A Bi-objective Mathematical Model Toward Staff Planning Considering Cross-training

In this paper, the staff assignment problem considering cross-training of caregivers in health care systems is addressed to determine which staff should be cross-trained for each service and how they should be assigned to services. A bi-objective non-linear mathematical programming model is presented where the first objective function aims to minimize workload balancing, cross-training as well as maintenance and transportation costs, while the second objective function is concerned with maximization of caregivers’ satisfaction level. Several constraints with respect to budget capacity, staff absenteeism, maximum allowable consecutive shifts, multi-functionality and redundancy level and maximum allowable distance for transportation are taken into account to build a service plan. The behavior of the various elements and features of the model is evaluated in a real-world HC provider and the results reveal that the caregivers’ workload is relatively balanced and the caregivers’ preferences are satisfied.