مدیریت عملیات اعمال شده برای خدمات مراقبت در منزل: تجزیه و تحلیل مشکل ناحیه ای

In this paper, we focus on a specific operations management related issue faced by home health care (HHC) services, namely the districting problem. Our contribution consists of formulating the HHC districting problem as a mixed-integer programming model by considering criteria such as the indivisibility of the basic units (i.e. locations where patients live), compactness, workload balance between human resources and compatibility. The formulations developed are based either on balancing the personnel care workload or minimizing the travel distance to reach the patients. Computational results obtained from the models show that they enable to improve the service quality towards HHC patients as well as caregivers by optimizing the compactness and workload balance criteria.

Recent developments in technological, social and economical environment have dramatically increased the need for improved service systems. Well designed service systems allow reducing costs and increasing customer satisfaction. This paper deals with a well-known type of service system, namely the home health care service. Home health care (HHC) which represents an alternative to the traditional hospitalization has been developed in France fifty years ago in order to solve the problem of hospitals' capacity saturation by providing to patients, at their home, complex and coordinated medical and paramedical care for a limited period which can be extended depending on patients' needs. This care is comparable, in terms of nature and intensity, to the one which would be delivered to the patient within a traditional hospitalization framework where the patient stays in the hospital to receive his/her treatment. HHC can be prescribed either by the family doctor or the doctor in charge of the patient in the hospital. Once admitted to a HHC structure, patients who suffer from pathologies such as cancer, nervous system diseases, circulatory system diseases, etc., receive medical and paramedical care based on one or several protocols/standards of care. The French HHC structures use twenty four protocols of care listed in the circular of May 30th, 2000 such as: the chemotherapy, radiotherapy, breathing assistance, palliative care, post-operation treatment, etc. [14]. Based on these protocols as well as on patients' social conditions, their age and their autonomy measured by the Karnofsky Performance Scale Index, a therapeutic project is then designed for each patient so that the number and average duration of visits required during the treatment of the patient within the HHC as well as the type and number of human and material resources required for the care delivered can be determined. The diversity of human resources that can be involved in the care (e.g. physicians, nurses, physiotherapists, social workers, home support workers, pharmacists, etc.) explains, as it will be described in detail later in the paper, the necessity of assigning to each patient a reference caregiver who is in charge of coordinating the execution of the therapeutic project. At this level, it is important to mention that most of HHC structures classify patients' therapeutic projects into categories named “profiles”. Indeed, patients whose therapeutic projects have similarities in terms of the expected duration of care, type, number and average duration of visits are grouped into the same profile. During the last decade, HHC services have known an important growth. Indeed, the total number of HHC structures in France rose steadily from 68 structures in 1999 to 123 in 2005 and finally reached 271 structures in 2007. Despite the importance of the development of HHC services in practice, the amount of investigations dealing with operations management problems within the HHC context still remains modest, in comparison with earlier models developed for hospitals (e.g. [15], [21] and [26], etc.). Most of the investigations considering HHC services mainly focus on either the problem of assigning caregivers to patients (or to visits) or the routing problem. Among the existing works developed so far, some models have been able to capture some of the specificities of HHC operations, i.e. what makes this care service different from the one delivered by hospitals, with respect to the way operations are managed. Hence, a first characteristic we can identify is the issue of the continuity of care in the HHC context defined by Shortell [29] as being the extent to which the medical and paramedical care are delivered by means of a sequence of coordinated and uninterrupted activities consistent with patients' needs, if possible by the same human resources. In practice, in order to guarantee the continuity of care in HHC, a patient is often assigned to only one caregiver, the reference caregiver, who follows the treatment of the patient during the time spent in the HHC structure. Most of time, the reference caregiver is the nurse who gives the paramedical care and coordinates the overall care with other caregivers such as the physician, social worker, etc. This is an important quality requirement of the HHC service due to the fact that it enables to preserve the service quality perceived by the patient since he/she receives the care from the same caregiver and thus does not have to continuously change his/her relationships with a new caregiver. A second characteristic of HHC operations is the necessity to integrate the patients' home within the care supply chain and hence to move the different flows of human and material resources needed for the care towards the patients' home. However, the diversity of human resources delivering the care and the variety of clinical and organizational decisions involved in the care delivery process need a tight coordination between different types of caregivers and material resources. Note that this coordination is especially difficult within this context since these resources are not grouped in the same health unit [12]. Another interesting problem which seems to us specific to HHC services concerns the consideration of human aspects while choosing the best organization for caregivers' teams. More specifically, if we consider one type of HHC caregivers, let's say the nurses, one may be interested in investigating the difference between two organizations: in the first organization, we assume that all nurses are grouped in a single team so that all the patients are treated by the same nurses' team independently of the basic unit where they live, while in the second organization, the area where the HHC structure operates is partitioned into several clusters (subareas), each of them being managed by a dedicated nurses' team. In our terminology, each cluster will be called a district. This second organization may enable not only to answer to a patient demand more quickly but also to increase the quality of service provided to him/her due to the diminution of the average time spent to reach him/her. Therefore, caregivers can spend more time in delivering care to patients. Furthermore, working in smaller areas, i.e. districts, within a smaller team may enhance caregivers' motivation since they can find a reinforced collaboration inside the team they belong to as well as a closer proximity with the HHC manager in charge of their team. Hence, the aim of a HHC structure in considering a districting approach may be to better manage its employees and, as a consequence, to satisfy patients more efficiently. In this paper, we focus our attention on the districting problem due to the importance of such a decision in the achievement of HHC objectives in terms of improvement of the care delivery efficiency. Indeed, as explained above, the districting of a territory is a strategic HHC decision which aims at grouping basic units (a set of patients) into larger clusters, i.e. districts, so that these districts are “good” according to relevant criteria. These criteria can be related to the activity, demography or geographic characteristics of the basic units. Even if the districting approach can be viewed as time and resource consuming, it can have important impacts on caregivers' team structure and patients' satisfaction level. This paper is organized as follows. In Section 2, we survey the literature related to our work: the first part of investigations reviewed concerns models that are developed in the operations management literature applied to HHC services while the second part is more related to the districting approach. In Section 3, we propose two mathematical formulations for the HHC districting problem. Results of computational experiments carried out on randomly generated instances to validate these two models are presented in Section 4. Finally, Section 5 presents some conclusions and perspectives that can be considered for future research.

