基于线性规划的护士排班优化问题

基于线性规划的护士排班优化问题

姓名1： 学号： 专业： 姓名1： 学号： 专业：

日期：2011年7月15日

基于线性规划的护士排班优化问题

摘要

本文研究的是关于医院护士排班最优问题，本文的主要思想是根据约束条件建立相关的线性规划模型，利用Lingo求解，分别计算出每天，每星期的最少护士数，并给出具体的排班方案。

问题一：计算每天该科所需的最少护士数。针对这一问，从各班次护士需求量考虑，依据每个护士每天至多工作8个小时，即上两个班次且两个班次不连上这一假定条件，假设每个时间段开始登记上班的人数为xi，建立规划模型，进而运用Lingo软件进行求解，从而求出每天该科所需最少护士数为145人。

问题二，以一个星期为周期，计算该科最少需签约多少护士。针对第二问，依据题目给出的约束条件：时间段02:00-06:00（大夜班）每个星期最多只排一次，且第二天必须休息。经过本文规划约束可以得出每个星期该科至少需签约210名护士。

问题三，以一个星期为周期，试给出具体的排班方案。依据问题二得出的结果，综合考虑题目中各约束条件，将一个星期（七天）六个班次设为42个班次，

?1第j号护士上第i班次引进0,1变量，即xij??，建立线性规划模型，给出具

i班次?0第j号护士不上第体的排班方案，见附录1，由于有的排班人数大于该次排班的最少要求人数所以

该方案不唯一。

问题四，计算最少需要多少护师职称以上的护士。运用问题三的方法，增加约束条件，即每班次上 班的护士中护师以上（包括护师）职称的所占比例不低

?1第i班次有护师级别以上于40%。同样引进0,1变量，即xi??，以需要最少

?0第i班次无护师级别以上的护师职称以上的护士为目标函数，同样建立线性规划模型。得出需要最少的护师（包括护师）职称以上的护士为：84人。

关键词：护士排班 线性规划 0-1变量 Lingo

目录

1、问题重述·················································································································· 4 2、问题分析·················································································································· 5 3、模型假设·················································································································· 5 4、符号说明·················································································································· 5 5、模型建立与求解······································································································ 6

5.1问题一求解······································································································ 6 5.2问题二求解······································································································ 6 5.3问题三求解······································································································ 7 5.4问题四求解······································································································ 9 6、模型评价与改进···································································································· 10 参考文献······················································································································ 10 附录······························································································································ 11

附录一 ：············································································································· 11 附录二：··············································································································· 12

1、问题重述

1.1基本条件

某医院某科室的一个工作日分为6个4小时时间长的时间段，每个时间段所需要的护士人员数各不相同。每日每个时间段的人员需求量如下所示：

班次 该班时间段（24小时） 该班所需最少护士数 1 2 3 4 5 6 6:00-10:00 10:00-14:00 14:00-18:00 18:00-22:00 22:00-02:00 02:00-06:00 60 70 60 50 20 30 每班的护士在值班开始时向病房报道，排班需满足：

(1) 每天至多工作8个小时，即上两个班次，两个班次不连上； (2) 第一天排班在时间段22:00-02:00（小夜班）的护士，第二天在时间段

06:00-10:00不排班； (3) 时间段02:00-06:00（大夜班）每个星期最多只排一次，且第二天必须休

息； (4) 每个星期每位护士工作40小时； 1.2需解决的问题

问题1：每天该科所需的最少护士数？

问题2：以一个星期为周期，该科最少需签约多少护士？

问题3：以一个星期为周期，试给出具体的排班方案，该方案是否唯一？ 问题4：根据医院要求，每班次上班的护士中护师以上（包括护师）职称的

所占比例不低于40%，问在护士数最少的条件下（第二问决定的最少护士数），最少需要多少护师职称以上（包括护师职称）的护士才能满足院方对职称的要求。 注：护士职称评定共分五级别，分别是：护士、护师、主管护师、副主任护师、主任护师。