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A review of Static, Dynamic and Stochastic Vehicle Routing Problems in Home Healthcare
Abstract
The demand for Home Health care (HHC) service increases gradually in all of its sectors. Vehicle Routing Problem (VRP) is an everyday challenging task for the HHC administrative team. Because of its multi-dimensional resources such as physicians, nurses, medical equipment, drugs, etc. In this review article, we overview the current work of routing problems in HHC and emphasized the problems based on static, dynamic and stochastic strategies along with their solution methodologies, objectives, constraints, etc. Moreover, this paper displays that there exists only very less contribution to work on applying the dynamic and stochastic type of models using metaheuristic algorithms. Metaheuristic algorithm is a technique which is capable of generating good approximation solution within less execution time. Hence, insisting that HHC needs more focus on practical oriented problems such as dynamic and stochastic strategies in the mere future.
... Several alternatives to hospitalization have been proposed as a way to shorten hospital stays and increase access to care as the need for hospitalizations continues to rise. One of the alternatives to overcome these challenges, it is necessary to understand the advantages of home-based health care, which is enabling the Home Health Care (HHC) system [4,5]. In widespread pandemics like COVID-19, the access to healthcare facilities becomes a very challenging one because individuals are unable to travel. ...
... The primary goal of this study is to identify an appropriate Nature-Inspired Optimization (NIO) technique or metaheuristic algorithm that can serve as decisionmaking systems to support the proposed variant DSRPMFSS of HHC [5,15]. In order to meet multiple objectives, all test instances are focused on reducing the total transportation costs and time while increasing the number of nodes visited. ...
... The novel variant of DSRPMFSS proposed in this paper has never been considered in the literature [5] of HHC before. Here, patients are scattered geographically. ...
Globally, the growing number of elderly people, chronic disorders and the spread of COVID-19 have all contributed to a significant growth of Home Health Care (HHC) services. One of HHC’s main goals is to provide a coordinated set of medical services to individuals in the comfort of their own homes. On the basis of the current demand for HHC services, this paper attempts to develop a novel and effective mathematical model and a suitable decision-making technique for reducing costs associated with HHC service delivery systems. The proposed system of decision making identifies the real needs of HHCs which incorporate dynamic, synchronized services and coordinates routes by a group of caregivers among a mixed fleet of services. Initially, this study models the optimization problem using Mixed Integer Linear Programming (MILP). The Revised Version of the Discrete Firefly Algorithm is designed to address the HHC planning decision-making problem due to its unique properties and its computational complexity. To evaluate the scalability of this proposed approach, random test instances are generated. The results of the experiments revealed that the algorithm performed well even with the different scenarios such as dynamic and synchronized visits. Furthermore, the improved version of nature-inspired solution methodology has proven to be effective and efficient. As a result, the proposed algorithm has significantly reduced costs and time efficiency.KeywordsDecision-making systemRevised version of firefly algorithm (RVFA)Dynamic scheduling and routing problemSynchronize
We identify 135 articles published in scholarly, academic journals from January 2005 to June 2022 that survey various aspects of the Vehicle Routing Problem (VRP) ranging from exact and heuristic solution methods to new problem variants such as drone routing to new research areas such as green routing. We catalog and classify these articles, make key observations about publication history and overall contributions, and identify trends in VRP research and practice. Our book should be valuable to researchers and practioners with ongoing or unfolding research efforts into the VRP.
Human resource planning in home healthcare is gaining importance day by day since companies in developed and developing countries face serious nurse and caregiver shortages. In the problem considered in this paper, the decision of patient assignment must be made immediately when the patient request arrives. Once patients have been accepted, they are serviced at the same days, times and by same nurse during their episode of care. The objective is to maximise the number of patient visits for a set of nurses during the planning horizon. We propose a new heuristic based on generating several scenarios which include current schedules of nurses, the new request under consideration, as well as randomly generated future requests to solve three decision problems: first, do we accept the patient? If so, which nurse services the patient? Finally, which days and times are weekly visits of the patient assigned to? We compare our approach with a greedy heuristic from the literature by considering some real-life aspects such as clustered service areas and skill requirements, and empirically demonstrate that it achieves significantly higher average daily visits and shorter travel times compared to the greedy method.
