conic optimization reformulation for the continuous center location problem under uncertainty

In this paper, we consider the euclidean continuous minimax location problem under uncertainty. we consider the single-facility and the multifacility case with uncertain location of demand points and uncertain transportation costs. we study these two problems under two kinds of uncertainty, the interval and the ellipsoidal uncertainty. equivalent formulations of robust counterparts of the single facility and multi facility euclidean continuous minimax location problems under interval and ellipsoidal uncertainty are given as conic optimization problems.