Euclidean push–pull partial covering problems

This paper considers a bicriteria model to locate a semi-obnoxious facility within a convex polygon. Assuming that a given number of closest points and farthest points may be neglected in the analysis, it considers simultaneously the resulting push and pull partial covering criteria with Euclidean distances. Although both objectives are neither concave or convex, low complexity polynomial algorithms to find all the efficient solutions and the tradeoffs involved are developed by way of higher-order Voronoi diagrams. Comparison of the tradeoff for full covering and partial covering enables decision makers to understand to what extent the maximin and minimax criteria are improved at the expense of neglecting some points. The extensions to different sets of points pulling and pushing the facility and to weighted points are discussed. All methods are illustrated via small scale examples.