眼科病床合理安排

1、2009高教社杯全国大学生数学建模竞赛题目（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

2、手术，此类病人的术前准备时间只需1、2天。做两只眼的病人 比做一只眼的要多一些，大约占至ij 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

3、。当前该住院部对全 体非急症病人是按照fcfs （first come, first 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， 以根据己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

4、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12345678910第二次门诊时第一次手出院时类型间入院时间术时间手术时间间2008-7-2008-7-12008-7-12008-7-外伤1345/19视网膜疾2008-7-2008

5、-7-22008-7-2/2008-8-病135782008-7-2008-7-22008-7-22008-7-白内障1358/31视网膜疾2008-7-2008-7-22008-7-2/2008-8-病135742008-7-2008-7-22008-7-22008-8-青光眼1357/5视网膜疾2008-7-2008-7-22008-7-2/2008-8-病136911白内障（双2008-7-2008-7-22008-7-22008-7-2008-8-眼）1368302视网膜疾2008-7-2008-7-22008-7-2/2008-8-病14696白内障（双2008-7-2008-7-2

6、2008-7-22008-7-2008-8-眼）1468301白内障2008-7-2008-7-22008-7-2/2008-7-1112131415161718192021146830视网膜疾病2008-7-142008-7-262008-7-29/2008-8-8白内障（双2008-7-2008-7-22008-7-22008-7-2008-8-眼）1468302白内障（双2008-7-2008-7-22008-7-22008-7-2008-8-眼）1468302青光眼2008-7-142008-7-272008-7-29/2008-8-4视网膜疾病2008-7-142008-7-2720

7、08-7-29/2008-8-9视网膜疾病2008-7-142008-7-272008-7-29/2008-8-6视网膜疾病2008-7-152008-7-272008-7-29/2008-8-12白内障2008-7-152008-7-272008-7-28/2008-7-30青光眼2008-7-152008-7-272008-7-29/2008-8-5白内障（双2008-7-2008-7-22008-7-22008-7-2008-8-眼）1578302视网膜疾2008-7-2008-7-22008-7-2/2008-8-病157992008-7-2008-7-22008-7-22008-8-

8、青光眼1579/62008-7-2008-7-22008-7-22008-7-白内障1578/302008-7-2008-7-22008-7-22008-7-白内障1578/30白内障（双2008-7-2008-7-22008-8-42008-8-2008-8-眼）15869视网膜疾2008-7-2008-7-22008-7-3/2008-8-病1581102008-7-2008-7-22008-7-32008-8-青光眼1681/72008-7-2008-7-22008-7-32008-8-白内障1680/32008-7-2008-7-12008-7-12008-7-外伤1678/22白内障

9、（双2008-7-2008-7-22008-8-42008-8-2008-8-眼）16869视网膜疾2008-7-2008-7-22008-7-3/2008-8-病1681102223242526272829303132白内障（双 2008-7- 2008-7-2 2008-8-4 2008-8- 2008-8-眼）16869视网膜疾2008-7-2008-7-22008-7-3/2008-8-病168111视网膜疾2008-7-2008-7-22008-7-3/2008-8-病1781102008-7-2008-7-22008-7-32008-8-白内障1790/3视网膜疾2008-7-20

10、08-7-22008-7-3/2008-8-病17918视网膜疾2008-7-2008-7-22008-7-3/2008-8-病179110白内障（双2008-7-2008-7-22008-8-42008-8-2008-8-眼）17968白内障（双2008-7-2008-7-22008-8-42008-8-2008-8-眼）179682008-7-2008-7-12008-7-12008-7-外伤1789/282008-7-2008-7-22008-7-32008-8-青光眼1791/7白内障（双2008-7-2008-7-22008-8-42008-8-2008-8-眼）1796933343

11、53637383940414243白内障（双 2008-7- 2008-7-3 2008-8-4 2008-8- 2008-8-眼）17068白内障（双2008-7-2008-7-32008-8-2008-8-442008-8-4眼）170610白内障（双2008-7-2008-7-32008-8-2008-8-452008-8-4眼）17068视网膜疾2008-7-2008-7-32008-8-462008-8-1/病1808白内障（双2008-7-2008-7-32008-8-2008-8-472008-8-4眼）1806102008-7-2008-7-12008-7-22008-7-48

