# The Centralization and Sharing of Information for Improving a Resilient Approach Based on Decision-Making at a Local Home Health Care Center

Guillaume Dessevre, Cléa Martinez, Liwen Zhang, Christophe Bortolaso, Franck Fontanili

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Guillaume Dessevre, Cléa Martinez, Liwen Zhang, Christophe Bortolaso, Franck Fontanili. The Centralization and Sharing of Information for Improving a Resilient Approach Based on Decision-Making at a Local Home Health Care Center. Applied Sciences, 2023, 13 (15), pp.8576. 10.3390/app13158576. hal-04203358

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Article

# The Centralization and Sharing of Information for Improving a Resilient Approach Based on Decision-Making at a Local Home Health Care Center

Guillaume Dessevre<fnref n="1" />,*, Cléa Martinez<fnref n="1" /> ID, Liwen Zhang <fnref n="1" />/<fnref n="2" />, Christophe Bortolaso<fnref n="2" /> and Franck Fontanili<fnref n="1" />

**Featured Application:** In this article, we propose a resilient approach toward the centralization and sharing of information for improving the decision-making of caregivers in local healthcare centers in addition to reducing the number of late arrivals, the total time of late arrivals, and the number of routes ending after the work end time. Coupled with a connected IT tool, such as a smartphone application, this approach would improve the working lives of caregivers.

**Abstract:** Home care centers face both an increase in demand and many variations during the execution of routes, compromising the routes initially planned; robust solutions are not effective enough, and it is necessary to move on to resilient approaches. We create a close-to-reality use case supported by interviews of staff at home health care centers, where caregivers are faced with unexpected events that compromise their initial route. We model, analyze, and compare two resilient approaches to deal with these disruptions: a distributed collaborative approach and a centralized collaborative approach, where we propose a centralization and sharing of information to improve local decision-making. The latter reduces the number of late arrivals by 11%, the total time of late arrival by 21%, and halves the number of routes exceeding the end of work time (contrary to the distributed collaborative approach due to the time wasted reaching colleagues). The use of a device, such as a smartphone application, to centralize and share information thus, allows better mutual assistance between caregivers. Moreover, we highlight several possible openings, like the coupling of simulation and optimization, to propose a more resilient approach.

**Keywords:** home health care routing and scheduling problem; resilience; information sharing; discrete event simulation; optimization

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**Citation:** Dessevre, G.; Martinez, C.; Zhang, L.; Bortolaso, C.; Fontanili, F. The Centralization and Sharing of Information for Improving a Resilient Approach Based on Decision-Making at a Local Home Health Care Center. *Appl. Sci.* **2023**, *13*, 8576. https://doi.org/10.3390/app13158576

Academic Editor: Roger Narayan

Received: 16 May 2023

Revised: 13 July 2023

Accepted: 18 July 2023

Published: 25 July 2023

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**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## 1. Introduction

Thanks to scientific developments and concurrent improvements in healthcare, hygiene, nutrition, and social conditions, the life expectancy of humans has consistently increased in the developed world over the last century, coupled with a steadily declining birth rate over the course of recent decades, has resulted in an increasingly aging population. In 2020, 20% of the French population was over 60 years old in France, and according to the *Institut National de la Statistique et des Etudes Economiques*, this will rise to 30% by 2070 [1]. In addition, there is a desire to reduce the demand for medical structures (e.g., hospitals), exerting pressure on people to return home as quickly as possible. As a result, the demand for home health care services has increased sharply in recent years, as well as the number of studies on this topic.

In the scientific literature, the management of home care routes is known as the Home Health Care Routing and Scheduling Problem (HHCRSP) and has been studied for fifty years [2]. The goal is to find the best possible routes according to the characteristics of the

<footnote n="1">¹ Industrial Engineering Center, IMT Mines Albi, 81000 Albi, France; clea.martinez@mines-albi.fr (C.M.); liwen.zhang@berger-levrault.com (L.Z.); franck fontanili@mines-albi.fr (F.F.)</footnote>

<footnote n="2">² Berger-Levrault, 31670 Labège, France; christophe.bortolaso@berger-levrault.com</footnote>

