Solving a multi-objective model toward home care sta planning considering cross-training and sta preferences by NSGA-II and NRGA

Home Care (HC) sta assignment problem is dened as deciding which sta to assign to each patient. In this study, a multi-objective non-linear mathematical programming model is presented to address sta assignment problem considering crosstraining of caregivers for HC services. The rst objective of the model is to minimize the cost of workload balancing, cross-training, and maintenance. The second objective minimizes the number of employees for each service, while the third objective function maximizes the satisfaction level of caregivers. Several constraints including skill matching, sta preferences, regularity, synchronization, sta absenteeism, and multi-functionality are considered to build a service plan. Due to NP-hardness of the problem, a Non-dominated Sorting Genetic Algorithm (NSGA-II) with a proposed who-rule heuristic initialization procedure is applied. Due to the absence of benchmark available in the literature, a Non-dominated Ranking Genetic Algorithm (NRGA) is employed to validate the obtained results. The data required to run the model are gathered from a real-world HC provider. The results indicate that the proposed NSGA-II is superior to the NRGA with regard to comparison indexes. Based on the results obtained, it is now possible to determine which sta to cross-train for each service and how to assign sta to services.