A full multiobjective approach is employed in this paper to deal with a stochastic multiobjective capacitated vehicle routing problem (CVRP). In this version of the problem, the demand is considered to be deterministic, but the travel times are assumed to be stochastic. A soft time window is tied to every customer and there is a penalty for starting the service outside the time window. Two objectives are minimized, the total length and the time window penalty. The suggested solution method includes a non-dominated sorting genetic algorithm (NSGA) together with a variable neighborhood search (VNS) heuristic. It was tested on instances from the literature and compared to a previous solution approach. The suggested method is able to find solutions that dominate some of the previously best known stochastic multiobjective CVRP solutions.
The importance of home healthcare is growing rapidly since populations of developed and even developing countries are getting older and the number of hospitals, retirement homes, and medical staff do not increase at the same rate. We consider the Home Healthcare Nurse Scheduling Problem where patients arrive dynamically over time and acceptance and appointment time decisions have to be made as soon as patients arrive. The objective is to maximise the average number of daily visits for a single nurse. For the sake of service continuity, patients have to be visited at the same day and time each week during their episode of care. We propose a new heuristic based on generating several scenarios which include randomly generated and actual requests in the schedule, scheduling new customers with a simple but fast heuristic, and analysing results to decide whether to accept the new patient and at which appointment day/time. We compare our approach with two greedy heuristics from the literature, and empirically demonstrate that it achieves significantly better results compared to these other two methods.
Home Health Care (HHC) is a growing industry in the medical services business, mainly in Europe and North America. These care services are provided at patients’ home by a multidisciplinary team using a distribution network. In this paper, an overview of the HHC services in Portugal and Brazil is presented. Additionally, a review is also presented to identify the main logistics problems associated with HHC services such as districting, routing and inventory management and the lack of integrated approaches to address them, as well as the best practices of management in the area. A framework is proposed to represent the main elements and characteristics of HHC services and their relationships. The framework suggests the use of a Decision Support System (DSS) based on optimization models and simulation approaches to overcome some of the main challenges associated to integrated approaches to address main problems, filling the gaps in the current literature. With the development of this DSS it will be possible to assist in the logistic planning of HHC teams, especially in countries like Brazil and Portugal.
As a new service model, home health care can provide effective health care by adopting door-to-door service. The reasonable arrangements for nurses and their routes not only can reduce medical expenses, but also can enhance patient satisfaction. This research focuses on the home health care scheduling optimization problem with known demands and service capabilities. Aimed at minimizing the total cost, an integer programming model was built in this study, which took both the priorities of patients and constraints of time windows into consideration. The genetic algorithm with local search was used to solve the proposed model. Finally, a case study of Shanghai, China, was conducted for the empirical analysis. The comparison results verify the effectiveness of the proposed model and methodology, which can provide the decision support for medical administrators of home health care.
The home health care crew scheduling and routing problem with stochastic service times is studied in this paper. A stochastic programming model with recourse is constructed to describe the problem. The approximate formulation for the expected penalty for late arrival at a customer is obtained and analyzed. According to its features, the problem is transformed into a classical set partitioning problem (SPP) and an elementary shortest path problem with resource constraints (ESPPRC). The SPP is solved by the column generation algorithm, and the ESPPRC is solved by an effective label algorithm. To get integer feasible solutions, the column generation procedure is embedded within a branch and bound framework, which is also called branch and price approach. Its effectiveness is validated by the numerical experiment.
This paper presents a real-world optimization problem in home health care that is solved on a daily basis. It can be described as follows: care staff members with different qualification levels have to visit certain clients at least once per day. Assignment constraints and hard time windows at the clients have to be observed. The staff members have a maximum working time and their workday can be separated into two shifts. A mandatory break that can also be partitioned needs to be scheduled if the consecutive working time exceeds a certain threshold. The objective is to minimize the total travel- and waiting times of the care staff. Additionally, factors influencing the satisfaction of the clients or the care staff are considered. Most of the care staff members from the Austrian Red Cross (ARC) in Vienna use a combination of public transport modes (bus, tram, train, and metro) and walking. We present a novel model formulation for this problem, followed by an efficient exact solution approach to compute the time-dependent travel times out of the timetables from public transport service providers on a minute-basis. These travel time matrices are then used as input for three Tabu Search based solution methods for the scheduling problem. Extensive numerical studies with real-world data from the ARC show that the current planning can be improved significantly when these methods are applied.
