Randomized Rounding for the Preventive Healthcare Facility Location Problem

In the preventive healthcare facility location problems (PHFLPs), explicitly modeling realistic aspects of the location decisions such as potential participants’ latent utility functions related to various attributes of each candidate facility leads to a large-scale mixedinteger non-linear program (MINLP). In this paper, we develop a randomized rounding approach to efficiently solve computationally challenging PHFLPs formulated as an MINLP and rapidly identify optimal or near-optimal solutions. We use the previous results by Krohn, Müller and Haase [OR Spectrum (2021) 43, 59-87] and their publicly available data as a case study to demonstrate the efficiency and practical usefulness of the proposed computational approach. Our approach solves PHFLP instances with up to 400 demand nodes and 15 candidate locations within a few seconds and the real-world case of 9,679 demand nodes and 56 candidate locations within 10 minutes, significantly faster than the previous approaches.