Developed by Leonid V. Kantorovich (Mathematical Methods of Organizing and Planning Production, 1939) and George B. Dantzig, whose simplex algorithm (Maximization of a Linear Function of Variables Subject to Linear Inequalities, 1951) solves it.
Writes an allocation problem as a linear objective under linear constraints and solves for the best mix, along with what loosening each constraint is worth.
When to reach for it
When dividing limited capacity, budget, people, or material across uses, and the relationships are close to linear.
How it runs
- Define the decision variables.
- Write the objective to maximize or minimize.
- Write each limit as a linear constraint.
- Solve with a standard solver.
- Read the optimum and the shadow prices, then sanity-check both.
Where it sits in SOLVE eX
Go to the source
- Mathematical Methods of Organizing and Planning Production, 1939
- Maximization of a Linear Function of Variables Subject to Linear Inequalities, Activity Analysis of Production and Allocation, edited by Tjalling C. Koopmans, Wiley; the method dates from 1947, 1951