The Influence of Accurate Travel Times on a Home Health Care Scheduling Problem
Résumé
The home health care (HHC) problem deals with finding an optimal assignment of nurses to nursing services (at patients’ homes) such that the overall working (and travel) time is minimized while customer and nurse satisfactions are maximized. We consider a real-world HHC problem setup from a Viennese health care company where we have the following, partly soft side constraints:
• nurses are expected at the patients’ homes within certain time windows,
• for each job, we have a preferred start time,
• each job requires a minimum qualification that the nurse must hold (e.g. a nurse for cleaning may not perform a medical service),
• the schedule should meet preferences of patients, nurses and employer,
• the nurses’ work time must follow legal regulations and their contract (concerning e.g. resting periods, working hours per week),
• each nurse uses her/his preferred mode of transport (either motorized private transport or public transport)
Hence, the HHC problem combines two hard-to-solve combinatorial problems—the vehicle routing problem with time windows and the nurse rostering problem—which indicates that the HHC problem is member of the class of NP-complete problems.
Within this work, we study the influence of appropriate travel times on solving the realworld HHC problem as well as the quality of the obtained roster and tour plans. Therefore, we estimate driving times for motorized private transport via a large set of historical data while public transport travel times are provided by a local public transport data company.