In linear programming, what does 'reduced cost' refer to?

Reduced cost in linear programming specifically refers to the amount by which the objective function coefficient of a decision variable must improve before that variable can take on a positive value in the optimal solution. In other words, it measures how much the objective function would increase or decrease if one additional unit of a non-basic variable were introduced into the solution.

When a variable has a reduced cost of zero, it means that including it in the solution doesn't affect the current optimal value. Conversely, if the reduced cost is positive for a minimization problem (or negative for a maximization problem), it indicates that the variable would not be included at the current solution but may become beneficial if its coefficient improved sufficiently.

This concept is integral in understanding the implications of adjusting constraints or coefficients within the linear programming model, as it directly relates to the sensitivity of the solution concerning the variables involved. Reduced costs are essential for determining which variables to consider while optimizing the objective function further, thus reflecting the dual value related to the constraint associated with that variable.