to run scenarios with a range of input values generated randomly from a probability distribution to assess the impact on an outcome.
Sensitivity Range for Constraints
The range within which the right-hand side coefficients of the constraints can change without changing the optimal basis in a linear programming problem. This range is determined for each constraint to understand the flexibility in resource availability.
Objective Function Coefficient Range
The range of values over which an objective function coefficient can change without altering the optimal basis of the solution. This range is important in sensitivity analysis to understand how much a parameter can vary before the current solution is no longer optimal.
Shadow Price (Dual Price)
Refers to the marginal value of a resource or the rate of improvement in the objective function's value for a one-unit increase in the right-hand side of a constraint, given that all other coefficients remain constant.
Scenario Analysis
It involves creating and analyzing different 'what-if' scenarios to observe how changes in one or more inputs to a linear programming model affect the optimal solution.
Sensitivity Analysis
Sensitivity analysis determines how different values of an independent variable affect a particular dependent variable under a given set of assumptions. In the context of linear programming, it is used to understand how the changes in coefficients of the objective function or constraints can affect the optimal solution.
Parametric Analysis
A part of sensitivity analysis where a systematic approach is adopted to see the effect of varying one or more parameters (objective function coefficients or constraint values) while keeping other parameters constant, in order to observe the impact on the optimal solution.
Break-even Analysis
A component of sensitivity analysis that is used to determine the point at which total costs and total revenues are equal. It helps in understanding the impact of changes in costs, prices, and volumes on profitability.
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