<footnote>* Correspondence: guillaume.dessevre@mines-albi.fr</footnote>
problem, e.g., strategies to minimize travel times, maximize the stakeholders' satisfaction, take time windows and difficulty of care visit provisions into consideration, etc. Although the variability of HHCRSP systems is increasingly under scrutiny, most studies are carried out in a deterministic environment. For the past five years, an ever-growing number of publications have considered uncertainties, especially for travel times and visit times. Robust approaches build efficient solutions as long as the uncertainties are bound within a defined interval [3], whereas resilient approaches propose policies to recover after a disruption. In the vehicle routing literature, stochastic routing problems are often tackled with robust approaches, such as chance-constrained programming (CCP), or resilient approaches, such as stochastic programming with recourse (SPR). Gendreau et al. [4] argue that the objective functions in SPRs are more relevant than CCPs in solving a stochastic VRP. Moreover, a typical concern with robust approaches is that they can be too conservative and thus too far from optimality for the nominal problem [5]. That is why robust solutions are effective against small variations but become useless against strong disruptions; it is then necessary to turn to resilient approaches. The study of resilient approaches to counter high-impact disruptions remains one of the gaps to be filled in the spectrum of HHCRSP publications. In addition, it is difficult to find a clear, realistic, and readily available use case in the scientific literature.

The aim of this paper is to analyze and compare the performance of resilient approaches applied to a use case close to reality, open to the scientific community, and inspired by home health care centers in the department of Tarn (France) in an environment subject to both variations and high-impact disruptions. Two different approaches are analyzed and compared to a baseline approach using discrete event simulations, including an empirical approach modeling what is done today in the home health care centers interviewed and a new approach based on the centralization and sharing of information between caregivers to improve local decision-making. The two main contributions of the article are (1) creating a realistic case study based on home health care center interviews and making it available to the scientific community and (2) proposing a resilient approach based on the centralization and sharing of information for improving local decision-making when routes are disrupted.

This paper is organized as follows: Section 2 is dedicated to the review of literature on publications related to the topic. Then, Section 3 describes the use case and the design of experiments (resilient approaches and disruptions). Section 4 presents the results and analysis. Finally, Section 5 concludes and proposes avenues for further research.

## 2. Literature Review

The HHCRSP is a highly pertinent issue and is widely studied in the literature, as evidenced by the numerous state-of-the-art published recently [6,7]. In this section, we present an overview of the existing work to contextualize our contribution.

HHCRSP problems cover a wide range of constraints and objectives. They may include typical features of Vehicle Routing Problems (VRPs), such as time windows (hard or soft) [8] and temporal dependencies (precedence, synchronization, or disjunction) [9], but also more specific features related to the field such as continuity of care [10], skill requirements [11], or incompatibilities [12]. The objective is often cost-related, whether it comes to minimizing travel costs or staffing costs [13,14] or is stakeholder-oriented [8].

As a variant of VRP, approaches seeking to address the issues around HHCRSP are manifold. In small instances, exact methods are developed, e.g., mathematical programming [15], logic-based Benders decomposition [16], branch-and-price-and-cut [17], etc. Larger instances are generally solved with classic metaheuristics or approximation algorithms from the operations research field, such as population-based algorithms [18], neighborhood searches [19], and decomposition methods [20].

In practice, caregivers encounter various problems during their route that can impact the remainder of their working day. Hence, deterministic approaches do not enable us to capture the whole complexity of the HHCRSP, at least not at the operational decision-
making level. There are an increasing number of articles currently assessing the HHCRSP in view of various types of uncertainties (e.g., stochastic travel times or visit times, patient cancellations, emergencies, vehicle breakdown, etc.) and propose robust or resilient solutions: visits have an expected duration but can last longer [21] or they are normally distributed [11], and travel times are estimated with a kernel regression, for example [22].

In this paper, we focus on two forms of uncertainties regarding visit and travel times: small variations due to the stochasticity of the data and more punctual but also more impactful disruptions, such as traffic jams. The robustness of a system is defined as the ability “to maintain its function despite internal or external disruption” [23], whereas resilience is “the ability of a system to return to its original state, within an acceptable period of time, after being disturbed” [24]. A robust solution is, therefore, used to absorb a variation, and a resilient approach is used to counter disruption. As represented in Figure 1, a robust solution in blue on the left absorbs the variations (represented by σ in orange) around the mean value μ, so these variations do not affect the performance indicators on the bottom, which are protected by this solution. On the right, the disruption has an impact on these indicators, and that is why a resilient approach is necessary to return to a “normal” operating state.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Difference between variation and disruption and between robust solution and resilient approach.</figcaption></figure>

These uncertainties can be addressed at different decision-making levels. Nikzad et al. propose a two-stage stochastic programming model to tackle both uncertain visit and travel times [25], and Zhan et al. propose a mixed-integer linear program and adapt the L-shaped method to solve the HHCRSP with stochastic visit times [26]. Another option to deal with uncertainties is to anticipate different disrupted scenarios and build robust solutions; in the study by Shi et al., each visit and travel time belongs to an uncertainty set based on the theory of budget uncertainty [27]. Since their solutions to the deterministic problem are not robust, they adapt several classic heuristics to build a solution that always remains feasible, despite visit and travel time uncertainties. Cappanera et al. also choose a robust method to study uncertain demands from the patients and illustrate the need for a trade-off between a deterministic optimal solution that is particularly susceptible to any small disruption and an extremely robust solution that is very expensive and often “underused” [28].

