标题： 动态居家护理路线与调度，每次转介的访问次数不确定 显示英文标题

标题： Dynamic Home Care Routing and Scheduling with Uncertain Number of Visits per Referral

摘要： 尽管居家护理行业迅速增长，但在存在不确定性的情况下，关于居家护理访问的调度和路径规划的研究仍然有限。 本文研究了这个问题的一个动态版本，其中转介数量及其所需的访问次数是不确定的。 我们为单护士问题开发了一个马尔可夫决策过程（MDP）模型，以最小化拒绝、偏离、加班和旅行时间成本的期望加权总和。 由于最优求解MDP是难以处理的，我们采用了一种近似线性规划（ALP）来获得可行的策略。 典型的ALP方法只能解决非常小规模的问题实例。 我们在问题的一个特殊情况下推导出了最优ALP参数的直观可解释的显式解。 受此形式的启发，我们为一般问题中的ALP模型提供了两种启发式简化技术，以在可接受的时间内解决大规模实例。 数值结果表明，ALP策略优于反映当前实践的短视策略，并且在大多数考虑的实例中优于基于情景的策略。 显示英文摘要

摘要： Despite the rapid growth of the home care industry, research on the scheduling and routing of home care visits in the presence of uncertainty is still limited. This paper investigates a dynamic version of this problem in which the number of referrals and their required number of visits are uncertain. We develop a Markov decision process (MDP) model for the single-nurse problem to minimize the expected weighted sum of the rejection, diversion, overtime, and travel time costs. Since optimally solving the MDP is intractable, we employ an approximate linear program (ALP) to obtain a feasible policy. The typical ALP approach can only solve very small-scale instances of the problem. We derive an intuitively explainable closed-form solution for the optimal ALP parameters in a special case of the problem. Inspired by this form, we provide two heuristic reduction techniques for the ALP model in the general problem to solve large-scale instances in an acceptable time. Numerical results show that the ALP policy outperforms a myopic policy that reflects current practice, and is better than a scenario-based policy in most instances considered.