考虑下游ICU病床容量约束的鲁棒手术计划调度

手术计划调度是医疗资源配置的重要组成部分,也是复杂的组合优化问题.由于在手术计划调度过程中,存在手术时间、术后重症监护病房(intensive care unit,ICU)内住院时间、急诊病人的到达、病人取消等不确定因素.本文考虑手术后下游的ICU中病床资源的容量约束,基于不确定的手术时间和术后ICU住院时间,借助ellipsoid和box不确定集合刻画不确定性,提出一个手术计划调度两阶段鲁棒优化模型,得出易求解的鲁棒等价问题,并提出列生成启发式算法.算例结果表明,较之住院时间的不确定性,手术时间的不确定性对总成本和手术块的加班时间影响显著,而住院时间的不确定性对ICU内短缺病床数量有显著影响.管理者可选择恰当的手术时间和住院时间的不确定水平参数组合(Ω,Γ),综合权衡手术块的加班时间和ICU内病床的短缺数量,尽可能地最大化手术室、ICU病床资源的利用率.

Robust surgery planning and scheduling with downstream bed capacity constraint in ICU

As a critical part of the allocation of healthcare resources, planning and scheduling surgeries is a complicated combinatorial optimization problem because of the coupled effect of multiple sources of uncertainty, such as surgery duration, length-of-stay in ICU and so on. In this paper, we incorporate the downstream bed capacity in ICU, employ ellipsoid and box uncertainty set to capture the uncertainties of surgery duration and length-of-stay in ICU. Then, we formulate a two-stage robust model to address these uncertainties, derive the tractable robust counterpart and propose a column generation algorithm. Numerical results show that, compared with uncertainty of length-of-stay, surgery duration uncertainty has a significant effect on the total cost and the overtime of blocks, whereas uncertainty of length-of-stay has a dramatic impact on the amount of short beds in ICU. Hospital managers should choose the proper combination of uncertain level parameters, and make a balanced trade-off between overtime of block and the shortage of beds in ICU, so as to maximize the utilization of healthcare resources.