Organizations providing home care services are inclined to optimize their activities in order to meet the constantly increasing demand for home care. In this context, home care providers are confronted with multiple, often conflicting, objectives such as minimizing their operating costs while maximizing the service level offered to their clients by taking into account their preferences. This paper is the first to shed some light on the trade-off relationship between these two objectives by modeling the home care routing and scheduling problem as a bi-objective problem. The proposed model accounts for qualifications, working regulations and overtime costs of the nurses, travel costs depending on the mode of transportation, hard time windows, and client preferences on visit times and nurses. A distinguishing characteristic of the problem is that the scheduling problem for a single route is a bi-objective problem in itself, thereby complicating the problem considerably. A metaheuristic algorithm, embedding a large neighborhood search heuristic in a multi-directional local search framework, is proposed to solve the problem. Computational experiments on a set of benchmark instances based on real-life data are presented. A comparison with exact solutions on small instances shows that the algorithm performs well. An analysis of the results reveals that service providers face a considerable trade-off between costs and client convenience. However, starting from a minimum cost solution, the average service level offered to the clients may already be improved drastically with limited additional costs. © 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
Home health care (HHC) is defined as providing medical and paramedical services for patients at their own domicile. In the HHC industry, it is crucial for health care organisations to assign caregivers to patients and devise reasonable visiting routes to save total operational cost and improve the service quality. However, some special constraints make the problem hard to solve. For example, patients’ service times are usually stochastic due to their varying health conditions; caregivers are organised in a hierarchical structure according to their skills to satisfy patients’ demands. In this paper, we address a HHC scheduling and routing problem with stochastic service times and skill requirements. A stochastic programming model with recourse is proposed to formulate the problem in which the expected penalty for late arrival at customers is considered. To solve the problem, it is equivalently transformed into a master problem and a pricing sub-problem. A column generation algorithm is developed to solve the relaxation of the master problem and obtain its lower bound. A label algorithm and several effective accelerating techniques are devised to solve the pricing sub-problem. To obtain feasible solutions, the column generation procedure is embedded within the branch and bound framework. The effectiveness of the proposed algorithm is validated through numerical experiments.
As demographic trends show, the demand for home health care services will rise in future. Currently, the routing of the nurses is performed manually by the main service providers in Austria. This leads to a time-consuming process with a presumably suboptimal outcome. We present a model formulation and a metaheuristic solution approach, based on Variable Neighborhood Search, for optimizing the daily scheduling of the nurses. The objective function minimizes the traveling time of the nurses and the dissatisfaction level of clients and nurses. A feasible solution has to observe working time regulations, hard time windows, mandatory breaks, and a feasible assignment of nurses to clients. The proposed method finds the global optimal solutions for small problem instances. In extensive numerical studies it is shown that the algorithm is capable to solve real life instances with up to 512 home visits and 75 nurses. A comparison with a real life routing plan shows large savings potentials.
This paper presents a new model and solution methodology for the problem faced by companies that provide rehabilitative services to clinic and home-bound patients. Given a set of multi-skilled therapists and a group of geographically dispersed patients, the objective is to construct weekly tours for the therapists that minimize the travel, treatment, and administrative costs while ensuring that all patients are seen within their time windows and that a host of labor laws and contractual agreements are observed. The problem is complicated by three factors that prevent a daily decomposition: (i) overtime rates kick in only after 40 regular hours are worked during the week, (ii) new patients must be seen by a licensed therapist on their first visit, and (iii) for some patients only the frequency and not the actual days on which they are to be seen is specified. The problem is formulated as a mixed-integer linear program but after repeated attempts to solve small instances with commercial software failed, we developed an adaptive sequential greedy randomized adaptive search procedure. The phase I logic of the procedure builds one daily schedule at a time for each therapist until all patients are routed. In phase II, several neighborhoods are explored to arrive at a local optimum. Extensive testing with both real data provided by a U.S. rehab company and datasets derived from them demonstrated the value of the purposed procedure with respect to current practice. The results indicated that cost reductions averaging over 18.09 % are possible.
