Quantitative thresholds based decision support approach for the home health care scheduling and routing problem

In the domain of Home Health Care (HHC), precise decisions regarding patient's selection, staffing level, and scheduling of health care staff have a significant impact on the efficiency and effectiveness of the HHC system. However, decentralized planning, the absence of well defined decision rules, delayed decisions and lack of interactive tools typically lead towards low satisfaction level among all the stakeholders of the HHC system. In order to address these issues, we propose an integrated three phase decision support methodology for the HHC system. More specifically, the proposed methodology exploits the structure of the HHC problem and logistic regression based approaches to identify the decision rules for patient acceptance, staff hiring, and staff utilization. In the first phase, a mathematical model is constructed for the HHC scheduling and routing problem using Mixed-Integer Linear Programming (MILP). The mathematical model is solved with the MILP solver CPLEX and a Variable Neighbourhood Search (VNS) based method is used to find the heuristic solution for the HHC problem. The model considers the planning concerns related to compatibility, time restrictions, distance, and cost. In the second phase, Bender's method and Receiver Operating Characteristic (ROC) curves are implemented to identify the thresholds based on the CPLEX and VNS solution. While the third phase creates a fresh solution for the HHC problem with a new data set and validates the thresholds predicted in the second phase. The effectiveness of these thresholds is evaluated by utilizing performance measures of the widely-used confusion matrix. The evaluation of the thresholds shows that the ROC curves based thresholds of the first two parameters achieved 67% to 71% accuracy against the two considered solution methods. While the Bender's method based thresholds for the same parameters attained more than 70% accuracy in cases where probability value is small (p <= 0.5). The promising results indicate that the proposed methodology is applicable to define the decision rules for the HHC problem and beneficial to all the concerned stakeholders in making relevant decisions.