solving a multi-objective model toward home care staff planning considering cross-training and staff preferences by nsga-ii and nrga

Home care (hc) staff assignment problem is defined as deciding which staff to assign to each patient. in this study, a multi-objective non-linear mathematical programming model is presented to address staff assignment problem considering cross-training of caregivers for hc services. the first objective of the model minimizes costs of workload balancing, cross-training and maintenance. the second objective minimizes the number of employees for each service while the satisfaction level of caregivers is maximized through the third objective function. several constraints including skill matching, staff preferences, regularity, synchronization, staff 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 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 can be determined which staff should be cross-trained for each service and how the staff are assigned to services.