Facility Location Problem under Fuzzy Construction Cost and Preference of Candidate Sites

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 of construction. For each site, its construction cost is a fuzzy number due to the difficulty of the exact estimation and we should decide suitable facility construction places under the condition that each demand point is covered within some distance from at least one facility. Under this condition, the total cost should be minimized and minimal preference among facility constructed sites maximized. Since total construction cost is also fuzzy number, we consider the fuzzy order and seek some non-dominated solutions after definition of non-domination.