Minisum and minimax transfer point location problem with random demands points

Abdelaziz Foul; T. Mahrous; S. Djemili

Abdelaziz Foul Department of Statistics and Operations Research College of Science, King Saud University P.O.Box 2455, Riyadh 11451, Saudi Arabia
T. Mahrous Department of Statistics and Operations Research College of Science, King Saud University P.O.Box 2455, Riyadh 11451, Saudi Arabia
S. Djemili Department of Statistics and Operations Research College of Science, King Saud University P.O.Box 2455, Riyadh 11451, Saudi Arabia

Keywords: Transfer point location; Minisum facility location; Minimax facility; Probabilistic demands.

Abstract

This paper is concerned with analyzing some models of the weighted transfer point location problem under the minisum and minimax criterions when demand points are randomly distributed over regions of the plane and the location of the service facility is known. In case of minisum objective with rectilinear distance, an iterative procedure was constructed for estimating the optimal transfer point location using the hyperbolic application procedure. Exact analytic solution was obtained when the random demand points follow uniform distributions. A unified analytic optimal solution was provided for all types of probability distributions of the random demand points when the distance is the squared Euclidean distance. For minimax objective with squared Euclidean distance, an iterative procedure based on Karush-Kuhn-Tucker conditions was developed to produce an approximate solution to the optimal solution. Illustrative numerical examples were provided.

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