1 Human Resource Scheduling and Routing Problem in Home Health

Human Resource Scheduling and Routing Problem in Home Health Care Context: A Literature Review Semih Yalçındağ1,2, Andrea Matta2, Evren Şahin1 1 Laboratoire Génie Industriel, Ecole Centrale Paris. 2 Dipartimento di Meccanica, Politecnico di Milano. Abstract Home Health Care (HHC) service is an alternative to the conventional hospitalization. The goal is to deliver medical, paramedical and social services to patients at their homes, which help them to improve and keep their best clinical, psychological and social conditions. As a large number of resources (i.e., material and human) contribute to delivering the HHC service, there are many issues that should be considered. Among these, the resource scheduling and routing problem (i.e., deciding in which sequence each operator will visit patients assigned to him/her) is one of the most important issues to be addressed while planning HHC resources. In this paper, we review studies in the literature that address the scheduling and routing problem as a Traveling Salesman Problem (TSP) or Vehicle Routing Problem (VRP) in the HHC context. We analyze each study according to four main categories: i) study characteristics, ii) modeling characteristics, iii) network characteristics, and iv) data characteristics. The objective of this review is to highlight the unexplored issues in researches dealing with the resource scheduling and routing problem, formulated as either TSP or VRP in the HHC context. Keywords: literature review, home health care, routing, travelling salesman problem, vehicle routing problem. 1. Introduction The Home Health Care (HHC) concept emerged more than fifty years ago. Although this concept has been present for a long time, recently it has been attracting more attention. The development of the HHC concept can be attributed to the ageing of populations, an increase in the number of people with chronical diseases, the improvements in medical technologies, the advent of new drugs and the governmental pressures to contain health care costs. This concept was developed as an alternative to conventional hospitalization in an effort to address problems regarding the capacity of hospitals and rising health care costs (Chahed et al., 2006). This service provides the delivery of medical, paramedical and social services to patients at their homes to help them to improve and to keep their best clinical, psychological and social conditions. However, since a range of human resources (e.g., nurses, physicians, 1

physiotherapists, social workers, psychologists, home support workers, etc.) and material resources are involved in the HHC delivery service, there are many issues that should be considered in detail. These issues are identified as resource planning in the HHC services and can be classified as the resource dimensioning, the partitioning of a territory into districts, allocation of resources to districts, assignment of care providers to patients or visits, and the resource scheduling and routing. In this study, we focus on the resource scheduling and routing problem and we review studies in the literature that address the scheduling and routing problem as a Travelling Salesman Problem (TSP) or Vehicle Routing Problem (VRP) in the HHC context. We analyze each study according to the study characteristics, the modelling characteristics, the network characteristics, and the data characteristics. The objective of this analysis is to show unexplored issues in the existing studies and to point out the possible future research opportunities within this topic. The reminder of this paper is organized as follows. Section 2, details the TSP and VRP. Section 3 makes a survey on the existing literature for the resource scheduling and routing problem in the HHC. Based on this survey, in Section 4 we analyze each work in detail. Lastly, the concluding remarks are presented in Section 5. 2. The Travelling Salesman and the Vehicle Routing Problems In this section we briefly describe the TSP and VRP and the connections between these problems. 2.1. Deterministic and Static Cases The Travelling Salesman Problem (TSP) is one of the most studied combinatorial optimization problems in the literature. The general form of the TSP was first studied by Karl Menger. Then, Dantzig et al. (1954) provided notable contributions by introducing a new solution method for this problem. The goal of this problem is to determine a set of routes for a salesman when a specific number of nodes are given. The salesman starts and returns back to a depot node such that all the remaining nodes are visited exactly once and the total cost of visiting all nodes is minimized. Depending on the formulated problem, the cost can be defined in terms of time, distance, etc. A generalization of this problem is the multiple travelling salesman problem (MTSP) in which routes are determined for M salesmen instead of one. Since the TSP is a special case of the MTSP, all the formulations and algorithms developed in the literature for the TSP are valid for the MTSP and vice versa.