Resilient approaches must then be deployed at the operational level to repair the routes in the case of high-impact disruption. Among the classic recourse strategies for
stochastic VRP, most of them imply a return to the depot [29], which is not helpful for HHCRSP. Similarly, rescheduling strategies for routing problems may not be suited to HHC applications; Errico et al. study two alternative strategies to solve a VRP with time windows and stochastic service times, which both imply skipping customers [30]. To the best of our knowledge, only three articles propose reactive and resilient solutions to counter high-impact disruptions in the field of HHC. Alves et al. use a multi-agent system to deal with unexpected events, such as vehicle breakdown, where visits are dynamically reassigned to another vehicle [31]. Marcon et al. use a similar two-level architecture with an offline module that assigns caregivers to patients and an online multi-agent module that takes local decisions to optimize the routes [32]. No change in the caregiver-patient assignment is allowed, which prevents any collaboration in case of disruption, and none of these two articles take into account time windows. Yet, we consider temporal constraints as a key element to HHCRSP because delays in care delivery may not only have an impact on the quality of care but also on the satisfaction of the patient. In the study by Yuan et al., patients can cancel their appointments or require new visits during the execution of the routes, so they are re-optimized in real-time with a tabu-search, with the objective of minimizing deviations from the original plan [33]. The possibility of calling in additional workers and the cancellations of requests guarantee a stable workload. In our article, the perturbations on care durations have a major impact on the workload of the caregivers and, thus, on the feasibility of the routes and the quality of care.

In summary, the HHCRSP has been studied for a long time and increasingly in a stochastic environment, where many robust solutions have been proposed in the literature, but few resilient approaches have been published. Moreover, it is difficult to find a use case that is clear, realistic, and available to the scientific community. For this reason, in this article, we propose to examine a realistic use case, the result of numerous interviews, and we analyze and compare two resilient approaches to a baseline one to counter the disruptions of home care routes.

### 3. Methods

#### 3.1. *Use Case Creation*

In order to create a realistic use case to share with the HHCRSP scientific community, the staff at seven home health care or service structures were interviewed in the department of Tarn in France during the months of September and October 2022. The aim was to collect information on the working environment, e.g., operating methods, problems encountered, existing and envisaged solutions, tools used, needs, etc. Having identified the challenges of the home care centers, we decided to create a use case inspired by two of these nursing care structures, which have the following characteristics:

1. There are five caregivers performing five routes;

2. Routes start at 7 a.m. from the health care center and end between 12 p.m. and 1 p.m. at the same location;

3. There are 140 care visits to perform, which are requested by 140 patients (one visit per patient);

4. When the caregivers have finished their routes, they can help their colleagues, if needed, or do administrative tasks at the health care center until 1 p.m.;

5. Travel times are often short (usually less than five minutes) and are triangularly distributed more or less 30% around the average value;

6. Care visit times are generally five minutes but can sometimes last 10 min. They are both subject to variations (such as travel times, with the same distribution) and to disruptions (whose distribution is detailed in the design of experiments);

7. Time windows (i.e., time slot during which the caregiver must begin the care visit) last one hour for each visit;

8. There is an early and late tolerance of five minutes, and if the caregiver arrives more than five minutes early, then they must wait before starting the care visit;
9. The website "https://geodatamine.fr/" (accessed on 7 February 2023)" was used to generate random and unidentifiable addresses for patients (e.g., businesses, churches, parking spaces, etc.) around the city of Carmaux (France); the map is presented in Figure 2 on the left (1) where the library *folium* in Python was used to place the patients on a Leaflet map. The health care center was indicated in the city, and the 140 other addresses were randomly distributed to the patients. The website "https://openrouteservice.org/" (accessed on 7 February 2023)" was used by a query in a Python script to create a matrix of real travel times between patients.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Map of the surroundings of Carmaux with the patients (in black) and the health care center (in red) on the **left** and examples of care visits with durations and time windows on the **right**.</figcaption></figure>

There are two types of visits: the short visits of 5 min, which represent 75% of the visits, and the long visits lasting 10 min (Figure 2, (2)). Thus, 106 care visits last 5 min, distributed randomly among the patients, and the other 34 last 10 min.

