8. Branch-and-Price Decomposition for Assignment and Location Problems

This chapter addresses a number of models with an assignment-based structure that require allocating a set of demands to a set of resources. While we have already considered several types of assignment problem in previous chapters, each of these previous models assumed that a specific assignment cost could be specified a priori, which depends only on the particular demand and the resource to which it is assigned. In contrast, for the models considered in this chapter, the costs associated with a resource will sometimes depend on the collective set of demands assigned to the resource. The primary approach applied for solving these problems will be a branch-and-price decomposition method. Of particular interest in applying this approach are the so-called pricing problems that arise in the decomposition. As we will see, these pricing problems will be consistent with several of the models defined and analyzed in previous chapters.