A goal programming approach for multi objective, multi-trips and time window routing problem in home health care service

Abstract

Purpose: Apply a mixed integer programming model for multi trip vehicle routing with time window constraints (MTTW-HHCRP) for home health care services maximizing patient satisfaction while minimizing environmental effects. Theory and Methods: The problem addressed in this study has been defined as a multi-objective, multi-trip and time-windows home healthcare routing problem (MTTW-HHCRP). Weighted goal programming (GP) method is used to solve the problem. Results: Results are provided for a set of test problems generated from data obtained from a hospital in Ankara, Turkey for two different scenarios; 1- Analyze the effect of goal programming weights, 2- Analyze the effect of minimum percentage of patient demand to be met on solutions and performance metrics. For scenario 1, it is found that w1 ≥ 0.3 for the emissions to meet the target whereas in order to meet at least 50% of patient demands, w2 ≤ 0.9. For scenario 2, the increase in minimum percentage of patient demand to meet causes an increase in resource requirements as expected. Conclusion: Based on the data and the information obtained from the hospital in Ankara, test problems are produced and the solutions obtained for each scenario analysis are evaluated to guide the decision-making process.