Assignment Problem Based on Ordinal Preferences

The assignment problem, a well-known variant of which is the problem of optimal staff distribution, has formerly been treated as a problem of linear optimization starting with numerical evaluations of the assignments. In this paper the assignment problem is regarded as a problem of social choice, where preference orders are used as the sole initial information. A formal definition of an assignment function is given and various conditions for such functions are suggested. Some conditions are found to be incompatible. Several reasonable assignment functions are examined with respect to which conditions they fulfil. Finally, some problems, related to the assignment problem, are informally discussed.