眼科病床合理安排

1、2009高教社杯全國(guó)大學(xué)生數(shù)學(xué)建模競(jìng)賽題目（請(qǐng)先閱讀“全國(guó)大學(xué)生數(shù)學(xué)建模競(jìng)賽論文格式規(guī)范”）b題眼科病床的合理安排醫(yī)院就醫(yī)排隊(duì)是大家都非常熟悉的現(xiàn)象，它以這樣或那樣的形式 出現(xiàn)在我們面前，例如，患者到門診就診、到收費(fèi)處劃價(jià)、到藥房取 藥、到注射室打針、等待住院等，往往需要排隊(duì)等待接受某種服務(wù)。我們考慮某醫(yī)院眼科病床的合理安排的數(shù)學(xué)建模問題。該醫(yī)院眼科門診每天開放，住院部共有病床79張。該醫(yī)院眼科 手術(shù)主要分四大類：白內(nèi)障、視網(wǎng)膜疾病、青光眼和外傷。附錄中給 出了 2008年7月13日至2008年9月11日這段時(shí)間里各類病人的情 況。白內(nèi)障手術(shù)較簡(jiǎn)單，而且沒有急癥。目前該院是每周一、三做白 內(nèi)障

2、手術(shù)，此類病人的術(shù)前準(zhǔn)備時(shí)間只需1、2天。做兩只眼的病人 比做一只眼的要多一些，大約占至ij 60%。如果要做雙眼是周一先做一 只，周三再做另一只。外傷疾病通常屬于急癥，病床有空時(shí)立即安排住院，住院后第二 天便會(huì)安排手術(shù)。其他眼科疾病比較復(fù)雜，有各種不同情況，但大致住院以后2-3 天內(nèi)就可以接受手術(shù)，主要是術(shù)后的觀察時(shí)間較長(zhǎng)。這類疾病手術(shù)時(shí) 間可根據(jù)需要安排，一般不安排在周一、周三。由于急癥數(shù)量較少， 建模時(shí)這些眼科疾病可不考慮急癥。該醫(yī)院眼科手術(shù)條件比較充分，在考慮病床安排時(shí)可不考慮手術(shù) 條件的限制，但考慮到手術(shù)醫(yī)生的安排問題，通常情況下白內(nèi)障手術(shù) 與其他眼科手術(shù)（急癥除外）不安排在同一天做

3、。當(dāng)前該住院部對(duì)全 體非急癥病人是按照fcfs （first come, first serve）規(guī)則安排住院， 但等待住院病人隊(duì)列卻越來越長(zhǎng)，醫(yī)院方面希望你們能通過數(shù)學(xué)建模 來幫助解決該住院部的病床合理安排問題，以提高對(duì)醫(yī)院資源的有效 利用。問題一：試分析確定合理的評(píng)價(jià)指標(biāo)體系，用以評(píng)價(jià)該問題的病 床安排模型的優(yōu)劣。問題二：試就該住院部當(dāng)前的情況，建立合理的病床安排模型， 以根據(jù)己知的第二天擬出院病人數(shù)來確定第二天應(yīng)該安排哪些病人 住院。并對(duì)你們的模型利用問題一中的指標(biāo)體系作出評(píng)價(jià)。問題三：作為病人，自然希望盡早知道自己大約何時(shí)能住院。能 否根據(jù)當(dāng)時(shí)住院病人及等待住院病人的統(tǒng)計(jì)情況，在病人門

4、診時(shí)即告 知其大致入住時(shí)間區(qū)間。問題四：若該住院部周六、周日不安排手術(shù)，請(qǐng)你們重新回答問 題二，醫(yī)院的手術(shù)時(shí)間安排是否應(yīng)作出相應(yīng)調(diào)整？問題五：有人從便于管理的角度提出建議，在一般情形下，醫(yī)院 病床安排可采取使各類病人占用病床的比例大致固定的方案，試就此 方案，建立使得所有病人在系統(tǒng)內(nèi)的平均逗留時(shí)間（含等待入院及住 院時(shí)間）最短的病床比例分配模型?！靖戒洝?008-07-13到2008-09-11的病人信息序 號(hào)12345678910第二次門診時(shí)第一次手出院時(shí)類型間入院時(shí)間術(shù)時(shí)間手術(shù)時(shí)間間2008-7-2008-7-12008-7-12008-7-外傷1345/19視網(wǎng)膜疾2008-7-2008

