We consider a home health care routing problem with scarce resources which is a variation of the vehicle routing problem with resource constraints. In this problem, the services are provided by nurses and aids at patients’ homes. There are different types of patients that are categorized based on the services they demand and should be serviced by appropriate staff teams or single personnel where the teams are transported by rental vehicles. In this problem, the objective is to minimize the total transportation cost, by considering the patients’ requirements and the qualification of the staff, as well as the resource limitations. In this paper, we present a mathematical formulation of the problem that is modeled similar to a vehicle routing problem and propose a branch-and-price algorithm to solve it. Our proposed algorithm utilizes speed up techniques from the literature to enhance the effectiveness of the proposed solution method. A comprehensive computational study is conducted on Solomon based instances and the results illustrate the efficiency of the algorithm and the effective use of available resources.

我们考虑具有稀缺资源的家庭卫生保健路线选择问题，它是具有资源约束的车辆路线选择问题的一种变体。在这个问题上，服务由病人家中的护士和辅助人员提供。根据患者所需的服务将其分类为不同类型的患者，应由适当的工作人员小组或由租赁车辆运送这些小组的单身人员为他们提供服务。在这个问题中，目标是通过考虑患者的需求和工作人员的资格以及资源的限制，使总运输成本最小化。在本文中，我们提出了一个类似于车辆路径问题的数学模型，并提出了一种分支价格算法来解决该问题。我们提出的算法利用文献中的加速技术来提高提出的解决方法的有效性。对基于Solomon的实例进行了全面的计算研究，结果说明了该算法的效率和对可用资源的有效利用。