Finally, the time windows must be determined for each visit (Figure 2, (3)). There are 11 possible time windows between 7 a.m. and 1 p.m. (7 a.m.–8 a.m., 7:30 a.m.–8:30 a.m., 11:30 a.m.–12:30 p.m., and 12 p.m.–1 p.m.), evenly distributed among the visits in order to find feasible and realistic solutions.

The map, the coordinates of the addresses, and the care visits file are available in the data archive available at "http://dx.doi.org/10.13140/RG.2.2.28201.98402" (accessed on 15 May 2023)" (Supplementary Material).

## 3.2. Home Health Care

The discrete-event simulation was chosen as the tool-based method, as it allows complex environments with several sources of variability to be easily modeled and analyzed [34].

The simulation model, represented in Figure 3, is built as follows: (1) the five caregivers are created, and their attributes are assigned to them, then they retrieve the information for their next visit; (2) if they have finished their route, they go back to the center, or they help their colleagues (not represented here, more details in the next subsection); if not (3), the travel time to the next patient is calculated; (4) if the caregiver arrives more than 5 min early at the patient's address, the total number of early arrivals is incremented, and the caregivers wait. If they arrive more than 5 min late, the total number of late arrivals is incremented; and (5) the care visit is carried out before they move on to the next patient.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Representation of the main simulation model.</figcaption></figure>

The performance measures of the model are (i) the total number of early arrivals and the cumulative early arrival time; (ii) the total number of late arrivals and the cumulative late arrival time; and (iii) the end time of each route (knowing that a caregiver must normally finish before 1 p.m.).

### 3.3. *Design of Experiments*

The Design of Experiments (DoEs) consists of three dimensions detailed below: the three approaches, the different disruptions, and the schedule solutions.

#### 3.3.1. The Resilient Approaches

Two different resilient approaches, as represented in Figure 4 as a complement to the previous figure, are compared to a baseline approach without any collaboration: a distributed collaborative approach (the one used today by the interviewed nursing care structures) and a centralized collaborative approach.

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Decision-making algorithm modeling the two resilient approaches and the baseline.</figcaption></figure>

In the baseline approach (named “approach 0” because it is not a resilient approach and is represented in red), there is no cooperation between the caregivers; when a caregiver finishes their route, they return to the health care center to carry out administrative tasks.

In the distributed collaborative approach (named “approach 1” and represented in orange), when a caregiver finishes their route, they try to reach their colleagues to help
them. The caregiver knows each colleague's work areas and, therefore, starts by calling those closest to them. A colleague does not answer the call if they are out on a care visit unless the latter is disrupted, whereas a colleague who is driving will always respond using a hands-free kit. If the colleague does not answer the call, the caregiver moves on to the next closest individual. Otherwise, they ask them if they need help (i.e., if they are late because they experienced a disruption during their route). If this is the case, they will take a care visit from them; otherwise, they will remove this colleague from the list and move on to the next one. If they have called and spoken to all their colleagues, they go back to the health care center to carry out administrative tasks. Otherwise, they wait five minutes and call their colleagues who are still on the list again.

In the centralized collaborative approach (named "approach 2" and represented in green), the information is centralized and easily available to everyone. Using a device (e.g., a smartphone application), a caregiver knows directly if their colleagues need help and where they are. If this is the case, they will take a care visit; otherwise, they go back to the health care center to carry out administrative tasks.

Finally, for the two approaches, 1 and 2, there are three possible sub-approaches. These sub-approaches are subsequently named X-1, X-2, and X-3, where X = approach 1 or 2. For X-1 approaches, when a colleague needs help, the available caregiver will take the next care visit closest to them. For X-2, they will take the next care visit indicated on the route, regardless of their distance from the patient. And for X-3, they will take the last care visit on the route.

The three approaches (baseline and the two resilient ones) and the three sub-approaches are summarized in Table 1.

