Abstract The focus of this work is the numerical application of a stochastic decision support model for the patient admission scheduling problem with random arrivals and departures. Here, we discuss the methodology for applying our model to real-world problems. We outline a solution approach for efficient computation, provide a numerical analysis of the model, and illustrate the methodology with examples. A key component of the model is an integer linear program which formulates the patient admission scheduling problem as an optimization of the total expected cost accumulated over a finite planning horizon. We rewrite some of the components of this integer linear program in order to improve numerical efficiency. We use Poisson processes and discrete phase-type distributions to model the random arrivals and departures, respectively. We argue that this stochastic component is essential for an accurate treatment of real-world problems which are stochastic in nature. We support our claim with simple numerical examples, and show that the optimal solutions obtained from deterministic models are inadequate when compared with the solutions of our stochastic model. We also construct more complex numerical examples for large-scale problems using heuristics that approximate the objective function, in order to demonstrate that our model can be efficiently applied to real-world problems, which typically involve large data sets.

中文翻译：

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随机到达和离开患者入院调度问题的决策支持模型：一种求解方法

摘要 这项工作的重点是随机决策支持模型在随机到达和离开的患者入院调度问题中的数值应用。在这里，我们讨论将我们的模型应用于实际问题的方法。我们概述了有效计算的解决方法，提供了模型的数值分析，并通过示例说明了该方法。该模型的一个关键组成部分是一个整数线性程序，它将患者入院调度问题表述为在有限规划范围内累积的总预期成本的优化。我们重写了这个整数线性程序的一些组件，以提高数值效率。我们使用泊松过程和离散相类型分布分别对随机到达和离开进行建模。我们认为，这种随机成分对于准确处理本质上是随机的现实世界问题至关重要。我们用简单的数值例子支持我们的主张，并表明与我们的随机模型的解相比，从确定性模型获得的最优解是不够的。我们还使用近似目标函数的启发式为大规模问题构建了更复杂的数值示例，以证明我们的模型可以有效地应用于通常涉及大型数据集的实际问题。并表明与我们的随机模型的解相比，从确定性模型获得的最优解是不够的。我们还使用近似目标函数的启发式为大规模问题构建了更复杂的数值示例，以证明我们的模型可以有效地应用于通常涉及大型数据集的实际问题。并表明与我们的随机模型的解相比，从确定性模型获得的最优解是不够的。我们还使用近似目标函数的启发式为大规模问题构建了更复杂的数值示例，以证明我们的模型可以有效地应用于通常涉及大型数据集的实际问题。