Pattern-based decompositions for human resource planning in home health care services

Home health care services play acrucial role in reducing the hospitalization costs due to the increase of chronic diseases of elderly people. At the same time, they allow us to improve the quality of life for those patients that receive treatments at their home. Optimization tools are therefore necessary to plan service delivery at patients' homes. Recently, solution methods that jointly address the assignment of the patient to the caregiver (assignment), the definition of the days (pattern) in which caregivers visit the assigned patients (scheduling), and the sequence of visits for each caregiver (routing) have been proposed in the scientific literature. However, the joint consideration of these three level of decisions may be not affordable for large providers, due to the required computational time. In order to combine the strength and the flexibility guaranteed by a joint assignment, scheduling and routing solution approach with the computational efficiency required for large providers, in this study we propose a new family of two-phase methods that decompose the joint approach by incrementally incorporating some decisions into the first phase.The concept of pattern is crucial to perform such a decomposition in a clever way. Several scenarios are analyzed by changing the way in which resource skills are managed and the optimization criteria adopted to guide the provider decisions. The proposed methods are tested on realistic instances. The numerical experiments help us to identify the combinations of decomposition techniques, skill management policies and optimization criteria that best fit with problem instances of different size

Diversity-based adaptive genetic algorithm for a workforce scheduling and routing problem

The Workforce Scheduling and Routing Problem refers to the assignment of personnel to visits across various geographical locations. Solving this problem demands tackling numerous scheduling and routing constraints while aiming to minimise total operational cost. One of the main obstacles in designing a genetic algorithm for this highly-constrained combinatorial optimisation problem is the amount of empirical tests required for parameter tuning. This paper presents a genetic algorithm that uses a diversity-based adaptive parameter control method. Experimental results show the effectiveness of this parameter control method to enhance the performance of the genetic algorithm. This study makes a contribution to research on adaptive evolutionary algorithms applied to real-world problems

Home care routing and scheduling problem with teams’ synchronization

Funding Information: This work is funded by Portuguese funds through the FCT - Fundação para a Ciência e a Tecnologia , I.P., under the scope of the projects UIDB/00297/2020 (Center for Mathematics and Applications), UIDB/00097/2020 (CEGIST), and the PhD scholarship grant SFRH/BD/148773/2019 . Publisher Copyright: © 2023 The AuthorsThe demand for home care (HC) services has steadily been growing for two main types of services: healthcare and social care. If, for the former, caregivers' skills are of utter importance, in the latter caregivers are not distinguishable in terms of skills. This work focuses social care and models caregivers' synchronization as a means of improving human resources management. Moreover, in social care services, several visits need to be performed in the same day since patients are frequently alone and need assistance throughout the day. Depending on the patient's autonomy, some tasks have to be performed by two caregivers (e.g. assist bedridden patients). Therefore, adequate decision support tools are crucial for assisting managers (often social workers) when designing operational plans and to efficiently assign caregivers to tasks. This paper advances the literature by 1) considering teams of one caregiver that can synchronize to perform tasks requiring two caregivers (instead of having teams of two caregivers), 2) simultaneously modelling daily continuity of care and teams' synchronization, and 3) associating dynamic time windows to teams' synchronizations introducing scheduling flexibility while minimize service and travel times. These concepts are embedded into a daily routing and scheduling MIP model, deciding on the number of caregivers and on the number and type of teams to serve all patient tasks. The main HC features of the problem, synchronization and continuity of care, are evaluated by comparing the proposed planning with the current situation of a home social care service provider in Portugal. The results show that synchronization is the feature that most increases efficiency with respect to the current situation. It evidences a surplus in working time capacity by proposing plans where all requests can be served with a smaller number of caregivers. Consequently, new patients from long waiting lists can now be served by the “available” caregivers.publishersversionpublishe

A survey of workforce scheduling and routing

In the context of workforce scheduling, there are many scenarios in which personnel must carry out tasks at different locations hence requiring some form of transportation. Examples of these type of scenarios include nurses visiting patients at home, technicians carrying out repairs at customers' locations, security guards performing rounds at different premises, etc. We refer to these scenarios as Workforce Scheduling and Routing Problems (WSRP) as they usually involve the scheduling of personnel combined with some form of routing in order to ensure that employees arrive on time to the locations where tasks need to be performed. This kind of problems have been tackled in the literature for a number of years. This paper presents a survey which attempts to identify the common attributes of WSRP scenarios and the solution methods applied when tackling these problems. Our longer term aim is to achieve an in-depth understanding of how to model and solve workforce scheduling and routing problems and this survey represents the first step in this quest

