We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality.Expand

A combination of problem preprocessing, cutting planes, and clever branch-and-bound techniques permit the optimization of sparse large-scale zero-one linear programming problems, even those with no apparent special structure, in reasonable computation times.Expand

We present a single model and solution approach to solve simultaneously the fleet assignment and aircraft routing problems, which can capture costs associated with aircraft connections and complicating constraints such as maintenance requirements.Expand

Redistricting, the redrawing of congressional district boundaries within the states, may occur every 10 years on the basis of the population census. Many redistricting plans are designed with… Expand

In this paper, we present a mathematical formulation for the aircraft rotation problem (ARP) and discuss its similarity with the asymmetric traveling salesman problem.Expand

A theory is developed for a group problem arising from mixed integer programming. This theory gives descriptions of functions on the unit hypercube from which cutting planes can be constructed for… Expand