# Constraint

A constraint is a limitation of possibilities.

## Mathematics

In mathematics, a constraint is a restriction of the feasible solutions in an optimization problem.

## Theory of constraints

In the theory of constraints, it is any factor that limits the performance of a system with respect to its goal. In a for-profit business, this would be the factors that limit the ability to make money.

To take a simple example: a chain has 5 links, each link capable of holding a maximum weight of 5, 7, 4, 8 and 6 tonnes respectively. The maximum weight the chain can hold is clearly 4 tonnes – the limit imposed by the weakest link. In this case, all 5 links have limits to their strength, but the 3rd link is the constraint because it is the greatest restriction on the system.

Eliyahu M. Goldratt maintains that any business system has

• at least one constraint, otherwise its performance would be infinite
• very few constraints, otherwise it would be unstable and cease to exist

Constraints are physical or systemic limits on capacity (such as equipment, people new product development, "the market"). In the past, TOC experts talked about "policy constraints," but these are no longer considered to be true constraints. Policies and behaviors are barriers to be overcome when implementing changes, they are not constraints.

The concept of constraint is the basis for Goldratt's process of focused improvement.

## Literature

For constraints in literature, see constrained writing.