Planar expropriation problem with non-rigid rectangular facilities

In this paper, we introduce the planar expropriation problem with non-rigid rectangular facilities. The facilities considered in this study are two-dimensional facilities of rectangular shape. Moreover, we allow the facility dimensions to be decision variables and introduce the concept of non-rigid facilities. Based on the geometric properties of such facilities, we developed a new formulation for this continuous covering location model which does not require employing distance measures. This model is intended to determine the location and formation of facilities simultaneously. For solving this new model, we proposed a continuous branch-and-bound framework utilizing linear approximations for the tradeoff curve associated with the facility formation alternatives. Further, we developed new problem generation and bounding strategies suitable for our particular problem structure. Computational experience shows that the branch-and-bound procedure we developed performs better than conventional mixed-integer nonlinear programming solvers BARON and SBB for solving this particular location model.