基于机会约束的手术计划随机模型与算法

本文研究多服务台手术计划调度问题,考虑手术时间的不确定性,提出手术室加班时间的机会约束,以一定的概率保证病人的手术时间不超过手术室的开放时间,建立随机优化机会约束手术计划调度模型,确定手术室的开放和分配决策.基于手术时间离散的概率情景,引入0-1变量转化机会约束,得到了0-1整数线性规划的等价模型.为了提高模型的求解效率,提出两类有效不等式,并设计最长路径算法分离第二类有效不等式,利用分支切割方法进行模型求解.算例分析,基于北京某医院的实际数据,验证算法的有效性,确定最优的手术计划调度方案,有效地优化配置手术室资源.

Stochastic chance-constrained surgery planning model and algorithm

To address the uncertainty of surgery duration, this paper investigates surgery planning scheduling problem with multiple servers, which proposes chance constraints of operating rooms overtime to guarantee the surgery durations of patients is no more than the time limit of operating rooms with a high probability. A stochastic chance-constrained program is proposed to determine which operating rooms to operate, and surgeries to operating rooms allocation. Based on a finite support set of the surgery duration, this paper introduces 0-1 variables to formulate the chance constraints, and derives 0-1 integer linear program counterpart. To improve the efficiency of the model, this paper presents two classes of valid inequalities and uses the longest path algorithm to separate the second class of valid inequalities, which are implemented in a branch-and-cut framework. Computational experiments based on real-life data from hospital in Beijing are conducted to verify the algorithm performance and determine the optimal planning scheme, so as to take full utilization of healthcare resources, i.e. operating rooms.