A survey of workforce scheduling and routing

In the context of workforce scheduling, there are many scenarios in which personnel must carry out tasks at different locations hence requiring some form of transportation. Examples of these type of scenarios include nurses visiting patients at home, technicians carrying out repairs at customers' locations, security guards performing rounds at different premises, etc. We refer to these scenarios as Workforce Scheduling and Routing Problems (WSRP) as they usually involve the scheduling of personnel combined with some form of routing in order to ensure that employees arrive on time to the locations where tasks need to be performed. This kind of problems have been tackled in the literature for a number of years. This paper presents a survey which attempts to identify the common attributes of WSRP scenarios and the solution methods applied when tackling these problems. Our longer term aim is to achieve an in-depth understanding of how to model and solve workforce scheduling and routing problems and this survey represents the first step in this quest

Decomposition techniques with mixed integer programming and heuristics for home healthcare planning

We tackle home healthcare planning scenarios in the UK using decomposition methods that incorporate mixed integer programming solvers and heuristics. Home healthcare planning is a difficult problem that integrates aspects from scheduling and routing. Solving real-world size instances of these problems still presents a significant challenge to modern exact optimization solvers. Nevertheless, we propose decomposition techniques to harness the power of such solvers while still offering a practical approach to produce high-quality solutions to real-world problem instances. We first decompose the problem into several smaller sub-problems. Next, mixed integer programming and/or heuristics are used to tackle the sub-problems. Finally, the sub-problem solutions are combined into a single valid solution for the whole problem. The different decomposition methods differ in the way in which subproblems are generated and the way in which conflicting assignments are tackled (i.e. avoided or repaired). We present the results obtained by the proposed decomposition methods and compare them to solutions obtained with other methods. In addition, we conduct a study that reveals how the different steps in the proposed method contribute to those results. The main contribution of this paper is a better understanding of effective ways to combine mixed integer programming within effective decomposition methods to solve real-world instances of home healthcare planning problems in practical computation time

Conceptual multi-agent system design for distributed scheduling systems

With the progressive increase in the complexity of dynamic environments, systems require an evolutionary configuration and optimization to meet the increased demand. In this sense, any change in the conditions of systems or products may require distributed scheduling and resource allocation of more elementary services. Centralized approaches might fall into bottleneck issues, becoming complex to adapt, especially in case of unexpected events. Thus, Multi-agent systems (MAS) can extract their automatic and autonomous behaviour to enhance the task effort distribution and support the scheduling decision-making. On the other hand, MAS is able to obtain quick solutions, through cooperation and smart control by agents, empowered by their coordination and interoperability. By leveraging an architecture that benefits of a collaboration with distributed artificial intelligence, it is proposed an approach based on a conceptual MAS design that allows distributed and intelligent management to promote technological innovation in basic concepts of society for more sustainable in everyday applications for domains with emerging needs, such as, manufacturing and healthcare scheduling systems.This work has been supported by FCT - Fundação para a Ciência e a Tecnologia within the R&D Units Projects Scope: UIDB/00319/2020 and UIDB/05757/2020. Filipe Alves is supported by FCT Doctorate Grant Reference SFRH/BD/143745/2019.info:eu-repo/semantics/publishedVersio

Service Consistency in Vehicle Routing

This thesis studies service consistency in the context of multi-period vehicle routing problems (VRP) in which customers require repeatable services over a planning horizon of multiple days. Two types of service consistency are considered, namely, driver consistency and time consistency. Driver consistency refers to using the fewest number of different drivers to perform all of the visits required by a customer over a planning horizon and time consistency refers to visiting a customer at roughly the same time on each day he/she needs service. First, the multi-objective consistent VRP is defined to explore the trade-offs between the objectives of travel cost minimization and service consistency maximization. An improved multi-objective optimization algorithm is proposed and the impact of improving service consistency on travel cost is evaluated on various benchmark instances taken from the literature to facilitate managerial decision making. Second, service consistency is introduced for the first time in the literature to the periodic vehicle routing problem (PVRP). In the PVRP, customers may require multiple visits over a planning horizon, and these visits must occur according to an allowable service pattern. A service pattern specifies the days on which the visits required by a customer are allowed to occur. A feasible service pattern must be determined for each customer before vehicle routes can be optimized on each day. Various multi-objective optimization approaches are implemented to evaluate their comparative competitiveness in solving this problem and to evaluate the impact of improving service consistency on the total travel cost. Third, a branch-and-price algorithm is developed to solve the consistent vehicle routing problem in which service consistency is enforced as a hard constraint. In this problem, the objective is to minimize the total travel cost. New constraints are devised to enhance the original mixed integer formulation of the problem. The improved formulation outperforms the original formulation regarding CPLEX solution times on all benchmark instances taken from the literature. The proposed branch-and-price algorithm is shown to be able to solve instances with more than fourteen customers more efficiently than either the existing mixed integer formulation or the one we propose in this paper

