Linear programming, sensitivity analysis, decision trees, expected value and simulation.
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- What is linear programming?
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A mathematical technique for optimizing a linear objective function subject to linear constraints, used to find the best allocation of resources.- What is the objective function in linear programming?
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The linear expression that is being maximized or minimized, such as profit, cost, or revenue.- What are constraints in a linear programming model?
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Linear inequalities or equalities that represent resource limitations, requirements, or relationships that the solution must satisfy.- What is the feasible region in linear programming?
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The set of all points that satisfy all constraints simultaneously, representing all possible solutions.- What is the corner point method?
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An algorithm that evaluates the objective function at each corner point of the feasible region to find the optimal solution.- Where is the optimal solution located in a linear program?
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At a corner point (vertex) of the feasible region, provided a finite optimal solution exists.- What is a shadow price?
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The rate of change in the optimal objective function value per unit increase in the right-hand side of a constraint.- What is a slack variable?
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A non-negative variable added to a less-than-or-equal constraint to convert it to an equation, representing unused resource capacity.- What is a binding constraint?
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A constraint where the slack variable is zero, meaning the constraint is active at the optimal solution and limits further improvement.- What is a non-binding constraint?
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A constraint where the slack variable is positive at the optimal solution, meaning the constraint does not limit the objective value.- What is a degenerate solution?
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An optimal solution where more than the minimum required number of constraints are binding, potentially indicating multiple optimal solutions.- What is sensitivity analysis?
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The study of how changes in parameters affect the optimal solution and objective function value of an optimization model.- What is a reduced cost?
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For a non-basic variable, the amount by which the objective coefficient must change before it becomes part of the optimal solution.- What is an allowable range?
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The interval of values over which a parameter can change without altering the optimal basis or the structure of the solution.- What is the range of optimality?
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The allowable range for an objective function coefficient over which the current optimal basis remains optimal.
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