Technical Note—A Note on Parametric Analysis in Linear Assignment

A classic application of the linear assignment problem is the assignment of people to jobs (or jobs to people). In this context, it is interesting to measure competition for jobs and to generate a suitable list of jobs from which a person can choose; the length of the list is a parameter. A known list-generation procedure is based on an interior-point method followed by a parametric analysis. We describe a more efficient procedure, exploiting linear assignment theory and shortest-path computations. Further, we propose an alternative list-generation procedure, based on a special type of dual values for the linear assignment problem.