2009高教社杯全国大学生数学建模竞赛题B

1、（请先阅读“全国大学生数学建模竞赛论文格式规范”）B题 眼科病床的合理安排医院就医排队是大家都非常熟悉的现象，它以这样或那样的形式出现在我们面前，例如，患者到门诊就诊、到收费处划价、到药房取药、到注射室打针、等待住院等，往往需要排队等待接受某种服务。我们考虑某医院眼科病床的合理安排的数学建模问题。该医院眼科门诊每天开放，住院部共有病床79张。该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。附录中给出了2008年7月13日至2008年9月11日这段时间里各类病人的情况。白内障手术较简单，而且没有急症。目前该院是每周一、三做白内障手术，此类病人的术前准备时间只需1、2天。做两只眼的病

2、人比做一只眼的要多一些，大约占到60%。如果要做双眼是周一先做一只，周三再做另一只。外伤疾病通常属于急症，病床有空时立即安排住院，住院后第二天便会安排手术。其他眼科疾病比较复杂，有各种不同情况，但大致住院以后2-3天内就可以接受手术，主要是术后的观察时间较长。这类疾病手术时间可根据需要安排，一般不安排在周一、周三。由于急症数量较少，建模时这些眼科疾病可不考虑急症。该医院眼科手术条件比较充分，在考虑病床安排时可不考虑手术条件的限制，但考虑到手术医生的安排问题，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。当前该住院部对全体非急症病人是按照FCFS（First come, Fir

3、st serve）规则安排住院，但等待住院病人队列却越来越长，医院方面希望你们能通过数学建模来帮助解决该住院部的病床合理安排问题，以提高对医院资源的有效利用。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，请你们重新回答问题二，医

4、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。【附录】 2008-07-13到2008-09-11的病人信息序号类型门诊时间入院时间第一次手术时间第二次手术时间出院时间1外伤2008-7-132008-7-142008-7-15/2008-7-192视网膜疾病2008-7-132008-7-252008-7-27/2008-8-83白内障2008-7-132008-7-252008-7-28/200

5、8-7-314视网膜疾病2008-7-132008-7-252008-7-27/2008-8-45青光眼2008-7-132008-7-252008-7-27/2008-8-56视网膜疾病2008-7-132008-7-262008-7-29/2008-8-117白内障(双眼)2008-7-132008-7-262008-7-282008-7-302008-8-28视网膜疾病2008-7-142008-7-262008-7-29/2008-8-69白内障(双眼)2008-7-142008-7-262008-7-282008-7-302008-8-110白内障2008-7-142008-7-26

6、2008-7-28/2008-7-3011视网膜疾病2008-7-142008-7-262008-7-29/2008-8-812白内障(双眼)2008-7-142008-7-262008-7-282008-7-302008-8-213白内障(双眼)2008-7-142008-7-262008-7-282008-7-302008-8-214青光眼2008-7-142008-7-272008-7-29/2008-8-415视网膜疾病2008-7-142008-7-272008-7-29/2008-8-916视网膜疾病2008-7-142008-7-272008-7-29/2008-8-617视网膜

7、疾病2008-7-152008-7-272008-7-29/2008-8-1218白内障2008-7-152008-7-272008-7-28/2008-7-3019青光眼2008-7-152008-7-272008-7-29/2008-8-520白内障(双眼)2008-7-152008-7-272008-7-282008-7-302008-8-221视网膜疾病2008-7-152008-7-272008-7-29/2008-8-922青光眼2008-7-152008-7-272008-7-29/2008-8-623白内障2008-7-152008-7-272008-7-28/2008-7-3

8、024白内障2008-7-152008-7-272008-7-28/2008-7-3025白内障(双眼)2008-7-152008-7-282008-8-42008-8-62008-8-926视网膜疾病2008-7-152008-7-282008-7-31/2008-8-1027青光眼2008-7-162008-7-282008-7-31/2008-8-728白内障2008-7-162008-7-282008-7-30/2008-8-329外伤2008-7-162008-7-172008-7-18/2008-7-2230白内障(双眼)2008-7-162008-7-282008-8-42008

