Home Healthcare Staff Dimensioning Problem for Temporary Caregivers: A Matheuristic Solution Approach

Staff dimensioning, defined as determining the required numbers of caregivers with different types of skills, is a key decision for home healthcare systems. Home healthcare providers often use a combination of permanent and temporary (casual) caregivers. Determining the required number of temporary caregivers with different skill sets considering uncertainty and routing cost is the main objective of this study. To this end, we propose a two-stage stochastic programming model for the staff dimensioning problem for temporary caregivers, taking into account uncertainties in the required class of service, the required number of visits, and the required service time for each patient. Staff dimensioning decisions are defined in the first stage, and assignment with routing are positioned in the second stage of the model. To solve the problem, a two-phase matheuristic algorithm is developed where an initial solution is generated in the first phase by using an intermediate mathematical model and solving a series of Traveling Salesman Problems (TSPs), then a fix-and-optimize strategy is developed in the second phase to improve the obtained solution. The efficiency of the proposed matheuristic algorithm is examined by various test problems. The results highlight that the proposed model and solution method can be used by HHC providers to effectively utilize the option of recruitment of temporary caregivers in their resource planning considering inevitable uncertain parameters.