In a majority of settings, rehabilitative services are provided at healthcare facilities by skilled therapists who work as independent contractors. Facilities include hospitals, nursing homes, clinics and assisted living centers, and may be located throughout a wide geographic area. To date, the problem of constructing weekly schedules for the therapists has yet to be fully investigated. This paper presents the first algorithm for supporting weekly planning at the agencies that do the contracting. The goal is to better match patient demand with therapist skills while minimizing treatment, travel, administrative, and mileage reimbursement costs.The problem was modeled as a mixed-integer program but has several complicating components, including different patient classes, optional weekly treatment patterns, and a complex payment structure, that frustrated the use of exact methods. Alternatively, we developed a parallel (two-phase) greedy randomized adaptive search procedure (GRASP) that relies on an innovative decomposition scheme and a number of benefit measures that explicitly address the tradeoff between feasibility and solution quality. In Phase I, daily routes are constructed for the therapists in parallel and then combined to form weekly schedules. In Phase II, a high-level neighborhood search is executed to converge towards a local optimum. This is facilitated by solving a series of newly formulated traveling salesman problems with side constraints. Extensive testing with both real data provided by a U.S. rehab agency and associated random instances demonstrates the effectiveness of the purposed procedure.
We present a general framework for solving a real-world multimodal home-healthcare scheduling (MHS) problem from a major Austrian home-healthcare provider. The goal of MHS is to assign home-care staff to customers and determine efficient multimodal tours while considering staff and customer satisfaction. Our approach is designed to be as problem-independent as possible, such that the resulting methods can be easily adapted to MHS setups of other home-healthcare providers. We chose a two-stage approach: in the first stage, we generate initial solutions either via constraint programming techniques or by a random procedure. During the second stage, the initial solutions are (iteratively) improved by applying one of four metaheuristics: variable neighborhood search, a memetic algorithm, scatter search and a simulated annealing hyper-heuristic. An extensive computational comparison shows that the approach is capable of solving real-world instances in reasonable time and produces valid solutions within only a few seconds.
Increase in ageing population and chronic diseases among the people create a huge demand for Home Healthcare (HHC) in recent years. HHC is a service delivery system that provides the service at the patient's home by the set of professional caregivers. Vehicle routing problem is an everyday challenging task for HHC operational team. Continuity of care is regarding the sustainability of caregivers. It is achieved by implementing a feasible routing plan of caregivers within their respective time horizon. This environment creates a necessity to apply metaheuristic or heuristic algorithms in HHC. In this paper, we proposed bi-objective to minimize both total travel time and idle time of heterogeneous capacitated vehicle routing problem in HHC. It is solved by using Elitism of Ant colony optimization (E-ACO) further enhanced with neighbourhood structures. This proposed algorithm has never been applied in the literature of HHC. Finally, compare the efficiency of E-ACO with ACO and PSO using randomly generated test instances for 100 nodes and achieved the desired output.
Home health care structures provide care for the elderly, people with disabilities as well as patients with chronic conditions. Since there has been an increase in demand, organizations providing home health care are eager to optimize their activities. In addition, the increase in patient numbers has led organizations to expand their geographical reach. As a result, home health care structures tend to be located in different offices to limit their travel time and, consequently, caregivers employed by these various structures must be assigned to one of the offices so they start and end their workday at their associated office. Unlike the existing literature where an upstream assignment of caregivers is performed to become a parameter of the model, the assignment of caregivers to offices is solved during the resolution of the problem in order to obtain the best possible combinations. Thus, we suggest a mixed-integer programming model of the multi -depot home health care assignment, routing, and scheduling problem without prior assignment of caregivers to the home health care offices. In addition, we propose an original matheuristic -based approach with different assignment strategies to assign visits and caregivers to the home health care offices in order to solve the problem. The experiments are conducted on a set of 56 heterogeneous instances of various sizes. Results are compared with best solutions obtained by a commercial solver, and with a lower bound obtained by Lagrangian relaxation. The results highlight the efficiency of the matheuristic -based approach since it provides a low deviation ratio with a faster computational time.
In this paper, we present a two-stage stochastic model for an assignment problem in the home health care structures. We search to assign nurses to patients during a planning horizon while considering the nurses’ skills and capacity. Furthermore, we take into account the randomness of the time required to give cares for patients (the nurse’s time resource consumption during cares) as the uncertainty parameter in this problem. As aim, we balance the nurses’ workload, reduce their travel load and secure the continuity of the care. We present a two-stage stochastic linear programming model and the computational tests were done using CPLEX.
In home health care (HHC) operations, nurses are scheduled and routed to perform various services at clients' homes. As this often requires a combination of vehicle routing and scheduling approaches, resulting optimization problems are complex and, hence, of high interest to stakeholders such as researchers, practitioners and policy-makers. With demand for HHC expected to increase substantially, future work is essential to decrease costs and to guarantee service quality. In this review, we provide a comprehensive overview of current work in the field of HHC routing and scheduling with a focus on considered problem settings. Recent advances in HHC optimization are highlighted and future research directions discussed.