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Similar to the connection between the TSP and MTSP, there is also a direct relation between the MTSP and VRP. The VRP can be considered as a variant of the MTSP, where the capacity restrictions on the vehicles are imposed. In other words, MTSP is a special kind of the VRP. We discuss the variants of the VRP as follows: • VRP with Capacity Restrictions (CVRP): Since there are other variants of the VRP, we name the MTSP with capacity restrictions as CVRP. • VRP with Single and Multiple Depots: In the single depot case, all of the salesmen start and end their routes at a single depot, whereas in the multiple depots case each salesman can start or end his/her routes at one of the common depots or at any other node. • Open VRP (OVRP): If each of the salesmen does not have to return back to the depot then the problem is named as OVRP. • VRP with Distance Constraints (DCVRP): The capacity constraint is replaced by a maximum route length (time) constraint and named as DCVRP. • VRP with Backhauls (VRPB): The node set is partitioned into two subsets: linehaul and backhaul. In the linehaul set, each node requires the delivery of a certain amount of products from the depot. In the backhaul set, each one requires the collection of a certain amount of products to the depot. • VRP with Picks and Deliveries (VRPPD): A number of goods need to be transported from certain pickup locations to other delivery locations. • VRP with Time Windows (VRPTW): Time windows are defined for all nodes and a visit for each node can only be carried out within these intervals. This way of modelling can be applied to all previously described variants. Note that all of these models can also be considered as variants of the TSP. Thus, we do not distinguish between them again in this part. In Figure 1, the relationship between TSP, VRP, and their variants is presented explicitly. For more detail on different versions of the VRP, please refer to the book of Toth and Vigo (2002). Till now, we have considered the deterministic and static versions of the TSP and VRP. The deterministic version corresponds to the case where the number of nodes, the number of vehicles, the demand of each node, and the travel time between each node, etc. are known in advance. In the static version, all relevant information for planning routes is assumed to be known before the routing process begins and this information does not change once the routes have been constructed. However, it is also important to consider probabilistic, stochastic and dynamic versions of these problems. In the section below, we briefly discuss these versions.

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Figure 1: Relationship between the TSP, VRP and variants 2.2. Probabilistic, Stochastic and Dynamic Cases Whilst dealing with the scheduling and routing problems, there can be some uncertain elements in the system. To this end, we will briefly discuss the probabilistic and stochastic variants of the TSP and VRP as follows: • Probabilistic Travelling Salesman Problem (PTSP): The PTSP can be considered as the variant of conventional TSP where the total distance of a priori tour is a random variable parameterized by the node probabilities. • Probabilistic Vehicle Routing Problem (PVRP): This problem is the probabilistic variation of the standard VRP, in which demands are probabilistic. • Stochastic Vehicle Routing Problem (SVRP): The SVRP is another variant of the classical VRP where more than one element of the problem is stochastic. The stochasticity can appear as a result of uncertain travel times, unknown demands and/or the set of customers to be visited. In the dynamic TSP and VRP, we do not know all the information for planning the routes when the routing process begins. In particular, after constructing the initial routes, the information can be updated due to various external factors. The first dynamic VRP study was provided by Powell (1986). In this section we have focused on the TSP, VRP and their variants. Besides some of the widely used application areas of these problems are as follows: the emergency management (Wang et al., 2009), the waste collection (Nuortio et al., 2006), the print press scheduling (Gorenstein, 1970), the crew scheduling (Lenstra and Rinnooy Kan, 1975), the school bus routing (Angel et al., 1972), the interview scheduling (Gilbert and 4