12、外伤/189026白内障（双2008-7-2008-7-32008-8-2008-8-492008-8-4眼）180692008-7-2008-7-32008-8-50 白内障2008-8-4/18062008-7-2008-7-32008-8-51 青光眼2008-8-1/1808视网膜疾2008-7-2008-7-32008-8-522008-8-1/病180112008-7-2008-7-12008-7-22008-7-53外伤/18902554 白内障2008-7-2008-7-32008-8-4/2008-8-55565758596061626364651817白内障（双2008-7

13、-2008-7-32008-8-2008-8-2008-8-4眼）18168白内障（双2008-7-2008-7-32008-8-2008-8-2008-8-4眼）18169视网膜疾2008-7-2008-7-32008-8-2008-8-2/病18113视网膜疾2008-7-2008-7-32008-8-2008-8-2/病191142008-7-2008-7-32008-8-白内障2008-8-4/1918白内障（双2008-7-2008-8-2008-8-2008-8-12008-8-4眼）1969视网膜疾2008-7-2008-8-2008-8-12008-8-3/病198视网膜疾20

14、08-7-2008-8-2008-8-12008-8-3/病19112008-7-2008-8-青光眼2008-8-12008-8-3/19112008-7-2008-8-白内障2008-8-12008-8-4/197外伤2008-7-2008-7-22008-7-2/2008-7-66676869707172737475761901252008-7-2008-8-白内障2008-8-22008-8-4/1982008-7-2008-8-青光眼2008-8-22008-8-5/1916视网膜疾2008-7-2008-8-2008-8-22008-8-5/病20132008-7-2008-8-白

15、内障2008-8-22008-8-4/208白内障（双2008-7-2008-8-2008-8-2008-8-22008-8-4眼）20692008-7-2008-8-白内障2008-8-22008-8-4/2072008-7-2008-8-白内障2008-8-22008-8-4/2072008-7-2008-7-22008-7-22008-7-外伤/2012292008-7-2008-7-22008-7-22008-7-外伤/201228视网膜疾2008-7-2008-8-2008-8-22008-8-5/病2014视网膜疾2008-7-2008-8-22008-8-5/2008-8-200

16、8-7-2008-8-77白内障2008-8-32008-8-4/2162008-7-2008-7-22008-7-22008-7-78外伤/212329白内障（双2008-7-2008-8-2008-8-792008-8-32008-8-4眼）2169白内障（双2008-7-2008-8-2008-8-802008-8-32008-8-4眼）21692008-7-2008-7-22008-7-22008-7-81外伤/2123272008-7-2008-8-82白内障2008-8-32008-8-4/216白内障（双2008-7-2008-8-2008-8-832008-8-32008-8-

17、4眼）2169白内障（双2008-7-2008-8-2008-8-842008-8-32008-8-4眼）2169白内障（双2008-7-2008-8-12008-8-2008-8-852008-8-4眼）21113162008-7-2008-7-22008-7-22008-7-86外伤/22342887青光眼2008-7-2008-8-42008-8-7/2008-8-病201622162008-7-2008-8-88白内障2008-8-42008-8-6/2292008-7-2008-8-89白内障2008-8-42008-8-6/22102008-7-2008-8-90白内障2008-8

18、-42008-8-6/229视网膜疾2008-7-2008-8-912008-8-42008-8-7/病22172008-7-2008-8-92青光眼2008-8-52008-8-7/23162008-7-2008-7-22008-7-22008-8-93外伤/234512008-7-2008-8-94白内障2008-8-52008-8-6/23102008-7-2008-8-95白内障2008-8-52008-8-6/2392008-7-2008-7-22008-7-22008-7-96外伤/2345302008-7-2008-8-97白内障2008-8-52008-8-6/23998白内障

19、（双2008-7-2008-8-62008-8-12008-8-2008-8-99100101102103104105106107108109眼）2311317视网膜疾2008-7-2008-8-2008-8-62008-8-8/病23182008-7-2008-8-12008-8-白内障2008-8-6/23113视网膜疾2008-7-2008-8-2008-8-62008-8-8/病23202008-7-2008-8-青光眼2008-8-62008-8-8/2316视网膜疾2008-7-2008-8-2008-8-62008-8-8/病2317视网膜疾2008-7-2008-8-2008-

20、8-62008-8-8/病2319白内障（双2008-7-2008-8-12008-8-2008-8-2008-8-6眼）23113152008-7-2008-8-12008-8-白内障2008-8-6/23115视网膜疾2008-7-2008-8-2008-8-72008-8-9/病2323视网膜疾2008-7-2008-8-2008-8-72008-8-9/病2419视网膜疾2008-7-2008-8-72008-8-9/2008-8-病24222008-7-2008-8-12008-8-110白内障2008-8-7/241152008-7-2008-8-111青光眼2008-8-7200

