Covering problems with polyellipsoids: A location analysis perspective

In this paper we analyze the extension of classical smallest enclosing disk problem to case location a polyellipsoid fully cover set demand points in Rd. We prove that is polynomially solvable fixed dimension and mathematical programming formulations for it. also consider some geometric approaches foci polyellipsoids are known. Extensions algorithm by Elzinga-Hearn derived new problem. Moreover, address two extensions problem, as where not given have be determined among potential or induced covering problems when instead polyellipsoids, one uses ordered median polyellipsoids. For these present Mixed Integer (Non) Linear Programming strategies lead efficient ways solve Extensive computational experiments on different datasets show usefulness our solution methods.