Push-Pull Partial Covering Problems

This paper considers a bicriteria model to locate a semi-obnoxious facility within a convex polygon, while employing Euclidean push and pull covering criteria. The partial covering context 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 expense of uncovering. This is illustrated via numerical examples.