Stochastic Facility Construction Problem with Preference of Candidate Sites

Abstract

This paper considers a facility construction problem in a rectangular urban area with some barriers and rectilinear distance. There exist some demand points and possible construction sites with preference. A random construction cost according to a normal distribution. The probability that the cost becomes below the budget should not be below the fixed level. One objective is that the budget should be minimized under the condition demand points are covered by at least one of facilities constructed within a certain critical distance. Another is that the minimal preference among constructed sites should be maximized. The other is to maximize minimal satisfaction degree with respect to critical distances among all demand points. We formulate our problem as a three criteria problem with a chance constraint. Since usually there exists no solution optimizing three objectives at a time, we seek some non-dominated solutions after the definition of non-domination.