Decomposition Methods

Decomposition methods are techniques for exploiting the tractable substructures of an integer program in order to obtain improved solution procedures. In particular, the goal is to derive improved methods of bounding the optimal solution value, which can then be used to drive a branch-andbound algorithm. Such methods are the preferred solution approaches for a wide range of important models arising in practice and have also been the basis for solution approaches for many well-known combinatorial problems. A small sample of the problems for which decomposition approaches have been proposed in the literature includes the Multicommodity Flow Problem [11], the Cutting Stock Problem [15, 37], the Traveling Salesman Problem [19], the Generalized Assignment Problem [18, 35], the Bin Packing Problem [39], the Axial Assignment Problem [2], The Steiner Tree Problem [25], the Single-Machine Scheduling Problem [36], the Graph Coloring Problem [27], and the Capacitated Vehicle Routing Problem (CVRP) [1, 10, 32, 12].