9、-8-62008-8-931视网膜疾病2008-7-162008-7-282008-7-31/2008-8-1032白内障(双眼)2008-7-162008-7-282008-8-42008-8-62008-8-933视网膜疾病2008-7-162008-7-282008-7-31/2008-8-1134视网膜疾病2008-7-172008-7-282008-7-31/2008-8-1035白内障2008-7-172008-7-292008-7-30/2008-8-336视网膜疾病2008-7-172008-7-292008-7-31/2008-8-837视网膜疾病2008-7-172008-

10、7-292008-7-31/2008-8-1038白内障(双眼)2008-7-172008-7-292008-8-42008-8-62008-8-839白内障(双眼)2008-7-172008-7-292008-8-42008-8-62008-8-840外伤2008-7-172008-7-182008-7-19/2008-7-2841青光眼2008-7-172008-7-292008-7-31/2008-8-742白内障(双眼)2008-7-172008-7-292008-8-42008-8-62008-8-943白内障(双眼)2008-7-172008-7-302008-8-42008-8-

11、62008-8-844白内障(双眼)2008-7-172008-7-302008-8-42008-8-62008-8-1045白内障(双眼)2008-7-172008-7-302008-8-42008-8-62008-8-846视网膜疾病2008-7-182008-7-302008-8-1/2008-8-847白内障(双眼)2008-7-182008-7-302008-8-42008-8-62008-8-1048外伤2008-7-182008-7-192008-7-20/2008-7-2649白内障(双眼)2008-7-182008-7-302008-8-42008-8-62008-8-950

12、白内障2008-7-182008-7-302008-8-4/2008-8-651青光眼2008-7-182008-7-302008-8-1/2008-8-852视网膜疾病2008-7-182008-7-302008-8-1/2008-8-1153外伤2008-7-182008-7-192008-7-20/2008-7-2554白内障2008-7-182008-7-312008-8-4/2008-8-755白内障(双眼)2008-7-182008-7-312008-8-42008-8-62008-8-856白内障(双眼)2008-7-182008-7-312008-8-42008-8-62008

13、-8-957视网膜疾病2008-7-182008-7-312008-8-2/2008-8-1358视网膜疾病2008-7-192008-7-312008-8-2/2008-8-1459白内障2008-7-192008-7-312008-8-4/2008-8-860白内障(双眼)2008-7-192008-8-12008-8-42008-8-62008-8-961视网膜疾病2008-7-192008-8-12008-8-3/2008-8-862视网膜疾病2008-7-192008-8-12008-8-3/2008-8-1163青光眼2008-7-192008-8-12008-8-3/2008-8

14、-1164白内障2008-7-192008-8-12008-8-4/2008-8-765外伤2008-7-192008-7-202008-7-21/2008-7-2566白内障2008-7-192008-8-22008-8-4/2008-8-867青光眼2008-7-192008-8-22008-8-5/2008-8-1668视网膜疾病2008-7-202008-8-22008-8-5/2008-8-1369白内障2008-7-202008-8-22008-8-4/2008-8-870白内障(双眼)2008-7-202008-8-22008-8-42008-8-62008-8-971白内障20

15、08-7-202008-8-22008-8-4/2008-8-772白内障2008-7-202008-8-22008-8-4/2008-8-773外伤2008-7-202008-7-212008-7-22/2008-7-2974外伤2008-7-202008-7-212008-7-22/2008-7-2875视网膜疾病2008-7-202008-8-22008-8-5/2008-8-1476视网膜疾病2008-7-202008-8-22008-8-5/2008-8-1677白内障2008-7-212008-8-32008-8-4/2008-8-678外伤2008-7-212008-7-2220