<table><caption>**Table 1.** Approaches and sub-approaches with their name.</caption><thead><tr><th>Approaches</th><th></th></tr></thead><tbody><tr><td>0</td><td>Baseline (not a resilient approach)</td></tr><tr><td>1-X</td><td>Distributed collaborative approach (existing)</td></tr><tr><td>2-X</td><td>Centralized collaborative approach (innovative)</td></tr><tr><th>Sub-approaches</th><th>When I help a colleague, which care visit should I take?</th></tr><tr><td>X-1</td><td>The closest to me</td></tr><tr><td>X-2</td><td>Next on the schedule</td></tr><tr><td>X-3</td><td>The last of the schedule</td></tr></tbody></table>

### 3.3.2. The Disruptions

According to the interviews, the disruptions encountered generally last one hour; if a patient dies, for example, a doctor, the family, and the funeral directors must be advised, and the caregivers have to wait until the patient is taken care of, or if a patient is drunk, the caregiver must wait until the patient is sober again to prevent injury.

To first analyze the impact of the variation, a first scenario without variation or disruption was modeled, as well as a second scenario by adding only the variations (modeled by a triangular distribution at ±30% around the mean value).

Then, four disruption scenarios were created: a case with a single one-hour disruption, a case with two 30-min disruptions, a case with two one-hour disruptions, and a case with one two-hour disruption. The disruptions are uniformly distributed among the patients for each replication.

### 3.3.3. The Schedule Solution

Two schedule solutions were compared: (1) a handmade schedule, as is the case in the health care centers interviewed and (2) an optimized schedule based on the simplified OptaPlanner-oriented model presented by Zhang et al. [35], with the utilization of one
embedded “Late Acceptance” metaheuristic for solution generation. The considered constraint is the respect for time windows (to limit the number of late or early arrivals), and the objective function was to minimize travel times.

For the two solutions, represented in Figure 5, the average occupation rates of the caregivers without disruption are 90% and 87%, respectively. The occupation rate includes travel times and care visit times, with the latter representing 55% of the occupation rate on average.

<figure><img src="image_8.png" /><figcaption>Figure 5. The five routes of the handmade schedule solution on the left and the optimized schedule solution on the right.</figcaption></figure>

Thus, the DoE is made of $2 \times (2 + 7 \times 4) = 60$ scenarios: two schedule solutions times two scenarios without disruption, plus seven resilient approaches times four scenarios with disruptions.

To ensure that we had significant results, we sought the number of replications necessary for each disruption (i.e., each disturbed patient by an unforeseen event) using the confidence interval method from [36]. Initially, 1000 replications for the same disturbed patient are carried out, where the output data were the total time of late arrival, and the percentage deviation of the confidence interval about the mean time of late arrival is calculated using Equation (1):

$$d = t_{n-1,\alpha/2} \frac{S}{X \times \sqrt{n}} \quad (1)$$

where:

$X$ = average total time of late arrival;

$S$ = standard deviation of the output data from the replications;

$n$ = number of replications;

$t_{n-1,\alpha/2}$ = value from Student’s t-distribution, with $n-1$ degree of freedom and a significance level of $\alpha/2$.

We chose a significance level $\alpha$ of 2.5% (i.e., there is a 97.5% probability that the value of the true mean lies within the confidence interval), and we sought a percentage deviation of a maximum of 2.5%. The percentage deviation depending on the number of replications for the first 150 replications is presented in Figure 6.

According to the calculation of the percentage deviation, it takes at least 85 replications per scenario. Therefore, in order to obtain significant and homogeneous results, we performed 100 replications for each scenario (i.e., disturbed patient), which is a total of 14,000 replications since there are 140 patients.

The model and the simulations were made using Python scripts to facilitate the exchange between the different files and applications.
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Percentage deviation of the confidence interval about the mean time of late arrival depending on the number of replications where the red arrow shows the number of replications needed.</figcaption></figure>

## 4. Results

All the results are available in the data archive. For reasons of space, and as it is the most likely outcome, only results on late arrivals for a scenario with a single one-hour disruption are presented in Figure 7. The baseline and the resilient approaches are on the abscissa, the mean total numbers of late arrivals are on the left, the mean total times of late arrival are on the right, and the results for the handmade schedule are hatched, unlike those for the optimized schedule.

