Linear Programming in Matrix Form

We first introduce matrix concepts in linear programming by developing a variation of the simplex method called the revised simplex method. This algorithm, which has become the basis of all commercial computer codes for linear programming, simply recognizes that much of the information calculated by the simplex method at each iteration, as described in Chapter 2, is not needed. Thus, efficiencies can be gained by computing only what is absolutely required. Then, having introduced the ideas of matrices, some of the material from Chapters 2,3, and 4 is recast in matrix terminology. Since matrices are basically a notational convenience, this reformulation provides essentially nothing new to the simplex method, the sensitivity analysis, or the duality theory. However, the economy of the matrix notation provides added insight by streamlining the previous material and, in the process, highlighting the fundamental ideas. Further, the notational convenience is such that extending some of the results of the previous chapters becomes more straightforward.