Developing an imperialist competitive algorithm based on two improvement strategies in a hierarchical capacitated health network

Official URL: https://dx.doi.org/10.1007/s00521-024-10513-7

The present paper on the location of clinic (C), hospital (H) and medical center (MC) in the Golestan province of Iran is motivated by its present condition coming from limited distribution and ease of access for related Cs, Hs, and MCs. Design of a median hierarchical location-allocation model for the needed healthcare facilities, from Cs to Hs and MCs, is a vital and valuable activity from the emergency viewpoints of both patients and the government. This model has been formulated as a mixed-integer linear mathematical framework for finding the optimal location of these capacitated healthcare facilities, the allocation of patients to these Cs, Hs, or MCs and also for the referrals of the patients' needs to them while minimizing the total demand-weighted travel distance. This problem is in the category of an NP-hard problem. An efficient and robust imperialist competitive algorithm based on two initialization and local mechanisms is also presented to improve the computational time and accuracy of simulation results. Comparative performance of the developed method with some well-known metaheuristics has been surveyed using a real case study for the healthcare network for different problems with a change in the model parameters' values. The novel method is reliable and valid according to accuracy and execution time. The sensitivity analysis results concerning the maximum number of locations (i.e., Cs, Hs and MCs). Furthermore, the percent of the referred demand determines the significance and practical observations related to the combination of the Cs, Hs, and MCs to be established. Our new model is illustrated to be gainful as it offers a robust build plan to designers for making location decisions for developing the Golestan healthcare network.