Hofstra, 1992) and the nurse scheduling and routing problems. Since we only focus on problems related to resource scheduling and routing problem within the HHC context in this study, the following section presents the literature devoted to this problem. 3. Review of the Resource Scheduling and Routing Problem As mentioned previously, there are several issues that should be considered in the resource planning of the HHC, such as the resource dimensioning, partitioning of a territory into districts, allocation of resources to districts, assignments of care providers to patients or the visits and the resource scheduling and routing. In this study, we only focus on the last one, that is, resource scheduling and routing and we present a detailed survey about the existing literature. Before providing details about the literature, it is crucial to illustrate the flow of the resource planning procedure to see what has to be done before the scheduling and routing process starts. The first step in the process is the resource dimensioning issue. Here, the number of resources is determined to meet the predetermined care demand with the minimum cost and the adequate service quality. The second step is partitioning of a territory into districts. This consists of grouping small geographic areas into larger clusters, which are named as districts, according to relevant criteria where each district is under the responsibility of a multidisciplinary team. Once districts are determined, resources are assigned to districts and then to patients equitably. After completing these steps the successive one is the routing process. Most of the existing works in the HHC literature are devoted to the resource scheduling and individual route construction problems. Hence, in the following discussion we provide a general overview for each existing paper on this topic. The main aim of this part is to explain the contributions achieved by each work.1 Begur et al. (1997) present a spatial decision support system (SDSS) that contains a special module for the daily scheduling of care providers' activities. This module assigns simultaneously care providers to visits and generates the sequence in which the visits would be carried out. It is based on a heuristic approach that combines a set of procedures for building and improving the daily routes of care providers. The objective of this heuristic is to minimize the total travelling time while respecting the constraints related to the route construction, care providers time 1 All papers presented in this part were found using the Web of Science and Google search engines with the following keywords: home health care, resource scheduling, routing, travelling salesman problem and vehicle routing problem. We also examine literature review parts of all papers to increase the depth of our review.

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windows, and skills requirements. In the work of Cheng and Rich (1998), a daily scheduling problem is developed as a multi-depot VRP with time windows and the compability information. The problem is formulated as a mixed integer linear program. The objective is to minimize the total cost associated with the amount of overtime hours of full-time nurses and the amount of hours assigned to part-time nurses. Meanwhile this objective is obtained with respect to visiting each patient exactly once, assigning each nurse at least one patient, starting and ending at his/her home, taking a lunch break within the given time interval and respecting the maximum nurse shift length constraints. The problem is solved by a two-phase heuristic: the first phase falls into the parallel tour-building procedure category and the second phase attempts to make an improvement on tours identified in the first phase. Later, Eveborn et al. (2006) develop a decision support system for the local authorities in Sweden, called Laps Care. In this system, they formulate the scheduling problem as a set partitioning model and solve by a repeated matching algorithm. The objective is to minimize a total cost related to the travel time, scheduled hours, preferences, etc., while respecting the following constraints: time windows for visits, operators’ skill requirements, and accomplishment of each visit by one operator. Bertels and Fahle (2006) propose a weekly plan that combines linear programming, constraint programming, and heuristics in order to assign operators to visits and sort visits assigned to each operator optimally. The objective is to minimize the total transportation cost while maximizing the satisfaction level of patients and operators with respect to a variety of soft constraints. These soft constraints include affinities between the patients and care providers, preferences for certain visits, and soft visits' and care providers' time windows. Besides, there are also some hard constraints that must be satisfied: skill requirements, work time limitations, time window constraints for visits, and the assignment of each visit exactly once. Moreover, Thomsen (2006) addresses the daily scheduling problem as a VRP with time windows and shared visits (visits by two operators). The objective of this model is to minimize the total travelling cost, the number of unshared (visit is carried out by a non-reference operator) and unlocked visits and the number of shared (visit is carried out by two nonreference operators) and unlocked visits. The constraints of the model are as follows: respecting the visits' and operators' time windows, assignment of at least one visit to each operator and starting, ending a shared visit at the same time. He solves this model by using an insertion heuristic and Tabu search technique. In a more recent study, Akjiratikarl et al. (2007) generate daily schedules by using the VRP with time windows. Since this problem is a combinatorial optimization problem, they develop a heuristic based approach to solve it. As a result they develop the Particle Swarm Optimization Problem (PSO). They incorporate also the Local Improvement Procedure (LIP) into the PSO solution approach to improve their solutions. Finally, they combine their approach with the Earliest 6

