A mathematical model and meta-heuristic algorithms to solve demographic areas partitioning problem in a hierarchical structure

Hospital waste collection is one of the most important issues in urban service management. In this research, a mathematical model is developed to partition demographic areas in the hospital services system. In this model, regarding the needs of some service providers, the hierarchical structure of the partitions is considered. For this purpose, in a unified decision-making process, populations are divided into main partitions, and then, each one is divided into a number of sub-partitions. The purpose of this type of segmentation is to provide an ordered structure to control the service flow from the operational level to managerial level. Since partitioning is an NP-hard problem, it is necessary to use meta-heuristic algorithms to solve numerical examples in the real world. Here, genetic and gray wolf algorithms have been developed to solve large-scale problems. Despite the high efficiency of both algorithms, the computational results showed that the gray wolf algorithm is more capable in solving large-scale problems. The results of this study can be used as a management tool in solving types of population-based partitioning problems, including the problems of health systems.