论文标题
综合家庭护理人员配备和能力计划：随机优化方法
Integrated Home Care Staffing and Capacity Planning: Stochastic Optimization Approaches
论文作者
论文摘要
我们提出了由家庭护理实践引起的人员配备和能力计划问题的随机优化方法。具体来说，我们考虑了一家家庭护理机构的观点，该机构必须决定在指定的计划范围内每天在每天在不同类型的服务（能力计划）中雇用的护理人员数量（人员配备）和分配雇用的护理人员。目的是最大程度地降低与人员配备（即就业），容量分配，人员过度和作品不足相关的总成本。我们提出了两阶段随机编程（SP）和分配强大的优化（DRO）方法，以建模和解决此问题，考虑到两种类型的决策者，即提前的决策者（EA）和灵活的调整决策者（FA）。在EA模型中，我们在观察需求之前确定了第一阶段的人员配置和能力分配决策。在FA模型中，我们决定在第一阶段的人员决策。然后，我们根据第二阶段的需求实现确定能力分配决策。我们为EA决策者的拟议的非线性DRO模型提供了同等的混合企业线性编程（MILP）重新汇版，该模型可以使用现成的优化软件可以实现并有效地解决。我们提出了一种具有有效不平等的计算有效的列和约束生成算法，以解决FA决策者的提出的DRO模型。最后，我们进行了广泛的数值实验，以比较拟议方法的运营和计算性能，并讨论对家庭护理人员配备和能力计划的见解和影响。
We propose stochastic optimization methodologies for a staffing and capacity planning problem arising from home care practice. Specifically, we consider the perspective of a home care agency that must decide the number of caregivers to hire (staffing) and the allocation of hired caregivers to different types of services (capacity planning) in each day within a specified planning horizon. The objective is to minimize the total cost associated with staffing (i.e., employment), capacity allocation, over-staffing, and under-staffing. We propose two-stage stochastic programming (SP) and distributionally robust optimization (DRO) approaches to model and solve this problem considering two types of decision-makers, namely an everything in advance decision-maker (EA) and a flexible adjustment decision-maker (FA). In the EA models, we determine the staffing and capacity allocation decisions in the first stage before observing the demand. In the FA models, we decide the staffing decisions in the first stage. Then, we determine the capacity allocation decisions based on demand realizations in the second stage. We derive equivalent mixed-integer linear programming (MILP) reformulations of the proposed nonlinear DRO model for the EA decision-maker that can be implemented and efficiently solved using off-the-shelf optimization software. We propose a computationally efficient column-and-constraint generation algorithm with valid inequalities to solve the proposed DRO model for the FA decision-maker. Finally, we conduct extensive numerical experiments comparing the operational and computational performance of the proposed approaches and discuss insights and implications for home care staffing and capacity planning.
