Mathematical Ranking Method for Emergency Facility Location Problem with Block-wisely Different Accident Occurrence Probabilities

Abstract

This paper provides a model of emergency facility location problem with block-wise different accident occurrence probabilities comparing our previous one [1]. That is, this paper consider the following problems. (1) There exists a polygonal area X where an ambulance service station should be located and there exists m hospitals. We assume that possible candidates of emergency construction are in X and finite number. If an accident (demand) occurs, the ambulance cars rush to the scene of accident (demand point) and bring the injured persons to the nearest hospital as soon as possible.(2) Demand points are distributed with block-wise uniform probabilities in X. (3) S(Q) denotes the nearest hospital to the point Q ∈ X . Weighted A-distance of the route from the station to the hospital via the accident point is considered. (4) For the maximum weighted distance from the station to each block with uniform accident occurrence probability, the satisfaction degree is considered with respect to this distance. (5) We also consider the preference function of the each candidate point. (6) Using these weighted distances, we exploit cross evaluation method [2] as ranking method and calculate the geometric mean score of each candidate point. It should be maximized. Further preference function should be maximum. (7) But since usually there exists no site optimizing both objectives at a time, we seek some non-dominated sites after the definition of non-domination.For the above problem, using Voronoi diagram of hospitals and extending some results of our previous paper ([3]), we propose a solution procedure to find some non-dominated solutions.