21、8-8-9/2417视网膜疾2008-7-2008-8-1122008-8-72008-8-9/病24192008-7-2008-8-12008-8-113白内障2008-8-7/24114视网膜疾2008-7-2008-8-12008-8-1142008-8-8/病240172008-7-2008-8-12008-8-115白内障2008-8-8/25114视网膜疾2008-7-2008-8-12008-8-1162008-8-8/病25022白内障（双2008-7-2008-8-12008-8-2008-8-1172008-8-8眼）2511315视网膜疾2008-7-2008-8-120

22、08-8-1182008-8-8/病25020白内障（双2008-7-2008-8-12008-8-2008-8-1192008-8-8眼）2511316120青光眼2008-7-2008-8-82008-8-1/2008-8-121122123124125126127128129130131260182008-7-2008-8-12008-8-白内障2008-8-8/261142008-7-2008-8-12008-8-白内障2008-8-8/261142008-7-2008-8-12008-8-青光眼2008-8-8/260172008-7- 2008-7-22008-7-22008-8-

23、外伤/278922008-7-2008-8-12008-8-青光眼2008-8-8/270192008-7-2008-8-12008-8-白内障2008-8-8/27114白内障（双2008-7-2008-8-12008-8- 2008-8-2008-8-8眼）27113152008-7-2008-8-12008-8-白内障2008-8-9/27113视网膜疾2008-7-2008-8-12008-8-2008-8-9/病272222008-7- 2008-7-22008-7-22008-8-外伤/27895视网膜疾2008-7- 2008-8-92008-8-1/2008-8-1321331

24、34135136137138139140141142病27223白内障（双2008-7-2008-8-12008-8-2008-8-2008-8-9眼）27113162008-7-2008-8-12008-8-青光眼2008-8-9/28220视网膜疾2008-7-2008-8-12008-8-2008-8-9/病282252008-7-2008-7-22008-7-32008-8-外伤/289062008-7-2008-8-12008-8-青光眼2008-8-9/282192008-7-2008-7-22008-7-32008-8-外伤/28905视网膜疾2008-7-2008-8-1200

25、8-8-2008-8-9/病282252008-7-2008-8-12008-8-青光眼2008-8-9/28220视网膜疾2008-7-2008-8-12008-8-2008-8-9/病28224白内障（双2008-7-2008-8-12008-8-2008-8-2008-8-9眼）2811316青光眼2008-7-2008-8-92008-8-1/2008-8-14314414514614714814915015115215328219视网膜疾2008-7-2008-8-12008-8-2008-8-9/病28224视网膜疾2008-7-2008-8-12008-8-2008-8-9/病2

26、82202008-7-2008-8-12008-8-青光眼2008-8-9/29222白内障（双2008-7-2008-8-12008-8-2008-8-2008-8-9眼）2911316视网膜疾2008-7-2008-8-12008-8-2008-8-9/病292242008-7-2008-8-12008-8-白内障2008-8-9/291142008-7-2008-8-12008-8-青光眼2008-8-9/292222008-7-2008-8-12008-8-12008-8-白内障/300115视网膜疾2008-7-2008-8-12008-8-12008-8-/病3002202008-

27、7-2008-8-12008-8-12008-8-白内障/300113外伤2008-7-2008-7-32008-8-1/2008-8-15415515615715815916016116216316430111白内障（双2008-7-2008-8-12008-8-12008-8-2008-8-眼）30011316外伤2008-7-302008-7-312008-8-1/2008-8-6外伤2008-7-312008-8-12008-8-2/2008-8-7青光眼2008-7-312008-8-102008-8-12/2008-8-18视网膜疾病2008-7-312008-8-102008-8

28、-12/2008-8-24青光眼2008-7-312008-8-102008-8-12/2008-8-16青光眼2008-7-312008-8-102008-8-12/2008-8-19白内障（双2008-7-2008-8-12008-8-12008-8-2008-8-眼）31011315视网膜疾病2008-7-312008-8-112008-8-14/2008-8-28外伤2008-7-312008-8-12008-8-2/2008-8-9视网膜疾2008-7-2008-8-12008-8-1/2008-8-病3114252008-7-2008-8-12008-8-12008-8-165 青

