In this paper, we treat a single-facility minisum model in the Euclidean plane with transportation costs that are increasing functions with respect to the Euclidean distances and subject to locational and distance constraints. We examine of the optimal locations and the nearoptimal regions by sensitivity analyses. Moreover, assuming the location problem of a obnoxious-facility, we present a near-optimality region with minimum distance constraints . We apply BSSS method, to the data of the

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... palities of Ibaraki and Yamagata prefectures in Japan. As a result, we found that the stability of optimal location differs depending on the coefficient of object function. Moreover, it was shown that the stability of optimal point and the shape of near-optimality region are greatly influenced by the population distribution of the study areas.