Abstract
We consider the following problem: 1) There are demand points and possible construction
sites in an urban area with some barriers. We adopt rectilinear distance. 2) We construct
two facilities, one is welcome facility and the other obnoxious facility We call welcome
facility as A and obnoxious facility as B. Two facilities A and B can be constructed at
the same site or constructed separately, that is, at two different sites. We assume that
each construction cost of A and B is a random variable with fuzzy mean respectively and
construction cost of both facilities simultaneously as a same site is also random variable with
fuzzy mean. These are distributed according to normal distributions with fuzzy means. 3)
The probability that total construction cost becomes below budget f should not be less than
the fixed probability level. α and further the possibility that this chance constraint holds
should be not less than the fixed level β. Under this possibility chance constraint f should
be minimized. 4) We consider three criteria, (a) maximum distance from the construction
site of A to all demand points to be minimized, (b) minimum distance from the construction
site of B to all demand points to be maximized, (c) budget to be minimized. Since usually
there exists no site optimizing three criteria at a time, we seek non-dominated solution
after definition of non-domination. Finally, we conclude results and discuss further research
problems