Start Time Priority with Minimum Distance Assignment technique to generate the initial solutions. Within this framework, they focus on the determination of routes for each operator while minimizing the total distance travelled with respect to visits' and operators' time windows and assignment of each visit to only one operator. Ben Bachouch et al. (2008) develop the VRP with time windows as a mixed linear programming model with the objective of minimizing the total distance travelled by the operators. The model is subject to visits' and operators' time windows, nurses' meal breaks, care continuity and the restriction on the nurses' maximum distance travel limit constraints. Bouazza et al. (2008) develop a model for determining routes for operators that incorporates constraints of the VRP with the medical and continuity of care constraints. Here, each patient is assigned to a region with respect to his/her home address. Similarly, each nurse is also assigned to a region but there can be more than one nurse in a specific region. They allow also a nurse to visit a different region with a certain penalty. In this model, they add blood sample related constraints as a medical constraint and they consider the objective function as minimizing the total travelling cost of operators. As a final step, they solve this problem with a meta-heuristic approach based on Tabu search. In a more recent work, Ben Bachouch et al. (2009) address the daily drug delivery problem in the French home care structure as a VRP with time windows. The objective of the model is to minimize the total distance travelled. In this model they assign carriers to specific regions so that each tour is realized by the same carrier. In addition, they develop four different strategies as follows: starting deliveries when a specified number of deliveries is received, starting deliveries if a specified distance is reached regarding to the planned deliveries, starting deliveries on a fixed number of deliveries per carrier, and starting deliveries on fixed hours. They use the solver Lingo to obtain and compare results for each strategy in order to identify which one is the most efficient to solve the drug delivery problem in the HHC context. Moreover, Chahed et al. (2009), couple the production and distribution of anti-cancer drugs within the context of the chemotherapy at home. They present six models based on three main criteria: time windows, objective function and distribution of drugs. The objective is either to minimize the delivery cost or maximize the number of visited patients. They present also numerical results for one of these models. Bredstörm and Rönnqvist (2008) develop a mathematical model that incorporates synchronization and precedence constraints between visits. The proposed model is based on the traditional VRP with the additional synchronization and precedence constraints. They use a heuristic approach based on the local branching heuristic to solve their model. In their previous study (see Bredstorm and Rönnqvist (2007)), they developed a branch-and-price algorithm to solve the same model without including the precedence constraints. Later, Kergosien et al. (2009) formulate the routing problem of the HHC operators as a MTSP with time windows. The objective of 7

the proposed model is to minimize the total travelling cost while respecting visits' and operators' time windows constraints, the assignment of each service to one operator constraints, synchronized (some visits require more than one operator) and disjunctive (some operators cannot work together) services constraints, continuity of care and the assignment of all operator constraints. They test the model on randomly generated instances with Cplex solver. More recently, Rasmussen et al. (2010) address the daily scheduling problem as a multi-depot VRP with time windows and connections between visits. They use a multi-criteria objective rather than only minimizing the total distance travelled. The proposed formulation is very similar to the one that is developed by Bredstörm and Rönnqvist (2007) but here they allow also a visit to be uncovered (visit is not carried out). Thus, the proposed multi-criteria objective includes the minimization of uncovered visits, the maximization of operator-visit preference and the minimization of the total distance travelling costs. In particular, in the objective function they assign a higher priority to the uncovered visit part than the other parts. Finally, the constraints of this model include: each visit can be covered exactly once or left as uncovered, operators can only handle allowed visits, visits' and operators' time windows and precedence relations of visits. Note that although there are some other works that incorporate the routing and scheduling aspects to the HHC structure, they do not include the VRP or TSP in their routing structure. In this work we consider only those that model the HHC problem by using the VRP or TSP. Until now we have provided details of each work that exists in the literature. However, it is also important to classify these works according to certain criteria to find the gaps in the literature. To this end, in the upcoming sections we first provide classification characteristics then, we classify each work according to these characteristics, and finally we provide the possible research paths. 4. Classification of Papers In the previous section, we presented only general details of each paper. In this section, we will provide more details by proposing and applying classification characteristics. By using these characteristics, we also compare each study and gather the possible research directions. 4.1. Classification Criteria In this section we present classification criteria. We also provide explanations for some of these criteria to underline their important aspects.

