Column Generation in Integer Programming with Applications in Multicriteria Optimization

This paper presents in a unified form a column generation scheme for integer programming. The scheme incorporates the two major algorithmic approaches in integer programming, the branch and bound technique and the cutting plane technique. With integrality conditions imposed on the variables it is of importance to limit the number of columns introduced in the integer programming problem. This is equally important in the case of multiple criteria where usually multiple alternative efficient solutions are required. The suggested scheme gives additional dual information that limits the work required to move among the alternatives to be generated.