16、08-7-23/2008-7-2979白内障(双眼)2008-7-212008-8-32008-8-42008-8-62008-8-980白内障(双眼)2008-7-212008-8-32008-8-42008-8-62008-8-981外伤2008-7-212008-7-222008-7-23/2008-7-2782白内障2008-7-212008-8-32008-8-4/2008-8-683白内障(双眼)2008-7-212008-8-32008-8-42008-8-62008-8-984白内障(双眼)2008-7-212008-8-32008-8-42008-8-62008-8-985白

17、内障(双眼)2008-7-212008-8-42008-8-112008-8-132008-8-1686外伤2008-7-222008-7-232008-7-24/2008-7-2887青光眼2008-7-222008-8-42008-8-7/2008-8-1688白内障2008-7-222008-8-42008-8-6/2008-8-989白内障2008-7-222008-8-42008-8-6/2008-8-1090白内障2008-7-222008-8-42008-8-6/2008-8-991视网膜疾病2008-7-222008-8-42008-8-7/2008-8-1792青光眼2008

18、-7-232008-8-52008-8-7/2008-8-1693外伤2008-7-232008-7-242008-7-25/2008-8-194白内障2008-7-232008-8-52008-8-6/2008-8-1095白内障2008-7-232008-8-52008-8-6/2008-8-996外伤2008-7-232008-7-242008-7-25/2008-7-3097白内障2008-7-232008-8-52008-8-6/2008-8-998白内障(双眼)2008-7-232008-8-62008-8-112008-8-132008-8-1799视网膜疾病2008-7-232

19、008-8-62008-8-8/2008-8-18100白内障2008-7-232008-8-62008-8-11/2008-8-13101视网膜疾病2008-7-232008-8-62008-8-8/2008-8-20102青光眼2008-7-232008-8-62008-8-8/2008-8-16103视网膜疾病2008-7-232008-8-62008-8-8/2008-8-17104视网膜疾病2008-7-232008-8-62008-8-8/2008-8-19105白内障(双眼)2008-7-232008-8-62008-8-112008-8-132008-8-15106白内障200

20、8-7-232008-8-62008-8-11/2008-8-15107视网膜疾病2008-7-232008-8-72008-8-9/2008-8-23108视网膜疾病2008-7-242008-8-72008-8-9/2008-8-19109视网膜疾病2008-7-242008-8-72008-8-9/2008-8-22110白内障2008-7-242008-8-72008-8-11/2008-8-15111青光眼2008-7-242008-8-72008-8-9/2008-8-17112视网膜疾病2008-7-242008-8-72008-8-9/2008-8-19113白内障2008-7

21、-242008-8-72008-8-11/2008-8-14114视网膜疾病2008-7-242008-8-82008-8-10/2008-8-17115白内障2008-7-252008-8-82008-8-11/2008-8-14116视网膜疾病2008-7-252008-8-82008-8-10/2008-8-22117白内障(双眼)2008-7-252008-8-82008-8-112008-8-132008-8-15118视网膜疾病2008-7-252008-8-82008-8-10/2008-8-20119白内障(双眼)2008-7-252008-8-82008-8-112008-8

22、-132008-8-16120青光眼2008-7-262008-8-82008-8-10/2008-8-18121白内障2008-7-262008-8-82008-8-11/2008-8-14122白内障2008-7-262008-8-82008-8-11/2008-8-14123青光眼2008-7-262008-8-82008-8-10/2008-8-17124外伤2008-7-272008-7-282008-7-29/2008-8-2125青光眼2008-7-272008-8-82008-8-10/2008-8-19126白内障2008-7-272008-8-82008-8-11/2008

23、-8-14127白内障(双眼)2008-7-272008-8-82008-8-112008-8-132008-8-15128白内障2008-7-272008-8-92008-8-11/2008-8-13129视网膜疾病2008-7-272008-8-92008-8-12/2008-8-22130外伤2008-7-272008-7-282008-7-29/2008-8-5131视网膜疾病2008-7-272008-8-92008-8-12/2008-8-23132白内障(双眼)2008-7-272008-8-92008-8-112008-8-132008-8-16133青光眼2008-7-282