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We use four branching levels from top to bottom in order to consider more details about existing works (see Figure 2). A paper might include many different categories in each branching level. The first branching level is used to identify each study according to four main aspects: i) classification of the study, ii) modeling characteristics, iii) network characteristics, and iv) data characteristics. In the first category, that is, study classification, we analyze each study according to the model used, the solution approach applied, and whether the implementation of the model exists or not. It is important to note that while classifying the papers according to the model used, we group them as either TSP or VRP. Although both TSP and VRP have different variants, for simplicity we do not specify each variant in this classification. For example, if a paper is modelled by using the TSP or MTSP we consider this work under the TSP group. Similarly, all variants of the VRP such as CVRP, VRPB, DCVRP and VRPPD are considered under the VRP group. The next category that we define is the modelling characteristics. Here, we group each work according to the time horizon, visiting structure, patient covering, service providing, provider type, objective and time window structure. The ‘time horizon’ characteristic is used to define for how long the model creates the routing structure. ‘Visiting structure’ is used to identify whether the visit is held by a single operator, multiple operators or operators with material resources. Moreover, ‘patient covering’ characteristic is defined to represent the covering constraints for visits. Numbers of services provided by operators (single or multiple) are classified under the ‘service providing’ characteristic. In particular, the service can be a drug delivery operation or doctor/nurse visit operation, so we classify them under the group of the ‘provider type’. The ‘objective’ characteristic is used to identify if the objective function is composed of a single criterion or multiple criteria. These criteria include the minimization of the total distance travelled, visiting outside regions, maximization of the satisfaction level of patients, and operators etc. As the last characteristic, we define the ‘time windows structures’ where soft (can be violated with a penalty), hard (no violation is allowed) or both types of time windows are considered. We should underline that, some of these categories can also be considered under the other categories. For example, visiting structure includes shared and unshared visits and it can also be considered under the patient covering group. But we rather choose to specify it separately, as it is one of the main contributions in the HHC context. Moreover, there are many subbranches under the patient covering branch. Among these, exclusion is one of the important sub-branches that require more detailed explanation. Exclusion is used to specify exclusion of a patient from the HHC structure. However, this aspect can only be considered when some uncertainty is available in the structure for example demand uncertainty. Furthermore, the third category is based on the network characteristics. 9

Here the geography, operators’ center, time window type, contract type of operator, operator homogeneity, quality of the system, travel times, demand and service times are considered. The ‘geography’ characteristic is proposed to identify the number of districts used in studies. To point out the number of depots (one or multiple) where operators start their daily tours, ‘operators’ center’ characteristic is considered. Since the visiting time of a patient depends on the time availability of the patient, operator or both, the ‘time window’ group is defined to point out this aspect. Moreover, a health care provider might employ an operator with a full time contract, half time contract or from external sources. Thus, the ‘contract type of operator’ characteristic is defined to show which one is applied. In the HHC structure, operators can be identical or have different qualifications, therefore ‘operator homogeneity’ is used to distinguish them. The characteristic defined as ‘Quality of the system’ is used to show if the study presents the quality from patients’ and/or operators’ point of view. The ‘travel time’ and the ‘demand’ characteristics are defined to present either papers use these issues deterministically or stochastically. Furthermore, service times of visits can be equal or variable thus, the ‘service time’ group is defined to show this issue. The fourth category of our analysis is based on the data characteristics. In this part, we group papers according to the used data type. The data can be a real life instance, randomly generated instance or widely applied state of the art instance.

