《《数学建模论文-动态规划模型下的眼科病床的优化设计》》由会员分享，可在线阅读，更多相关《《数学建模论文-动态规划模型下的眼科病床的优化设计》（16页珍藏版）》请在金锄头文库上搜索。
1、动态规划模型下的眼科病床的优化设计摘要：目前，群众看病难已成为最突出的社会问题之一。排队现象是由于病人对医院服务的需求远远大于医院所提供的服务。这说明医院的管理缺乏合理性、科学性和高效性。本文运用动态规划的方法，通过建立数学模型，借助Matlab软件计，制定出相对合理的病床安排方案。确定的评价指标体系为，一定时间段内安排入院总人数越多越好以及等待入院病人的排队长度越短越好。依据这个评价体系，我们建立了动态规划模型：模型经过调整优化后的眼科病人入院人数比原先平均每天增加2人次，最后一定时间段内增加了59人次，而且系统队伍不断缩短，病人等待时间也逐渐减少。依据门诊各类病人到达频率及住院部每周出院人
2、数，对患者提出最佳就诊日期的建议。病人按照此建议前来就诊，一般情况下一周之内即可入院(参见附录1)。医院根据住院的所有情况还可以推测就诊病人的大致入院时间。在周六周日不安排手术的情况下，根据白内障双眼的治疗方法，最终确定周二、周四进行白内障手术。最后，根据病床利用率和入院人数成正比拟得分配函数：由此得出各类病人占用病床的比例大致固定的方案为白内障、白内障双眼、青光眼、视网膜疾病和外伤的床位数为：7、14、12、37、9。关键词：动态规划、排队系统、入院人数、系统长度、等待时间 一、 问题的重述任何排队现象都有可能导致严重的无效率。而医院排队现象更是司空见惯，看病难已成为当今中国社会的一个重大问
3、题。排队现象是由于供给和需求的不平衡造成的。要改善这一情况，要么增加医疗设备和医务人员，要么减少病人。可是病源是无限的，同时增加设备会明显增加医院成本，因此医院希望能通过建立数学模型，提出关于合理安排病床的方案，以提高对医院资源的有效利用。本医院眼科手术主要分四大类：白内障、视网膜疾病、青光眼和外伤。现住院部共有79张病床，门诊部每天都上班。白内障手术比较简单，而且没有急症。一般安排在周一和周三做手术。手术前需准备1-2天。据统计，白内障双眼的病例要比单眼的多，大约占60%。为有效利用医疗资源，白内障双眼周一先做一只眼，周三再做另一只。外伤疾病通常属于急症，只要有空床位立即安排入院，住院后第二
4、天便会安排手术。其他眼科疾病比较复杂，情况各异，但大致住院以后2-3天内就可以接受手术，主要是术后的观察期较长。由于急症数量较少，建模时这些眼科疾病可不考虑急症。 该医院眼科住院部原则上按照FCFS（First come, First serve）规则安排住院，由于医院条件比较充分，因此只需考虑病床的空缺和手术医生的安排。通常情况下白内障手术与其他眼科手术（急症除外）不安排在同一天做。问题一：试分析确定合理的评价指标体系，用以评价该问题的病床安排模型的优劣。问题二：试就该住院部当前的情况，建立合理的病床安排模型，以根据已知的第二天拟出院病人数来确定第二天应该安排哪些病人住院。并对你们的模型利用
5、问题一中的指标体系作出评价。问题三：作为病人，自然希望尽早知道自己大约何时能住院。能否根据当时住院病人及等待住院病人的统计情况，在病人门诊时即告知其大致入住时间区间。问题四：若该住院部周六、周日不安排手术，请重新回答问题二，医院的手术时间安排是否应作出相应调整?问题五：有人从便于管理的角度提出建议，在一般情形下，医院病床安排可采取使各类病人占用病床的比例大致固定的方案，试就此方案，建立使得所有病人在系统内的平均逗留时间（含等待入院及住院时间）最短的病床比例分配模型。二、 符号说明Opinions and suggestions on the partys mass line education
6、al practiceAccording to the central and provincial, municipal unified deployment, according to municipal Party committee about carrying out the partys mass line educational practice activity in the citys implementation opinions, the spirit of the partys mass line educational practice activities from
7、 20* in January to 99 months, carried out at all levels of departments and directly affiliated institutions and grass-roots party organizations. According to my actual County, the county to carry out the education practice put forward the following implementation opinions.First, the overall requirem
8、entsCounty county education practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implement the spirit of general secretary Xi book series of important speech, earnestly implement the Central Committee
9、really, opinions and advice , party implementing the guiding ideology of opinions to determine the objectives and requirements, step method, in accordance with the look in the mirror, dress up, wash bath, cure treatment, the general requirements of for the people pragmatic honest people as the theme
10、, in carrying forward the spirit of Zhuanglang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to further implement the central eight regulations and The opposition party and government austerit
11、y waste regulations , double section provincial regulations, municipal provisions of the twelve plan and the implementation measures for on improving the work style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose formalism, bureaucracy,
12、 hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to further change the style of the wind, the masses to close, honest and pra
13、gmatic people honest image to further establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force of the county and the ecological culture of the county and county construction.In educational practice activit
14、ies of the unit is mainly: the county and below county departments under the organs, enterprises and institutions directly under the township, street, and community, village, non-public economic organizations, social organizations and other grass-roots organizations. Agencies and branches, each sing
15、le unit, follow the rules on internal institutions. Educational practice with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses of law supervision departments and window units, service industry,
16、educational practice, pay attention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the partys education.Always speak seriously as a basic attitude, adhere to positive education, t