24、008-8-92008-8-12/2008-8-20134视网膜疾病2008-7-282008-8-92008-8-12/2008-8-25135外伤2008-7-282008-7-292008-7-30/2008-8-6136青光眼2008-7-282008-8-92008-8-12/2008-8-19137外伤2008-7-282008-7-292008-7-30/2008-8-5138视网膜疾病2008-7-282008-8-92008-8-12/2008-8-25139青光眼2008-7-282008-8-92008-8-12/2008-8-20140视网膜疾病2008-7-28200

25、8-8-92008-8-12/2008-8-24141白内障(双眼)2008-7-282008-8-92008-8-112008-8-132008-8-16142青光眼2008-7-282008-8-92008-8-12/2008-8-19143视网膜疾病2008-7-282008-8-92008-8-12/2008-8-24144视网膜疾病2008-7-282008-8-92008-8-12/2008-8-20145青光眼2008-7-292008-8-92008-8-12/2008-8-22146白内障(双眼)2008-7-292008-8-92008-8-112008-8-132008-

26、8-16147视网膜疾病2008-7-292008-8-92008-8-12/2008-8-24148白内障2008-7-292008-8-92008-8-11/2008-8-14149青光眼2008-7-292008-8-92008-8-12/2008-8-22150白内障2008-7-302008-8-102008-8-11/2008-8-15151视网膜疾病2008-7-302008-8-102008-8-12/2008-8-20152白内障2008-7-302008-8-102008-8-11/2008-8-13153外伤2008-7-302008-7-312008-8-1/2008-

27、8-11154白内障(双眼)2008-7-302008-8-102008-8-112008-8-132008-8-16155外伤2008-7-302008-7-312008-8-1/2008-8-6156外伤2008-7-312008-8-12008-8-2/2008-8-7157青光眼2008-7-312008-8-102008-8-12/2008-8-18158视网膜疾病2008-7-312008-8-102008-8-12/2008-8-24159青光眼2008-7-312008-8-102008-8-12/2008-8-16160青光眼2008-7-312008-8-102008-8-

28、12/2008-8-19161白内障(双眼)2008-7-312008-8-102008-8-112008-8-132008-8-15162视网膜疾病2008-7-312008-8-112008-8-14/2008-8-28163外伤2008-7-312008-8-12008-8-2/2008-8-9164视网膜疾病2008-7-312008-8-112008-8-14/2008-8-25165青光眼2008-7-312008-8-112008-8-14/2008-8-23166视网膜疾病2008-7-312008-8-112008-8-14/2008-8-27167外伤2008-8-1200

29、8-8-22008-8-3/2008-8-10168视网膜疾病2008-8-12008-8-122008-8-14/2008-8-29169白内障(双眼)2008-8-12008-8-122008-8-182008-8-202008-8-22170青光眼2008-8-12008-8-132008-8-15/2008-8-23171白内障(双眼)2008-8-12008-8-132008-8-182008-8-202008-8-23172白内障(双眼)2008-8-12008-8-132008-8-182008-8-202008-8-24173视网膜疾病2008-8-12008-8-132008

30、-8-15/2008-8-23174视网膜疾病2008-8-12008-8-132008-8-15/2008-8-22175外伤2008-8-12008-8-22008-8-3/2008-8-9176外伤2008-8-12008-8-22008-8-3/2008-8-8177白内障(双眼)2008-8-12008-8-132008-8-182008-8-202008-8-23178视网膜疾病2008-8-22008-8-142008-8-16/2008-8-29179视网膜疾病2008-8-22008-8-142008-8-16/2008-8-25180视网膜疾病2008-8-22008-8-

31、142008-8-16/2008-8-27181白内障2008-8-22008-8-142008-8-18/2008-8-22182视网膜疾病2008-8-22008-8-142008-8-16/2008-8-28183白内障(双眼)2008-8-22008-8-142008-8-182008-8-202008-8-23184青光眼2008-8-32008-8-142008-8-16/2008-8-23185白内障(双眼)2008-8-32008-8-142008-8-182008-8-202008-8-23186青光眼2008-8-32008-8-142008-8-16/2008-8-241