Figure 2: Classification criteria In the following part we apply these characteristics to the previously examined papers to analyze each work in more detail. 10

4.2. Application of Classification Criteria Here we apply the characteristics provided in Figure 2 to the existing papers to present a comparison and to find the non-studied or rarely studied points that might be included in future works. All articles are identified in Figure 3. Note that while applying these characteristics, it is possible to end up with an empty cell. Having an empty cell for a article indicates that the work does not include the corresponding cell’s attribute. If a article includes the attribute, it is marked with the symbol “X”. The columns in black are used to identify the first branching level. We color these columns since they have sub-branches and it is not possible to directly assign the symbol “X”. Similarly, the grey color is used for most of the second branching levels that also have sub-branches. However, we do not assign any color to the third branching level although some of them have also sub-branches. Instead, we assign the symbol “X” to the third and fourth branching levels if they exist and include the corresponding attribute. As it can be seen from Figure 3, there are many blank cells and columns. This means that there may be gaps in the literature. Here is the list of attributes that are not included in any of the papers until now: 1.1.1.2, 1.1.2.2, 1.2.1.2, 1.2.2.3, 2.1.1, 2.2.3, 2.3.2.2, 2.4.7, 3.2.2.1, 3.4.3, 3.7.2, 3.8.2, 3.9.1, 3.9.2.2. Among these, modelling the problem with the stochastic versions of the TSP and VRP (1.1.1.2, 1.1.2.2), incorporating a shared visit with a material resource (2.3.2.2), excluding a patient from the system when needed (2.4.7), providing an operator from an outside source when required (3.4.3), adding stochasticity on travel time, demand and service time (3.7.2, 3.8.2, and 3.9.2.2) are the most important attributes according to our interests and according to the needs of health care providers. In particular, existing works have not incorporated these attributes because of their computational complexity. Adding these attributes makes the problem big in size and complex. On the other hand, the remaining excluded attributes such as 2.1.1, 2.2.3, and 3.9.1 have not been considered in any study because they do not reflect the requirements of the real life applications. Also note that, although adding stochasticity on travel time, demand or service time would result with the stochastic versions of the TSP or VRP, we prefer to mention them separately since there might be other parameters that might cause stochasticity (i.e., number of operators). There are also other important attributes that are not incorporated extensively in the existing literature: continuity (2.4.6), multiple service provision (2.5.2), and visiting multiple districts (3.1.2). Care continuity issue is considered in some of the existing studies but they are added as

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Figure 3: Classification summary according to papers soft constraints thus, incorporating them as a hard constraint will be a significant contribution. Until now it has not been added as a hard constraint due to complexity reasons. Similarly, almost all of works that we have discussed focus only on one service provision. They have generalized all services and named them as health care services and they have not distinguished services from each other. However, distinguishing services and imposing constraints on these aspects are also important. Only in the work of Bouazza et al. (2008), they consider two different services. They impose constraints for blood sample collection as well as for general care services. In addition to these attributes, dividing a region into districts and visiting more than one district are other important aspects. All in all, adding all these attributes in future studies will be a significant contribution to the field. 5. Conclusion The HHC domain has started to grow significantly in the past few years and it has become a real alternative to traditional hospitalization. In this study, we discussed that there are a large number of resources that participate in delivering the HHC service and we focused on the resource scheduling and routing problems. We reviewed studies that address the routing and scheduling problems as a TSP or VRP in the HHC context. Although there are also other alternatives for modelling the routing and scheduling aspects, we do not include them in this study. Note that there are only fourteen articles that present the routing and scheduling problems as a TSP or VRP in the HHC context. The main objective of our study is to compare the main characteristics of these 12