Home health care is one of the recent service systems where human resource planning has a great importance. The assignment of patients to care givers is a relevant issue that the home health care service provider must address before generating the daily routes. The assignment decision is typically made without knowing the visiting sequence, which creates some uncertainties and disparities regarding the effective workload of care givers. However, taking into account travel times in the care giver workload while solving the assignment problem is not straightforward, because travel times can also be affected by clinical conditions of patients and their homes. Providing good travel time estimates that would be used in the assignment decision is the specific topic this paper focuses on. In particular, we propose a data-driven method to estimate the travel times of care givers in the assignment problem when their routes are not available yet. The method, based on the Kernel regression technique, uses the travel times observed from previous periods to estimate the time necessary for visiting a set of patients located in specific geographical locations. The main advantage offered by this technique is the empirical modelling of the travel routes generated by care givers. Numerical results based on realistic problem instances indicate that the proposed estimation method performs better than the average value and k-nearest neighbor search methods and can be successfully used in a two-stage approach that first assigns patients to care givers and then defines their routes.
Landelijke Thuiszorg is a “social profit” organisation that provides home care services in several Belgian regions. In this paper, the core optimisation component of a decision support system to support the planning of the organisations’ home care service is described. Underlying this decision support system is an optimisation problem that aims to maximise the service level and to minimise the distance travelled by the caregivers of the organisation. This problem is formulated as a bi-objective mathematical program, based on a set partitioning problem formulation. A flexible two-stage solution strategy is designed to efficiently tackle the problem. Computational tests, as well as extensive pilot runs performed by the organisation’s personnel, show that this approach achieves excellent performance, both in terms of the service level and total travelled distance. Moreover, computational times are small, allowing for the weekly planning to be largely automated. The organisation is currently in the process of implementing our solution approach in collaboration with an external software company.
The planning of home health care services is still done manually in many industrial countries. However, efficient decision support is necessary to improve the working plans and relieve the nurses from this time consuming task. The problem can be summarized as follows: clients need to be visited one or several times during the week by appropriately skilled nurses; their treatments have predefined time windows. Additionally, working time requirements for the nurses such as breaks, maximum working time per day, and daily as well as weekly rest times have to be considered. We propose a Branch-Price-and-Cut solution approach to solve this problem exactly, using the solutions of a variable neighborhood search solution approach as upper bounds. The algorithm is capable of solving to optimality real-life based test instances with up to nine nurses, 45 clients, and 203 visits during the week. © 2014 Wiley Periodicals, Inc. NETWORKS, 2014
A multi-objective home health nurse routing and scheduling problem variant with the option of assigning some patient visits to remote monitoring devices is defined. A metaheuristic solution approach that approximates the Pareto optimal frontier for travel cost, nurse consistency and balanced workload objectives is developed. This set of objectives represents possibly conflicting interests - those of the agency, patients, and nurse workforce. A computational study is conducted to determine the tradeoffs among these objectives when creating nurse routes and schedules.
We deal with a Home Health Care Problem (HHCP) which objective consists in constructing the optimal routes and rosters for the health care staffs. The challenge lies in combining aspects of vehicle routing and staff rostering which are two well known hard combinatorial optimization problems. To solve this problem, we initially propose an integer linear programming formulation (ILP) and we tested this model on small instances. To deal with larger instances we develop a matheuristic based on the decomposition of the ILP formulation into two problems. The first one is a set partitioning like problem and it represents the rostering part. The second problem consists in the routing part. This latter is equivalent to a Multi-depot Traveling Salesman Problem with Time Windows (MTSPTW).
This paper presents a model for the daily planning of health care services carried out at patients' homes by staff members of a home care company. The planning takes into account individual service requirements of the patients, individual qualifications of the staff and possible interdependencies between different service operations. Interdependencies of services can include, for example, a temporal separation of two services as is required if drugs have to be administered a certain time before providing a meal. Other services like handling a disabled patient may require two staff members working together at a patient's home. The time preferences of patients are included in terms of given time windows. In this paper, we propose a planning approach for the described problem, which can be used for optimizing economical and service oriented measures of performance. A mathematical model formulation is proposed together with a powerful heuristic based on a sophisticated solution representation.
