Before we start discussing more about the constraint optimization, we need to understand what a constraint is all about.
The simplest definitions for an optimization is “Doing the most with the least”.
If you are attempting to maximize the objective function, typical constraints might involve time, money, and resources. As we know the amounts of these things are limited, and these limits also place limits on the best possible value of the objective function, if we are attempting to minimize, the constraints are more particular to the situation.
Every industry/sector has their own constraints, and they need to optimize it to reduce the cost and increase the profitability.
- Business firms and industries make decisions related to their production to maximize their profits subject to the constraint that they have limited production capacity.
- Firms/Industries to minimizing costs subject to the constraint that they have orders to fulfil.
- Consumers make decisions on what to buy constrained by the fact that their choice must be affordable.
- Households make decisions on how much to work/play with the constraint that there are only so many hours in the day.
All of these above problems fall under the category of constrained optimization.