Home health care (HHC) consists of care services provided to patients at their domicile rather than in hospitals or other health facilities. HHC human resources are largely studied in the optimization literature, to improve service quality and efficiency. However, the growth of complex HHC services that include the delivery of devices and disposable materials makes it necessary to include them in the decision-making process together with human resources. In fact, they may represent a high cost item, and their release may affect the scheduling of HHC visits. Unfortunately, as far as our knowledge, devices and materials are not considered together with the technical staff required to support their utilization. In this paper, we address the dimensioning problem for new HHC services that also involve devices and materials, considering the joint dimensioning of human and material resources. We include three categories of staff (nurses, physicians and technicians), a set of devices and a set of materials; also, we assume that the requirements from patients are in terms of frequencies, i.e., the maximum number of days between two consecutive visits, two supplies of a material or two uses of a device. We propose a linear programming model and a matheuristic approach for solving instances of realistic dimension. The model allows determining the number of nurses, physicians, and technicians to be hired, as well as the number of devices to be acquired to meet the demand. As for the matheuristics, we combine a decomposition step and a heuristics inspired by the Local Branching idea. Results show the capability of the approach to solve the problem and provide good dimensioning solutions, which can be actually adopted in real-life problems. Moreover, the matheuristic approach performs well in a variety of instances.

中文翻译：

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一种优化工具，可通过设备和一次性材料确定创新的家庭保健服务的尺寸

家庭保健（HHC）包括在住所而不是医院或其他医疗机构中为患者提供的护理服务。HHC人力资源在优化文献中进行了大量研究，以提高服务质量和效率。但是，包括设备和一次性材料交付在内的复杂HHC服务的增长使得必须将它们与人力资源一起纳入决策过程。实际上，它们可能代表着高成本的项目，它们的释放可能会影响HHC探访的时间安排。不幸的是，就我们所知，设备和材料并未与支持其使用所需的技术人员一起考虑。在本文中，我们解决了新的HHC服务的尺寸问题，该服务还涉及设备和材料，考虑人力和物力资源的共同规模。我们包括三类人员（护理人员，医师和技术人员），一套设备和一套材料。同样，我们假设患者的要求是在频率方面，即两次连续就诊，两次供应材料或两次使用设备之间的最大天数。我们提出了一个线性规划模型和一种数学方法来求解实际尺寸实例。该模型可以确定要聘用的护士，医生和技术人员的数量，以及为满足需求而要购买的设备的数量。至于数学，我们结合了分解步骤和受本地分支思想启发的启发式方法。结果表明该方法能够解决问题并提供良好的尺寸标注解决方案，可以在实际问题中实际采用。此外，数学方法在各种情况下都表现良好。