<figure><img src="image_10.png" /><figcaption>**Figure 7.** Number of late arrivals (on the left) and total time of late arrival (on the right) depending on the resilient approach—Scenario with a single one-hour disruption.</figcaption></figure>

The approach 0 in red presents the worst performances: 15.8 late arrivals on average (i.e., 11.3% of care visits are late), with a total of 6.7 h of late arrival in the optimized schedule as well as 14.9 late arrivals and 7.2 h in the handmade schedule. Overall, the two other approaches (in yellow and green) are better, with the X-1 sub-approaches yielding the best results. With approach 1-1, the number of late arrivals is reduced by 9% in the optimized schedule (7% in the handmade one), with the total time of late arrival reduced by 18% (16% in the case of the handmade one). With approach 2-1, the number of late arrivals is reduced by 11% in the optimized schedule (10% in the handmade one), with the total time of late arrival reduced by 21% (19% in the case of the handmade one). The 2-1 approach, therefore, improves performance. The X-2 approaches are the worst performing sub-approaches, while the X-3 performs better than the X-1, with regard to the number of late arrivals but not in terms of the total time of late arrival. Finally, there is a slight difference between the two schedule solutions, but the previous remarks are valid for both.
To better understand the effect of the resilient approaches on the route end times, their distribution and cumulative distribution are presented in Figure 8. Since caregivers must finish before 1 p.m., a dashed blue line has been added to the center of each graph.

Results for the scenario with a single one-hour disruption and the handmade schedule

<figure><img src="image_11.png" /><figcaption>**Figure 8.** Distribution of route end times (on the **left**) and cumulative distribution (on the **right**) for the handmade schedule—Scenario with a single one-hour disruption.</figcaption></figure>

The dotted black curve represents the distribution when there is no disruption: in this case, all routes end before 1 p.m. with an average of 12:24 p.m. With approach 0 in red, the distribution splits into two parts, and 20% of the routes finish after 1 p.m. (this corresponds to the disrupted route out of the five) with an average of 12:36 p.m. With approach 1-1 in yellow, the average rises to 12:50 p.m., with almost 21% of the routes ending after 1 p.m. because of time wasted reaching colleagues. Finally, thanks to approach 2-1 in green, only 10% of the routes go beyond 1 p.m. (i.e., twice less), with the average end time dropping to 12:44 p.m.

Approach 2-1, thus, enables a reduction in the number of late arrivals, the total time of late arrival, and the number of routes ending after 1 p.m.

**5. Conclusions and Openings**

In this paper, we first created a use case close to reality, which was available to the scientific community working on the HHCRSP. This use case was the result of several interviews with staff at different home health care centers in France. Then, we modeled two different resilient approaches to counter the high-impact disruptions encountered by caregivers on their routes. Hence, we analyzed and compared the existing solution to a baseline approach and a proposal for the centralization and sharing of information to improve local decision-making.

By using discrete event simulation, we showed that the centralized collaborative approach enabled both a reduction in the number of late arrivals and the total time of late arrival, but above, it led to all the number of routes ending before the work end time to be halved (contrary to the distributed collaborative approach). These results hold true, regardless of the number and duration of disruptions we tested, as well as the initial schedule solution (handmade or optimized).

With regard to managerial insights, we recommend that home health care centers:

* Promote the centralization and sharing of information between caregivers to improve mutual aid. The three resilient “2-X” sub-approaches outperform the “1-X” ones according to both the total number of late arrivals, the total time of late arrival, and especially the number of routes finishing before the target end time;

* In cases of mutual assistance between two caregivers, the helper must take the care visit closest to them. Among the three resilient sub-approaches studied, those whose rule is to take the next care visit closest to the helper (the “X-1” sub-approaches) are those that reduce the number of delays and the total time of delay.

To take this line of research further, other resilient approaches are considered, in particular, to improve the response times to disruptions and, thus, reduce recovery time
(which we do not discuss in this paper). The coupling of optimization and simulation seems
to be a powerful and appropriate tool. Moreover, the simulation plays a double role: firstly,
to compare resilient approaches with each other, as is the case here, and secondly, to find a
better initial or intermediate schedule solution. Finally, it is also possible to no longer plan
the routes but to monitor them in real-time by assigning the care visits on an ongoing basis
and taking variations and disruptions in the environment into consideration. However,
online scheduling would raise the question of the reliability of real-time communication
between the HHC center and the caregivers, which today remains an obstacle to the use of
these digital tools in practice.

**Supplementary Materials:** The following supporting information can be downloaded at: http://dx.doi.org/10.13140/RG.2.2.28201.98402, (Use_Case.zip).

**Author Contributions:** Literature research, G.D., C.M. and L.Z.; study design, G.D.; data collection, G.D.; data analysis, G.D.; data interpretation, G.D.; writing, G.D., C.M. and L.Z.; supervision, C.B. and F.F.; validation, F.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Plan France Relance and Berger-Levrault.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Conflicts of Interest:** The authors declare no conflict of interest.

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