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For a publ ic faci lity con struction, usua lly we use min-ma x or m ax-min criterio n depen ding on fac ility nature, i.e., useful or obnoxious. City hall, hospital etc. are considered to be typical useful facility. While a disposal center, a waste disposal center etc. are considered to be a typical obnoxious facility. But even city center or hospital has many aspects and so users are divided into two groups. Each user in a group considers distance from the facility should be as close as possible (we call this group welcome group) and each user in the other group considers its distance should be as far as possible (we call the group not welcome group). Therefore, we seek a facility construction site in an urban area minimizing the maximum among all rectilinear distances from it to users of welcome group and maximizing the minimum among all rectilinear distances from it to users of not welcome group under the presence of barriers. But usually there are no fa cility construction site op timizing bo th criteria s imultaneously. T herefore we find some nondominated sites after defining non-domination about facility construction site. In order to find them, we utilize an id ea of fo rbidden regions where we cann ot const ruct a faci lity. First we consider the fi nite number case of candidate facility construction site and next discuss the infinite number case of them. For the finite nu mber case, we reduce our pro blem into the shortest path problem with special network and obtain some non-dominated sites. For the infinite number case, we divide the feasible region of problem into s ub-regions. For sub-probl em corres ponding to each sub-region , we propose an efficient solu tion procedure utilizing the res ults in th e fini te num ber case. B ased on th e optimal soluti on of ea ch s ubproblem, we obtain some non-dominated sites. Finally we summarize the result of this paper and discuss further research problems.

Facility location problem under users with two type criteria, min-max and max-min