articles and to find possible research directions as well. Thus, we analyze each study according to different characteristics and, as a result, we determined that imposing qualification constraints into the TSP and VRP structure by some of the existing works provides an important contribution to the TSP, VRP and HHC field. We also revealed that there is no previous study that incorporates any kind of stochasticity into the resource scheduling and routing problem in the HHC context. References Akjiratikarl C. , Yenradee P., Drake P.R. (2007), “PSO-based algorithm for home care worker scheduling in the UK”, Computers and industrial engineering, 53: 559-583. Angel R.D., Caudle W.L., Noonan R., Whinston A. (1972), “Computer Assisted School Bus Scheduling”, Management Science, 18: 279-88. Begur S.V., Miller D.M., Weaver J.R. (1997), “An integrated spatial Decision Support System for scheduling and routing home health care nurses”, Interfaces, 27: 35-48. Ben Bachouch R., Fakhfakh M., Guinet A., Hajri-Gabouj S. (2008), Planification de la tournée des infirmiers dans une structure de soins à domicile, Conférence Francophone en Gestion et Ingénierie des Systèmes Hospitaliers (GISEH), Switzerland. Ben Bachouch R., Fakhfakh M., Guinet A., Hajri-Gabouj S. (2009), A model for scheduling drug deliveries in a French homecare, International Conference on Industrial Engineering and Systems Management (IESM), Montreal, Canada. Bertels S., Fahle T. (2006), “A hybrid setup for a hybrid scenario: combining heuristics for the home health care problem”, Computers and Operations Research, 33: 2866-2890. Bouazza E., Ferland J.A., Viviane G. (2008), Mathematical Programming Approach for Routing Home Care Nurses, Proceedings of the 2008 IEEE. Bredstörm D., Rönnqvist M. (2007), A branch and price algorithm for the combined vehicle routing and scheduling problem with synchronization constraints. Technical report, Department of Finance and Management Science, Norwegian School of Economics an Business Administration. Bredstörm D. and Rönnqvist M. (2008), “Combined vehicle routing and scheduling with temporal precedence and synchronization constraints”, European Journal of Operational Research, 191, 1: 1931. Chahed, S., Matta, A., Sahin, E., Dallery Y. (2006), Operations management related activities in home health care structures, Proceedings of INCOM Conference (Information Control Problems in Manufacturing), Saint-Etienne, France, 3: 641-646.

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Chahed S., Marcon E., Sahin E., Feillet D., Dallery Y. (2009). “Exploring new operational research opportunities within the Home Care context: the chemotherapy at home”, Health Care Management Science, 12: 179-191. Cheng E., Rich J.L. (1998), A home care routing and scheduling problem. Technical Report TR98-04, Department of Computational And Applied Mathematics, Rice University. Dantzig G., Fulkerson R., Johnson S (1954), “Solution of a large-scale travelling salesman problem”, Operations Research, 2: 393-410. Eveborn P., Flisberg P., Ronnqvist M. (2006), “LAPS CARE—an operational system for staff planning of home care”, European Journal of Operational Research, 171: 962-976. Gorenstein S. (1970), “Printing press scheduling for multi-edition Periodicals”, Management Science, 16, 6: B373–B383. Gilbert K.C., Hofstra R.B. (1992), “A new multi period multiple travelling salesman problem with heuristic and application to a scheduling problem”, Decision Sciences, 23: 250-259. Kergosien Y., Christophe L., Jean-Charles B. (2009), Home health care problem: An extended multiple Traveling Salesman Problem, Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA ), Dublin, Ireland. Lenstra J.K., Rinnooy Kan A.H.G. (1975), “Some simple applications of the traveling salesman problem”, Operations Research Quarterly, 26: 717–733. Nuortio T., Kytojoki J., Niska H., Braysy O. (2006), “Improved route planning and scheduling of waste collection and transport”, Expert Systems with Applications, 30, 2: 223-232. Powell W.B. (1986), “A stochastic model of the dynamic vehicle allocation problem”, Transportation Science, 20, 2: 117-129. Rasmussen M.S., Justesen T., Dohn A., Larsen J. (2010), The Home Care Crew Scheduling Problem: Preference-Based Visit Clustering and Temporal Dependencies, in series: DTU Management. Thomsen K., Optimization on home care. Thesis Report, Informatics and Mathematical Modeling, Technical University of Denmark, 2006. Toth P., Vigo D. (2002), The vehicle routing problem, SIAM Monographs on Discrete Mathematics and Applications, Philadelphia. Wang J., Hu X., Xie B. (2009), Emergency Vehicle Routing Problem in Post-Earthquake City Road Network, International conference on transportation engineering, Proceedings Of The Second International Conference On Transportation Engineering.

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