Linear programming is used daily in the real world to optimize the allocation of resources or activities to generate the most benefit or profit. Linear programming can take multiple factors into account into the thousands and is used extensively by business managers, economists and public planners.
Linear programming takes relevant variables of a situation into account and their effect on the desired outcome, and any constraints such as the availability of a limited resource. In real-life situations, linear programming may have to be extended to include additional constraints as they come up.
Real world examples using linear programming include:
- Optimizing the operations of transportation networks to ensure the most efficient patterns of transporting goods and people; in its most basic sense, finding out what trains should go where and when.
- Minimizing production costs at a manufacturing facility by determining the optimal balance of production according to resources and customer demand.
- Maximizing a company's profits by determining the best possible combination of activities to bring in the most money at the least cost.
- Reducing risk in a potentially hazardous operation by determining the best possible combination of human and other resources.
The so-called Simplex algorithm, which lies at the heart of linear programming, was invented by George Dantzig in 1947.