This paper considers a bicriteria model to locate a semi-obnoxious facility within a convexpolygon, while employing Euclidean push and pull covering criteria. The partial coveringcontext is introduced into an ordinary bicriteria location framework. Although both objectives are neither concave nor convex, low complexity polynomial algorithms to find the efficient solutions and the tradeoffs involved are developed with the help of higher-order Voronoi diagrams. Comparing the tradeoff for the full covering with the others enable decision makers to understand what to extent the maximin and minimax criteria are improved at the expenseof uncovering. This is illustrated via numerical examples.Includes bibliographical reference