Méthodes exactes et approchées pour le problème de planification des soins à domicile

RÉSUMÉ: De par le vieillissement de la population ainsi que le souhait des patients de rester le plus longtemps possible chez eux, auprès de leur famille, la dernière décennie a vu émerger la démocratisation des soins à domicile. Ces services peuvent prendre différentes formes telles que des soins infirmiers (piqûres, changement de pansement), de l’aide à la personne (pour prendre un bain, pour manger) ou encore du soutien psychologique. Au-delà du confort de vie qu’ils permettent chez les patients, ces soins à domicile donnent aussi la possibilité aux gouvernements de réduire le flux de patient dans les hôpitaux, de décentraliser les décisions de soins et de réduire le coût de prise en charge des patients. Néanmoins, afin de prendre en compte un maximum de patients tout en gardant un haut niveau de service, il a été montré qu’une planification des visites faite à la main était sousoptimale. Pour parer à cela, de nombreux outils d’aide à la décision ont été développés durant les vingt dernières années. Ces outils, capables de prendre en compte les nombreuses contraintes métier rencontrées par les agences de soins à domicile, permettent de créer en quelques secondes ou quelques minutes, des horaires hebdomadaires optimisés pour des dizaines d’employés. Cette thèse porte sur l’élaboration de ces outils d’aide à la décision et sur l’amélioration des processus opérationnels des agences de soins à domicile. Ces améliorations permettent alors de prendre en charge plus de patients, tout en conservant un haut niveau de service et de bonnes conditions de travail pour le personnel infirmier. Dans la première partie de cette thèse, nous présentons un travail réalisé en collaboration avec une compagnie montréalaise, Alayacare. Dans ce projet, nous listons l’ensemble des contraintes métier rencontrées pour les agences de soins à domicile et nous développons une modélisation du problème sous la forme d’un partitionnement d’ensemble. Pour résoudre le problème, nous développons une matheuristique, se décomposant en deux grandes parties. Tout d’abord un algorithme à voisinage large (LNS) est développé afin d’itérativement générer de nouvelles solutions réalisables et déterminer de nouveaux horaires hebdomadaires possibles pour les soignants. Ensuite, une résolution de la relaxation linéaire du problème de partitionnement d’ensemble, basée sur les horaires trouvés précédemment, est appelée. Sur des instances réelles issues de notre partenaire industriel, cette méthode de résolution a montré que l’on pouvait réduire de 37% le temps de trajet total, mais aussi augmenter de 16% la continuité des soins entre les patients et le personnel soignant. Dans la seconde partie de cette thèse, nous mettons l’emphase sur l’importance d’avoir une régularité dans les heures et jours de visites des patients. Pour cela, nous prenons en compte le fait que les patients restent plusieurs semaines dans le système des agences de soins à domicile et donc, lors de l’acceptation de nouveaux patients, il faut prendre en compte les contraintes associées aux patients existants (jours et heures de visite, personne soignante affectée). L’objectif est alors d’accepter le plus de nouveaux patients possibles, tout en gardant les horaires des patients existants inchangés. Afin de résoudre ce problème, nous reprenons et améliorons une décomposition de Benders et nous développons l’idée d’utiliser des patterns de visites pour les patients (comprenant les jours et heures de visite ainsi que l’employé affecté). Les expérimentations faites sur des instances réelles de la littérature montrent que notre nouvelle formulation permet de réduire drastiquement les temps de calcul. Enfin, nous montrons que pour les instances les plus difficiles à résoudre, nous pouvons adapter la LNS présentée dans l’article 1 afin d’obtenir les solutions optimales pour un temps de calcul ne dépassant pas les 20 secondes. Enfin, le troisième projet de cette thèse consiste à prendre en compte l’aspect dynamique du problème. En effet, nous avons expliqué précédemment que certains patients restaient dans le système durant plusieurs semaines, conservant leurs jours et heures de visites ainsi que leur personnel soignant affecté. Dans cette dernière partie, nous prenons un horizon roulant sur plus d’un an et étudions l’impact des décisions d’acceptation et de planification prises chaque semaine, sur le nombre de visites moyen. Dans ce contexte, nous recevons donc plusieurs offres de patients chaque jour et nous devons décider si le patient peut être accepté et si oui, qui le visitera, quels jours et à quelle heure. Pour cela, nous développons différentes heuristiques et mettons l’emphase sur les effets positifs que permet la flexibilité lors de la planification des visites. Cette flexibilité vient dans un premier temps du moment auquel nous prenons la décision pour l’acceptation des patients (à la réception de l’offre, à la fin de la journée, à la fin de la semaine). L’autre flexibilité vient du fait que l’on va non pas attribuer une heure exacte de visite au patient pour l’ensemble de son plan de soin, mais plutôt une fenêtre de temps, de soixante minutes par exemple, dans laquelle il sera visité. Les résultats de ces différentes heuristiques ainsi que des différentes flexibilités montrent que, sans modifications massives des processus de décision des agences, il est possible d’accepter jusqu’à 12% de visites en plus chaque semaine.