The bicriterion semi-obnoxious location problem solved by an ε-approximation

Locating an obnoxious (undesirable) facility is often modeled by the maximin or maxisum problem. But the obnoxious facility is often placed unrealistically far away from the demand points (nodes), resulting in prohibitively high transportation cost/time. One solution is to model the problem as a semi-obnoxious location problem. Here we model the problem as a bicriterion problem, not in advance determining the importance of the obnoxious objective compared to the cost/time objective. We consider this model for both the planar and the network case. The two problems are solved by an approximation algorithm, and the models are briefly compared by means of a real-life example.