Linear Programming allows us to tackle various real life problems, some of which we have already gone over in previous articles, such as the Transportation Problem, the Product Mix Problem and the Diet Problem. In the following article we will analyze a different classic application known as the Production Inventory Problem. This problem is essentially […]

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## What does a Shadow Price of Zero mean in Linear Programming

As we have discussed in previous articles, the Shadow Price of a constraint represents the rate of change of the optimal value as a result of a marginal change in the right-hand side of a constraint. “Marginal” is understood as a modification that does not change the geometry of the problem, that is to say, […]

## What is a Degenerate Optimal Solution in Linear Programming

When applying the Simplex Method to calculate the minimum coefficient or feasibility condition, if there is a tie for the minimum ratio or minimum coefficient it can be broken arbitrarily. In this instance, at least one basic variable will become zero in the following iteration, confirming that in this instance the new solution is degenerate. […]

## Vogel Approximation Method (Transportation Algorithm in Linear Programming)

The Vogel Approximation Method is an improved version of the Minimum Cell Cost Method and the Northwest Corner Method that in general produces better initial basic feasible solution, which are understood as basic feasible solutions that report a smaller value in the objective (minimization) function of a balanced Transportation Problem (sum of the supply = […]

## Northwest Corner Method (Transportation Algorithm in Linear Programming)

The Northwest Corner Method (or upper left-hand corner) is a heuristic that is applied to a special type of Linear Programming problem structure called the Transportation Model, which ensures that there is an initial basic feasible solution (non artificial). Other methods for obtaining an initial basic solution are the Minimum Cell Cost Method and the […]