We define and study the concept of Contraction Functions to solve the point formation problem in robotics. Interestingly, the discussion leads to the Weber point that plays an important role in facility location. We introduce the notion of Convex Core and show that this helps to locate the Weber point.

The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. We follow Dendievel [10], [11], (where a bibliography can be found) who studies several types of such problems, mainly initiated by Bruss [3...

The Multisource Weber problem, also known as the continuous locationallocation problem, or as the Fermat-Weber problem, is considered here. A particular case of the Multisource Weber problem is the minimum sum-of-distances clustering problem, also known as the continuous p-median problem. The mathematical modelling of this problem leads to a min− sum−min formulation which, in addition to its in...

In this survey, we examine an important class of facility location problems known as the multisource Weber problem (also referred to as the continuous location-allocation problem). We also show how recent advances in the use of metaheuristic rules have significantly improved the ability to solve problems of this type. The new solution methods are discussed for both the well known multisource W...