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Home Care (HC) sta assignment problem is de ned 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.

Abstract. One of the important aspects neglected in the literature related to cell formation problem is human issues. In this study, a bi-objective mathematical model is developed in which human issues and dynamic cell formation are taken into consideration simultaneously. The rst objective function deals with costs associated with machines and human issues. The costs of human issues relate to salary, hiring, ring, reward/penalty policy, and worker assignment. The second objective function takes into account labor utilization as a criterion for reward/penalty policy. Since the available time in di erent real conditions is not constant, we include learning e ect to consider the real workers time. The nature of dynamic cell formation problem is NP-hard, and thus a Linear Programming embedded Genetic Algorithm (LP-GA) is employed to solve the model. In order to improve the performance of the applied GA, its parameters are tuned by means of Central Composite Design (CCD) method. Moreover, to validate the LP-GA, some test problems are solved and the results are compared with those obtained from an exact method and GA. The computational results show that the near optimal solutions yielded by LP-GA are better than GA in large-sized problems.