The simplex algorithm extended to piecewise linearly constrained problems II: an application to the gas transmission problem

We present an extension of the Simplex method for solving problems with piecewise-linear functions of individual variables within the constrains of otherwise linear problems. This work generalizes a previous work of Fourer that accommodate piecewise-linear terms in objective functions. The notion of nonbasic variable is extended to a variable fixed at a breakpoint. This new algorithm was implemented through an original extension of the XMP library and successfully applied to solve an industrial problem. Subject classification: Piecewise-linear programming, Simplex method.