An Exact Criterion Space Search Method for a Bi-Objective Nursing Home Location and Allocation Problem

A health care system will be survived if it is economically affordable and elderly people can receive its services in case of availability. Hence, a network should be designed for home nursing of elderly people considering both economic and well-fare objectives. Finding optimal solutions to both mentioned objectives in health care systems, especially for elderly people, is challenging nowadays. Hence, it is necessary to find near-optimal solutions in action. This paper presents a new criterion space search algorithm for achieving all non-dominated points in a bi-objective nursing home location–allocation problem. Concepts of Box and Balanced Box methods and modified e-constraint are used in designing the proposed algorithm. The main focus of the research is to decrease potential areas that could involve non-dominated points by defining Minimum Feasible Rectangles during the search procedure. The performance of the proposed algorithm is analyzed by using two real data sets taken from the literature in the field of nursing home location–allocation problems. The proposed algorithm can outperform previous recently developed exact methods based on obtained results, especially from a computational time viewpoint.