29、光眼/311423视网膜疾2008-7-2008-8-12008-8-12008-8-166/病3114272008-8-2008-8-167 外伤2008-8-22008-8-3/110视网膜疾2008-8-2008-8-12008-8-12008-8-168/病12429白内障（双2008-8-2008-8-12008-8-12008-8- 2008-8-169眼）12820222008-8-2008-8-12008-8-12008-8-170 青光眼/13523白内障（双2008-8-2008-8-12008-8-12008-8- 2008-8-171眼）1382023白内障（双2008

30、-8-2008-8-12008-8-12008-8- 2008-8-172眼）1382024视网膜疾2008-8-2008-8-12008-8-12008-8-173/病13523视网膜疾2008-8-2008-8-12008-8-12008-8-174/病13522175 外伤2008-8-2008-8-22008-8-3/2008-8-19176外伤2008-8-12008-8-22008-8-3/2008-8-8白内障（双2008-8-2008-8-12008-8-12008-8-2008-8-177眼）1382023视网膜疾2008-8-2008-8-12008-8-12008-8-1

31、78/病24629视网膜疾2008-8-2008-8-12008-8-12008-8-179/病24625视网膜疾2008-8-2008-8-12008-8-12008-8-180/病246272008-8-2008-8-12008-8-12008-8-181白内障/24822视网膜疾2008-8-2008-8-12008-8-12008-8-182/病24628白内障（双2008-8-2008-8-12008-8-12008-8-2008-8-183眼）24820232008-8-2008-8-12008-8-12008-8-184青光眼/34623白内障（双2008-8-2008-8-12

32、008-8-12008-8-2008-8-185眼）3482023186青光眼2008-8-2008-8-12008-8-1/2008-8-34624视网膜疾2008-8-2008-8-12008-8-1/2008-8-病35726白内障（双2008-8-2008-8-12008-8-12008-8-2008-8-眼）35820232008-8-2008-8-12008-8-12008-8-白内障358/21白内障（双2008-8-2008-8-12008-8-12008-8-2008-8-眼）3582023视网膜疾2008-8-2008-8-12008-8-1/2008-8-病35726视网

33、膜疾2008-8-2008-8-12008-8-1/2008-8-病35729视网膜疾2008-8-2008-8-12008-8-1/2008-8-病35730视网膜疾2008-8-2008-8-12008-8-1/2008-8-病36928白内障（双2008-8-2008-8-12008-8-12008-8-2008-8-眼）4682024视网膜疾2008-8-2008-8-12008-8-1/2008-8-病46927187188189190191192193194195196197白内障（双 2008-8- 2008-8-1 2008-8-1 2008-8- 2008-8-眼）46820

34、232008-8-2008-8-外伤42008-8-52008-8-6/13白内障（双2008-8-2008-8-12008-8-12008-8-2008-8-眼）46820232008-8-2008-8-12008-8-12008-8-白内障468/21视网膜疾2008-8-2008-8-12008-8-1/2008-8-病56929视网膜疾2008-8-2008-8-12008-8-1/2008-8-病569242008-8-2008-8-12008-8-12008-8-白内障568/212008-8-2008-8-12008-8-12008-8-白内障568/202008-8-2008-

35、8-12008-8-12008-8-青光眼569/25视网膜疾2008-8-2008-8-12008-8-1/2008-9-病66912008-8-2008-8-12008-8-12008-8-白内障668/21198199200201202203204205206207208白内障（双 2008-8- 2008-8-1 2008-8-1 2008-8- 2008-8-眼）67820232008-8-2008-8-12008-8-12008-8-209 白内障/67820视网膜疾2008-8-2008-8-12008-8-12008-8-210/病679292008-8-2008-8-1200

36、8-8-12008-8-211 白内障/67820白内障（双2008-8-2008-8-12008-8-12008-8-2008-8-212眼）6782024白内障（双2008-8-2008-8-12008-8-22008-8-2008-8-213眼）68527302008-8-2008-8-214 外伤2008-8-72008-8-8/615视网膜疾2008-8-2008-8-12008-8-22008-9-215/病69112008-8-2008-8-12008-8-22008-8-216 白内障/69023白内障（双2008-8-2008-8-12008-8-22008-8-2008-8-217眼）6952730白内障（双2008-8-2008-8-12008-8-22008-8-2008-8-218眼）6952730219 视网膜疾2008-8-2008-8-12008-8-2/2008-9-病6911视网膜疾病2008-8-72008-8-202008-8-22/2008-9-2视网膜疾病2008-8-72008-8-202