limitscost

Limitscost is a term used in optimization and cost analysis to describe the marginal or incremental cost associated with a system resource approaching its limit or binding constraint. The concept is used to quantify how total cost responds as a constraint tightens, such as capacity, budget, or time limits, and to distinguish the effect of nearing the limit from the benefits of relaxing the constraint.

In mathematical terms, limitscost can be framed as the rate of change of the optimal objective value with respect to a constraint bound. Consider a parametric optimization problem where a bound B governs a constraint; the limitscost at B reflects how the minimum or maximum objective changes as B is varied. In continuous optimization, this can be expressed as a derivative of the optimal value with respect to the bound, when such a derivative exists. In linear programming, the concept aligns with the idea that the cost impact near the boundary is governed by the dual price (shadow price) of the binding constraint; if the constraint is non-binding, the limitscost is typically zero.

Applications of limitscost appear in production planning, inventory management, energy systems, and network design, where understanding costs near resource limits supports risk assessment and pricing decisions. Limitations include potential non-differentiability at binding or degenerate solutions and the need for appropriate modeling of discrete decisions.

See also: marginal cost, shadow price, dual values, constraint programming, parametric optimization.