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

Integer programming can be used to provide solutions to complex decision and planning problems occurring in a wide variety of situations. Applying integer programming to a real life problem basically involves a first phase where a mathematical model is constructed, and a second phase where the problem described by the model is solved. While the nature of the challenges involved in the respective two phases differ, the strong relationship between the properties of models, and which methods that are appropriate for their solution, links the two phases. This thesis constitutes of three papers, of which the third one considers the modeling phase, while the first and second one consider the solution phase. Many applications of column generation yield master problems of set partitioning type, and the first and second papers present methodologies for solving such problems. The characteristics of the methodologies presented are that all successively found solutions are feasible and integral, where the retention of integrality is a major distinction from other column generation methods presented in the literature. The third paper concerns nurse scheduling and describes the results of a pilot implementation of a scheduling tool at a Swedish nursing ward. This paper focuses on the practical aspects of modeling and the challenges of providing a solution to a complex real life problem.