New stochastic models for minimax transfer point location problem

The transfer point location problem has been introduced recently and for the case of minimax objective and planar topology, has only been studied for situations in which demand points are not weighted and have known coordinates. In this paper we consider the case in which demand points are weighted and their coordinates have a bivariate uniform distribution. Also the problem is developed from a conceptual view and different distance measures are used to make models more applicable in real world situations. The problem is to find the best location for the transfer point such that the maximum expected weighted distance to all demand points through the transfer point is minimized. Depending on assumptions for uniform distributions, two models are considered, convexity conditions are discussed, properties of the optimal solution are obtained and methods to solve the problems are proposed. Finally numerical examples are given.