# Definitions for reduced costre·duced cost

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1. Reduced cost

In linear programming, reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (so increase for maximization problem, decrease for minimization problem) before it would be possible for a corresponding variable to assume a positive value in the optimal solution. It is the cost for increasing a variable by a small amount, i.e., the first derivative from a certain point on the polyhedron that constrains the problem. When the point is a vertex in the polyhedron, the variable with the most extreme cost, negatively for minimization and positively maximization, is sometimes referred to as the steepest edge. Given a system minimize c T x {\displaystyle \mathbf {c} ^{T}\mathbf {x} } subject to A x ≤ b , x ≥ 0 {\displaystyle \mathbf {Ax} \leq \mathbf {b} ,\mathbf {x} \geq 0} , the reduced cost vector can be computed as c − A T y {\displaystyle \mathbf {c} -\mathbf {A} ^{T}\mathbf {y} } , where y {\displaystyle \mathbf {y} } is the dual cost vector. It follows directly that for a minimization problem, any non-basic variables at their lower bounds with strictly negative reduced costs are eligible to enter that basis, while any basic variables must have a reduced cost that is exactly 0. For a maximization problem, the non-basic variables at their lower bounds that are eligible for entering the basis have a strictly positive reduced cost.

### ChatGPTRate this definition:0.0 / 0 votes

1. reduced cost

Reduced cost refers to the measure of how much the objective function value would decrease if the value of a decision variable in a linear programming model is reduced by one unit. It represents the opportunity cost or shadow price of reducing the value of a decision variable in terms of the objective function.

### Numerology

1. Chaldean Numerology

The numerical value of reduced cost in Chaldean Numerology is: 1

2. Pythagorean Numerology

The numerical value of reduced cost in Pythagorean Numerology is: 9

### Examples of reduced cost in a Sentence

1. Shelters can be a valuable resource for pet owners who are struggling, they can often provide direct support, recommendations for trainers or behavioralists, and access to reduced cost medical care and pet food.

## Translations for reduced cost

• 降低成本

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"reduced cost." Definitions.net. STANDS4 LLC, 2024. Web. 14 Apr. 2024. <https://www.definitions.net/definition/reduced+cost>.

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