Identifying quantitative thresholds for the home health care problem

This paper presents a mixed integer linear programming (MILP) model for the daily planning of home health care (HHC) services provided by the crew of HHC firms. The model takes into account the time window of patients, compatibility requirements, workload limits of staff and distance of patients. The quantitative values of these parameters along with the similarity or difference within the values of a certain parameter are very important to explain the solution of the MILP model. Therefore, we further investigated the relationship between the values of parameters and decisions made in the HHC problem. Our MILP model deals with the scheduling and routing issues along with patient's selection and waiting aspects. The MILP model is solved using the commercial software Ilog-CPLEX and its results are further used to find the association between the relative quantitative gap values linked to certain parameters and decisions obtained through solution of the MILP model. Logistic regression based receiver operating characteristic (ROC) curve approach is used to identify the threshold values for the decision outcome of waiting patients against the related parameters. Subsequent validation and performance evaluation suggest that the proposed thresholds are well defined and can play an important role in making strategies for the HHC system.