----------ABSTRACT: Due to the population’s aging and people’s will to stay at home with family and friends, the last decade has been the decade of home health care services democratization. Those home care services have different aspects such as nursing acts (injection, band-aid replacement),personnal support (bathing, cooking) or social work for the psychological support of the patients. Beyond the fact that those services positively impact patients’ life, they also give governments the possibility of reducing flows of patients in the hospitals, decentralize the decisions and reduce the costs. Nevertheless, keeping up a high level of service for the patients is challenging and it has been shown that the manual scheduling of the visits by the head nurses usually leads to sub-optimal solutions. To cope with this issue, decision-making tools have been developed during the last decades in order to help the home care agencies in this scheduling task. These tools, capable to take into account a large set of practical constraints, allow the users to quickly (in a few seconds or minutes) and efficiently design weekly visit schedules for dozens of nurses. This thesis focuses on the elaboration of efficient decision-making tools and resolution methods in the context of home health care services. In the first part of this thesis, we present a work realised in colalboration with a company from Montréal, Alayacare. In this project, we list the different practical constraints met by their users (worldwide home care agencies) and we propose a set partitioning-based formulation. In order to solve the problem, we propose a matheuristic, composed of two main elements. Firstly, a large neighborhood search (LNS) method is implemented, allowing to iteratively generate new feasible solutions and retrieve a set of feasible weekly schedules for the different nurses. Secondly, a relaxed version of the set partitioning is solved using the weekly schedules previously found. On real instances provided by our industrial partner, experiments show that our method allows to reduce by 37% the travel time and increase by 16% the continuity of care between the patients and the nurses. In the second part of this thesis, we focus on the patients’ visits’ recurrency aspect. To do so, we take into account the fact that patients stay multiple weeks in home care agencies’ system and so, when we accept new patients, we have to take into account resource constraints from the existing patients (visit time and days, assigned nurse). The objective is then to maximize the number of new patients accepted without modifying old patients’ assignment and scheduling. In order to solve this problem, we extend a Benders decomposition and propose a new decomposition using visit patterns (composed of visit time and days and an assigned caregiver). Computational experiments show that our new decomposition allows to dramatically reduce the computation times on benchmark instances. For the largest instances, we show that we can adapt the LNS proposed in the first paper using visit patterns and solve optimally all the instances in less than 20 seconds. Finally, the third research projet consists in taking into account the dynamic aspect of the home health care services. Indeed, we previously presented the fact that patients stay multiple weeks in the system and so have to be taken as constraints when accepting new patients. In this last part of the thesis, we take into account the rolling horizon aspect of the problem (on more than a year) and we study the impact of the weekly decisions over time. The metric corresponds to the maximization of the average number of weekly visits. In this context, we receive multiple patient offers per day and we have to decide which patients we can accept and how they will be scheduled. To solve this problem, we propose different heuristics and focus on the impact of flexibility during the acceptance and scheduling process. On the one hand, this flexibility corresponds to the moment the decision is taken (when the offer is received, at the end of the day, at the end of the week). On the other hand, we also study flexibility on the visit time and propose not to assign the patients an exact visit time, but rather a visit time window. Results show that those heuristics and the flexiblity we propose allow the home care agencies, without drastic modification of their processes, to dramatically increase the average number of weekly visits with up to 12%