32、87视网膜疾病2008-8-32008-8-152008-8-17/2008-8-26188白内障(双眼)2008-8-32008-8-152008-8-182008-8-202008-8-23189白内障2008-8-32008-8-152008-8-18/2008-8-21190白内障(双眼)2008-8-32008-8-152008-8-182008-8-202008-8-23191视网膜疾病2008-8-32008-8-152008-8-17/2008-8-26192视网膜疾病2008-8-32008-8-152008-8-17/2008-8-29193视网膜疾病2008-8-3200

33、8-8-152008-8-17/2008-8-30194视网膜疾病2008-8-32008-8-162008-8-19/2008-8-28195白内障(双眼)2008-8-42008-8-162008-8-182008-8-202008-8-24196视网膜疾病2008-8-42008-8-162008-8-19/2008-8-27197白内障(双眼)2008-8-42008-8-162008-8-182008-8-202008-8-23198外伤2008-8-42008-8-52008-8-6/2008-8-13199白内障(双眼)2008-8-42008-8-162008-8-182008

34、-8-202008-8-23200白内障2008-8-42008-8-162008-8-18/2008-8-21201视网膜疾病2008-8-52008-8-162008-8-19/2008-8-29202视网膜疾病2008-8-52008-8-162008-8-19/2008-8-24203白内障2008-8-52008-8-162008-8-18/2008-8-21204白内障2008-8-52008-8-162008-8-18/2008-8-20205青光眼2008-8-52008-8-162008-8-19/2008-8-25206视网膜疾病2008-8-62008-8-162008-

35、8-19/2008-9-1207白内障2008-8-62008-8-162008-8-18/2008-8-21208白内障(双眼)2008-8-62008-8-172008-8-182008-8-202008-8-23209白内障2008-8-62008-8-172008-8-18/2008-8-20210视网膜疾病2008-8-62008-8-172008-8-19/2008-8-29211白内障2008-8-62008-8-172008-8-18/2008-8-20212白内障(双眼)2008-8-62008-8-172008-8-182008-8-202008-8-24213白内障(双眼

36、)2008-8-62008-8-182008-8-252008-8-272008-8-30214外伤2008-8-62008-8-72008-8-8/2008-8-15215视网膜疾病2008-8-62008-8-192008-8-21/2008-9-1216白内障2008-8-62008-8-192008-8-20/2008-8-23217白内障(双眼)2008-8-62008-8-192008-8-252008-8-272008-8-30218白内障(双眼)2008-8-62008-8-192008-8-252008-8-272008-8-30219视网膜疾病2008-8-62008-8-

37、192008-8-21/2008-9-1220视网膜疾病2008-8-72008-8-202008-8-22/2008-9-2221视网膜疾病2008-8-72008-8-202008-8-22/2008-9-5222白内障2008-8-72008-8-202008-8-25/2008-8-27223白内障2008-8-72008-8-202008-8-25/2008-8-28224视网膜疾病2008-8-72008-8-202008-8-22/2008-8-29225视网膜疾病2008-8-72008-8-202008-8-22/2008-8-31226白内障(双眼)2008-8-72008

38、-8-202008-8-252008-8-272008-8-30227白内障(双眼)2008-8-72008-8-202008-8-252008-8-272008-8-31228白内障2008-8-72008-8-202008-8-25/2008-8-27229白内障(双眼)2008-8-72008-8-202008-8-252008-8-272008-8-30230外伤2008-8-72008-8-82008-8-9/2008-8-16231白内障2008-8-72008-8-212008-8-25/2008-8-28232白内障(双眼)2008-8-72008-8-212008-8-252

39、008-8-272008-8-30233外伤2008-8-72008-8-82008-8-9/2008-8-12234青光眼2008-8-72008-8-222008-8-24/2008-9-5235视网膜疾病2008-8-82008-8-222008-8-24/2008-9-2236外伤2008-8-82008-8-92008-8-10/2008-8-14237视网膜疾病2008-8-82008-8-222008-8-24/2008-9-7238视网膜疾病2008-8-82008-8-222008-8-24/2008-9-6239白内障(双眼)2008-8-82008-8-222008-8-