This paper introduces the multi-activity combined timetabling and crew scheduling problem. The goal of this problem is to schedule the minimum number of workers required in order to successfully visit a set of customers characterized by services needed matched against schedule availability. Two solution strategies are proposed. The first is based on mathematical programming whilst the second uses a heuristic procedure in order to reduce computational time. The proposed model combines timetabling with crew scheduling decisions in one mixed integer programming model which considers multiple activities. The algorithms are tested on randomly generated and real instances provided by the Health to School Initiative, a program based at Bogotá’s local Health Department. The results show that the Initiative can increase its coverage by up to 68% using the proposed heuristic approach as a planning process tool.
The demand for home health care services is rising tremendously. It is important to maintain these services especially in
times of natural disasters. Therefore, powerful algorithms are required to assist decision making. This paper presents a model
formulation and solution approach for the daily planning of home health care services. In cooperation with the Austrian Red
Cross, one of the leading providers of these services in Austria, we defined seven aims for the objective function. It minimizes
the sum of driving times and waiting times, and the dissatisfaction levels of clients and nurses. A feasible solution has
to observe assignment constraints, working time restrictions, time windows, and mandatory break times. The model formulation
is implemented with the solver software Xpress 7.0 and solved for small problem instances. Real life-sized problems are tackled
with a variable neighborhood search (VNS)-based heuristic that is capable of solving even large instances covering 512 jobs
and 75 nurses. Extensive numerical studies with real life data from three districts in Upper Austria are presented. A sensitivity
analysis shows how different natural disasters may influence home health care services. In 2002 a flood disaster devastated
the studied areas. Data from this time and standard flood scenarios, namely the 30, 100, and 200 year return period flood
discharges, are taken to depict the consequences on these services. Furthermore, a comparison of the heuristic solution values
with an actual route plan shows extensive improvements.
KeywordsVehicle routing–Metaheuristics–Variable neighborhood search–Home health care–Disaster management
This paper presents the novel application of a collaborative population-based meta-heuristic technique called Particle Swarm Optimization (PSO) to the scheduling of home care workers. The technique is applied to a genuine situation arising in the UK, where the provision of community care service is a responsibility of the local authorities. Within this provision, optimization routes for each care worker are determined in order to minimize the distance traveled providing that the capacity and service time window constraints are not violated. The objectives of this paper are twofold; first to exploit a systematic approach to improve the existing schedule of home care workers, second to develop the methodology to enable the continuous PSO algorithm to be efficiently applied to this type of problem and all classes of similar problems. For this problem, a particle is defined as a multi-dimensional point in space which represents the corresponding care activities and assignment priority. The Heuristic Assignment scheme is specially designed to transform the continuous PSO algorithm to the discrete job schedule. The Earliest Start Time Priority with Minimum Distance Assignment (ESTPMDA) technique is developed for generating an initial solution which guides the search direction of the particle. Local improvement procedures (LIP), i.e. insertion and swap, are embedded in the PSO algorithm in order to further improve the solution quality. The proposed methodology is implemented, tested, and compared with existing solutions on a variety of real problem instances.
This paper studies a version of stochastic vehicle routing problems, in which travel and service times are stochastic, and a time window constraint is associated with each customer. This problem is originally formulated as a chance constrained programming model and a stochastic programming model with recourse in terms of different optimization criteria. To efficiently solve these two models, a heuristic based on tabu search, which takes into account the stochastic nature of this problem, is then proposed. Finally, some testing instances with different properties are established to investigate the algorithmic performance, and the computational results are then reported.
Home health care, i.e. visiting and nursing patients in their homes, is a growing sector in the medical service business. From a staff rostering point of view, the problem is to find a feasible working plan for all nurses that has to respect a variety of hard and soft constraints, and preferences. Additionally, home health care problems contain a routing component: a nurse must be able to visit her patients in a given roster using a car or public transport. It is desired to design rosters that consider both, the staff rostering and vehicle routing components while minimizing transportation costs and maximizing satisfaction of patients and nurses.In this paper we present the core optimization components of the PARPAP software. In the optimization kernel, a combination of linear programming, constraint programming, and (meta-)heuristics for the home health care problem is used, and we show how to apply these different heuristics efficiently to solve home health care problems. The overall concept is able to adapt to various changes in the constraint structure, thus providing the flexibility needed in a generic tool for real-world settings.
The Future of Home Health Care: A Strategic Framework for Optimizing Value
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