On minimizing distance by the road less traveled (Q1879395)

The paper deals with location problems in one and two-dimensional spaces, in which fixed positions of ``customers'' are considered. On the contrary to the most of other contributors, the authors focused on the least absolute difference, which corresponds to \(\ell_1\) or ''Manhattan'' distance. This restriction enabled them to solve the location problems using tools of elementary mathematics. There are located two different objects in the studied cases, which are accompanied by a sequence of nice illustrative examples. In the first part of the paper, a location of such a point is sought so that sum of distances to the customers is minimal. In the second part, the best fitting location of a line in two-dimensional space is studied. The concluding part of the paper deals with discrete optimisation problem in two variables, where such a solution of Diophantine equation is sought, which minimizes the least absolute difference from the beginning of space coordinates. It can be stated that the authors provide an excellent insight into a part of location problems unless they avert off readers attention by employing special solving techniques.