In this paper, we developed two models for the districting problem applied to HHC structures. We also presented a numerical analysis based on different instances generated randomly. This enabled us to evaluate the impact of the key parameters on the workload balance and compactness criteria. Indeed, their analysis indicates that for a given M, pmax and dmax (Model 1) or τ (Model 2), by increasing N, the feasibility percentage and the mean distance are weakened while the mean gap_max is improved. Similarly, for a given N, pmax and dmax (Model 1) or τ (Model 2), the feasibility percentage decreases and the mean gap_max or distance increases as long as pmax increases or the value of dmax (Model 1) or τ (Model 2) decreases. Furthermore, for a fixed value of N, the higher is the number of districts to design M, the higher is the mean gap_max and the less is the mean distance. Since this work was based on instances generated randomly, we consider, in our ongoing research, to apply the proposed models to a real case of a HHC structure. In this context, developing a heuristic approach for solving the real instances represents also an interesting research priority. Furthermore, we intend to consider several extensions of the models we propose. The first extension concerns the periodic revision of the districting problem on a rolling horizon so that new information on demand related to the number of patients who need the care, level of care required by each patient, changes in the number of caregivers, etc. can be integrated to the districting decision. This process of revision of the districting (i.e. the redistricting problem) can also respect additional constraints such as a maximum number of changes in basic unit–district assignments over a period of time in order to preserve the development of relationships between patients and caregivers, the organization of the work of caregivers with local community agencies, etc. A potential second extension would concern the possibility to optimize simultaneously the care workload and the travel distance criteria while forming the districts. This can be done by using a multi-criteria approach which consists on formulating the problem as a weighted sum of the maximum deviation of the district care workload from the average care workload and the maximum distance between two basic units that can be assigned to the same district. Such approaches have been applied for solving the districting problem in other realms such as the electrical power districting problem or the political districting. Overall, we must keep in mind that the objective of this work is not to develop a total automatic procedure but to propose a decision support system for the HHC managers who would modify solutions obtained by the mathematical models based on their experience. This interaction would probably conduct to more suitable solutions according to the criteria that are difficult to quantify. Furthermore, the HHC managers should verify the efficiency of adopting the districting approach for improving the human resources management in terms of its impact on increasing human resources motivation and work satisfaction.