40、252008-8-272008-8-30240视网膜疾病2008-8-82008-8-222008-8-24/2008-8-30241视网膜疾病2008-8-82008-8-222008-8-24/2008-8-29242青光眼2008-8-82008-8-232008-8-26/2008-9-3243视网膜疾病2008-8-92008-8-232008-8-26/2008-9-6244白内障2008-8-92008-8-232008-8-25/2008-8-28245视网膜疾病2008-8-92008-8-232008-8-26/2008-9-4246白内障(双眼)2008-8-92008-

41、8-232008-8-252008-8-272008-8-29247白内障2008-8-102008-8-232008-8-25/2008-8-27248白内障(双眼)2008-8-102008-8-232008-8-252008-8-272008-8-30249青光眼2008-8-102008-8-232008-8-26/2008-9-3250外伤2008-8-102008-8-112008-8-12/2008-8-20251外伤2008-8-102008-8-112008-8-12/2008-8-18252白内障(双眼)2008-8-102008-8-232008-8-252008-8-2

42、72008-8-30253白内障2008-8-102008-8-232008-8-25/2008-8-28254视网膜疾病2008-8-102008-8-232008-8-26/2008-9-5255视网膜疾病2008-8-112008-8-232008-8-26/2008-9-10256青光眼2008-8-112008-8-232008-8-26/2008-9-4257视网膜疾病2008-8-112008-8-232008-8-26/2008-9-1258视网膜疾病2008-8-112008-8-232008-8-26/2008-9-10259白内障(双眼)2008-8-112008-8-2

43、32008-8-252008-8-272008-8-29260视网膜疾病2008-8-112008-8-232008-8-26/2008-9-7261白内障2008-8-122008-8-242008-8-25/2008-8-28262白内障(双眼)2008-8-122008-8-242008-8-252008-8-272008-8-30263白内障(双眼)2008-8-122008-8-242008-8-252008-8-272008-8-30264白内障2008-8-122008-8-242008-8-25/2008-8-29265白内障(双眼)2008-8-122008-8-242008

44、-8-252008-8-272008-8-30266白内障2008-8-122008-8-242008-8-25/2008-8-28267视网膜疾病2008-8-122008-8-242008-8-26/2008-9-10268视网膜疾病2008-8-132008-8-242008-8-26/2008-9-5269白内障2008-8-132008-8-242008-8-25/2008-8-28270视网膜疾病2008-8-132008-8-242008-8-26/2008-9-5271视网膜疾病2008-8-132008-8-252008-8-28/2008-9-5272视网膜疾病2008-8

45、-132008-8-252008-8-28/2008-9-5273白内障(双眼)2008-8-132008-8-252008-9-12008-9-32008-9-7274青光眼2008-8-132008-8-252008-8-28/2008-9-4275白内障(双眼)2008-8-132008-8-252008-9-12008-9-32008-9-6276白内障(双眼)2008-8-132008-8-252008-9-12008-9-32008-9-7277白内障(双眼)2008-8-132008-8-262008-9-12008-9-32008-9-6278白内障(双眼)2008-8-132

46、008-8-262008-9-12008-9-32008-9-6279视网膜疾病2008-8-132008-8-272008-8-29/2008-9-5280视网膜疾病2008-8-132008-8-272008-8-29/2008-9-6281外伤2008-8-142008-8-152008-8-16/2008-8-24282青光眼2008-8-142008-8-272008-8-29/2008-9-7283视网膜疾病2008-8-142008-8-272008-8-29/2008-9-6284白内障(双眼)2008-8-142008-8-272008-9-12008-9-32008-9-6285白内障(双眼)2008-8-142008-8-272008-9-12008-9-32008-9-6286白内障(双眼)2008-8-142008-8-282008-9-12008-9-32008-9-7287视网膜疾病2008-8-1520