Demand uncertainty in robust Home Care optimization

Abstract

We study the Home Care Problem under uncertainty. Home Care refers to medical, paramedical and social services that may be delivered to patient homes. The term includes several aspects involved in the planning of home care services, such as caregiver-to-patient assignment, scheduling of patient requests, and caregiver routing. In Home Care, cancellation of requests and additional demand for known or new patients are very frequent. Thus, managing demand uncertainty is of paramount importance in limiting service disruptions that might occur when such events realize. We address uncertainty of patient demand over a multiple-day time horizon, when assignment, scheduling and routing decisions are taken jointly, both from a methodological and a computational perspective. In fact, we propose a non-standard cardinality-constrained robust approach, analyse its properties, and report the results of a wide experimentation on real-life instances. The obtained results show that, for instances of moderate size, the approach is able to efficiently determine robust solutions of good quality in terms of balancing among caregivers and number of uncertain requests that can be managed. Also, the robustness of the solutions with respect to possible realizations of uncertain requests, evaluated on a small subset of instances, appears to be significant. Furthermore, preliminary experiments on a decomposition method, obtained from the robust one by fixing the scheduling decisions, show a drastic gain in computational efficiency, with the determination of robust solutions of still good quality. Therefore, the approach appears to be very promising to cope with robustness even on Home Care instances of larger size

Operational research applied to decisions in home health care: A systematic literature review

“…We found that the OR literature concerning HHC remains dominated by papers proposing models and solution methods for combinations of operational decisions concerning the rostering of staff, the allocation of staff to patient visits, the scheduling of visits and the routing of staff. Previous reviews (Ciss e et al, 2017 andHirsch, 2017) have suggested a need for more stochastic formulations in such models and our review found that recent work has indeed incorporated stochastic patient demand, staff travel times and service times (for instance Shi et al, 2017aShi et al, , 2017bShi et al, , 2018Yuan et al, 2018;Cappanera et al, 2018). Other advances since previous reviews include moves to explore alternative approaches to the multiple aspects of system performance acknowledged to be important in HHC, with for instance Liu et al (2018) and Carello et al (2018) using multi-objective optimisation, as suggested by Ciss e et al 2017.…”

“…Other heuristic algorithm (Cappanera et al, 2018) Not specified -commercially available software (Carello & Lanzarone, 2014) Multi-agent modelling (n ¼ 1)…”

Matching daily home health-care demands with supply in service-sharing platforms

“…Caregivers start and finish their activities at their own homes (i.e., multi-depots) ( Bard et al, 2014 , Fathollahi-Fard et al, 2020 , Trautsamwieser et al, 2011 ). Each task is necessarily performed for a certain duration, which can be requested using either a fixed constant ( Cappanera et al, 2018 , Gomes and Ramos, 2019 , Liu et al, 2017 , Maya Duque et al, 2015 ) or a flexible range ( Mosquera et al, 2019 ). Yuan et al, 2018 , Shi et al, 2018 assume that the service duration is a random variable with known probability distributions, while Shi et al (2019) describe an uncertainty set for the service duration.…”

A bi-objective home healthcare routing and scheduling problem considering patients’ satisfaction in a fuzzy environment

“…They also considered a penalty function to better optimize the routes of caregivers known as travel balancing. In another study, Cappanera et al [29] proposed a robust optimization of the routing and scheduling problem for a home healthcare under uncertainty. As another multi-objective optimization, Fathollahi-Fard et al [9] contributed the environmental pollution to the home healthcare by considering the operational routing and scheduling decisions.…”

“…The following notations are defined and used:W r it Optimistic scenario for the working time of the patient i in time period t W q it Realistic scenario for the working time of the patient i in time period t W s it Pessimistic scenario for the working time of the patient i in time period t λ r int Optimistic scenario for the privilege from patient i to the caregiver n in time period t λ q int Realistic scenario for the privilege from patient i to the caregiver n in time period t λ s int Pessimistic scenario for the privilege from patient i to the caregiver n in time period t E r it Optimistic scenario for the earliest time of servicing to the patient i in time period t E q it Realistic scenario for the earliest time of servicing to the patient i in time period t E s it Pessimistic scenario for the earliest time of servicing to the patient i in time period t L r it Optimistic scenario for the latest time of servicing to the patient i in time period t L q it Realistic scenario for the latest time of servicing to the patient i in time period t L s it Pessimistic scenario for the latest time of servicing to the patient i in time period t T r ijt Optimistic scenario for the traveling time of patients i to j in time period t T q ijtRealistic scenario for the traveling time of patients i to j in time period t T s ijt Pessimistic scenario for the traveling time of patients i to j in time period t With regards to above definitions, the following certain auxiliary model is the equivalent to the main model in Section 3.4 as given in Eqs (24). to(29).Eq. (1)…”