Methods and Applications in Integer Programming: All-Integer Column Generation and Nurse Scheduling

TL;DR: In this paper, column generation methods for integer programs with a huge number of variables are discussed, including implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree.

TL;DR: The growing understanding of the dual point of view is emphasized, which has brought considerable progress to the column generation theory and practice, and is an ever recurring concept in "selected topics."

TL;DR: An exact column generation algorithm for integer programs with a large (implicit) number of columns is presented in this article, where the family of problems that can be treated includes standard partitioning problems such as bin packing and certain vehicle routing problems in which the columns generated have 0-1 compenents and a right-hand side vector of 1's.