Robust Location of New Housing Developments Using a Choice Model

We consider the issue of choosing a subset of locations to construct new housing developments maximizing the satisfaction of potential buyers. The allocation of demands to the selected locations is modeled by a choice model, based on the distance to the location, real-estate prices and incomes. We study two robust counterparts of the optimal location problem, where uncertainty lies on demand volumes for the first one, and on customer preferences for the second one. In both cases, the parameters subject to uncertainty appear both in the objective function and constraints. The second robust model combines a scenario-based approach with nominal, price-centric and distance-centric scenarios on customers preferences, and an uncertainty budget approach that limits the number of cities that can deviate from the nominal scenario. Computational experiments are conducted on instances of the Paris region to analyze the tractability of the problem and its robust counterparts, and derive insights for the new housing development issue