Monday, July 23, 2018

Mathematical view of assignment problem

Example from [2]



I was reading some old (really old) papers on the assignment problem. The style is much more verbose than we see nowadays, and examples are very small (that is actually not a bad thing).

In [2] (and referred to by [1]) is a well-known statement about mathematicians:

There are, as has been indicated, a finite number of permutations in the assignment of men to jobs. When the classification problem as formulated above was presented to a mathematician, he pointed to this fact and said that from the point of view of the mathematician there was no problem. Since the number of permutations was finite, one had only to try them all and choose the best. He dismissed the problem at that point. This is rather cold comfort to the psychologist, however, when one considers that only ten men and ten jobs mean over three and a half million permutations. Trying out all the permutations may be a mathematical solution to the problem, it is not a practical solution. 

This is a little bit like "applied mathematics is bad mathematics"...


References


  1. Tjalling C. Koopmans and Martin Beckmann, Assignment Problems and the Location of Economic Activities, Econometrica Vol. 25, No. 1 (Jan., 1957), pp. 53-76
  2. Robert L. Thorndike, The Problem of Classification of Personnel, Psychometrika, Vol. 15, No. 3, September, 1950