In the airline industry, optimizing and automating the building of crew pairings is a major financial and organizational issue. The general crew pairing problem with resource constraints problem (CPP-RC) can be formulated as a minimum cost multicommodity flow problem with additional variables and resource constraints. Even though in most applications the cost of a rotation is non-linear, this chapter restricts the case where the cost function is a linear approximation. It presents the ways of constructing a network of feasible pairings, and calculating the cost of the rosters, along with the associated mathematical program. The chapter gives an overview of classical solution techniques, with a focus on the column generation method, whose associated subproblem is studied.