Building Negative Reduced Cost Paths Using Constraint Programming

Abstract

Column Generation is a powerful method used to solve Constrained Set Partitioning problems. This method can be decomposed in two parts:the master problem and the sub-problem. The Master Problem that should be solved in Column Generation is derived from a simple Set Partitioning problem. Depending on the context the subproblem may become a variant of the simple Shortest-Path Problem; applications in scheduling generally present an acyclic graph (since one dimension of the graph is time) as opposed to routing problems that are cyclic by nature. However, most real life applications present resource constrained sub problems, typical resources being time, capacity, money, etc.

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