抄録
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 one. We call welcome one as A and obnoxious one as B and two facilities A, 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, B is a random variable respectively and construction cost of both facilities simultaneously as a same site is also random variable. These are distributed according to normal distributions.
3) The probability that total construction cost become below budget f should be not less than thefixed probability levelα and f should be minimized.
4) We consider three criteria, that is, maximum distance from the construction site of A to all demand points to be minimized, minimum distance from the construction site of B to all demand points to be maximized and budget to be minimized.
Since usually there exists no site optimizing three criteria at a time, we seek non-dominated solutionafter definition of non-domination. Finally we conclude results and discuss further research problems.
