A Bi-level Mixed Integer Programming Model to Solve the Multi-Servicing Facility Location Problem, Minimising Negative Impacts Due to an Existing Semi-Obnoxious Facility

We propose a bi-level multi-objective model to solve the multi-facility location problem with traffic equilibrium constraints. The main facility location problem within our proposed model consists of locating a set of buildings with varying sensitivity thresholds due to the negative impacts propagating from an existing semi-obnoxious facility. The traffic routing problem is modelled as a user equilibrium which is embedded using its Karush-Kuhn-Tucker optimality conditions. We use the convex scalarisation approach to deal with multiple objectives. Two solution methods are then contrasted: in the first method we solve our linearised model using an off-the shelf Mixed Integer Programming solver. In the second solution approach we use Benders Decomposition algorithm to improve computational tractability. Numerical results highlight the superiority of the decomposition approach when solving a realistic-sized instance.