5、-7-22008-7-2/2008-8-病135782008-7-2008-7-22008-7-22008-7-白內(nèi)障1358/31視網(wǎng)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視網(wǎng)膜疾2008-7-2008-7-22008-7-2/2008-8-病136911白內(nèi)障（雙2008-7-2008-7-22008-7-22008-7-2008-8-眼）1368302視網(wǎng)膜疾2008-7-2008-7-22008-7-2/2008-8-病14696白內(nèi)障（雙2008-7-2008-7-2

6、2008-7-22008-7-2008-8-眼）1468301白內(nèi)障2008-7-2008-7-22008-7-2/2008-7-1112131415161718192021146830視網(wǎng)膜疾病2008-7-142008-7-262008-7-29/2008-8-8白內(nèi)障（雙2008-7-2008-7-22008-7-22008-7-2008-8-眼）1468302白內(nèi)障（雙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視網(wǎng)膜疾病2008-7-142008-7-2720

7、08-7-29/2008-8-9視網(wǎng)膜疾病2008-7-142008-7-272008-7-29/2008-8-6視網(wǎng)膜疾病2008-7-152008-7-272008-7-29/2008-8-12白內(nèi)障2008-7-152008-7-272008-7-28/2008-7-30青光眼2008-7-152008-7-272008-7-29/2008-8-5白內(nèi)障（雙2008-7-2008-7-22008-7-22008-7-2008-8-眼）1578302視網(wǎng)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-白內(nèi)障1578/302008-7-2008-7-22008-7-22008-7-白內(nèi)障1578/30白內(nèi)障（雙2008-7-2008-7-22008-8-42008-8-2008-8-眼）15869視網(wǎng)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-白內(nèi)障1680/32008-7-2008-7-12008-7-12008-7-外傷1678/22白內(nèi)障

9、（雙2008-7-2008-7-22008-8-42008-8-2008-8-眼）16869視網(wǎng)膜疾2008-7-2008-7-22008-7-3/2008-8-病1681102223242526272829303132白內(nèi)障（雙 2008-7- 2008-7-2 2008-8-4 2008-8- 2008-8-眼）16869視網(wǎng)膜疾2008-7-2008-7-22008-7-3/2008-8-病168111視網(wǎng)膜疾2008-7-2008-7-22008-7-3/2008-8-病1781102008-7-2008-7-22008-7-32008-8-白內(nèi)障1790/3視網(wǎng)膜疾2008-7-20

10、08-7-22008-7-3/2008-8-病17918視網(wǎng)膜疾2008-7-2008-7-22008-7-3/2008-8-病179110白內(nèi)障（雙2008-7-2008-7-22008-8-42008-8-2008-8-眼）17968白內(nèi)障（雙2008-7-2008-7-22008-8-42008-8-2008-8-眼）179682008-7-2008-7-12008-7-12008-7-外傷1789/282008-7-2008-7-22008-7-32008-8-青光眼1791/7白內(nèi)障（雙2008-7-2008-7-22008-8-42008-8-2008-8-眼）1796933343

11、53637383940414243白內(nèi)障（雙 2008-7- 2008-7-3 2008-8-4 2008-8- 2008-8-眼）17068白內(nèi)障（雙2008-7-2008-7-32008-8-2008-8-442008-8-4眼）170610白內(nèi)障（雙2008-7-2008-7-32008-8-2008-8-452008-8-4眼）17068視網(wǎng)膜疾2008-7-2008-7-32008-8-462008-8-1/病1808白內(nèi)障（雙2008-7-2008-7-32008-8-2008-8-472008-8-4眼）1806102008-7-2008-7-12008-7-22008-7-48

12、外傷/189026白內(nèi)障（雙2008-7-2008-7-32008-8-2008-8-492008-8-4眼）180692008-7-2008-7-32008-8-50 白內(nèi)障2008-8-4/18062008-7-2008-7-32008-8-51 青光眼2008-8-1/1808視網(wǎng)膜疾2008-7-2008-7-32008-8-522008-8-1/病180112008-7-2008-7-12008-7-22008-7-53外傷/18902554 白內(nèi)障2008-7-2008-7-32008-8-4/2008-8-55565758596061626364651817白內(nèi)障（雙2008-7

13、-2008-7-32008-8-2008-8-2008-8-4眼）18168白內(nèi)障（雙2008-7-2008-7-32008-8-2008-8-2008-8-4眼）18169視網(wǎng)膜疾2008-7-2008-7-32008-8-2008-8-2/病18113視網(wǎng)膜疾2008-7-2008-7-32008-8-2008-8-2/病191142008-7-2008-7-32008-8-白內(nèi)障2008-8-4/1918白內(nèi)障（雙2008-7-2008-8-2008-8-2008-8-12008-8-4眼）1969視網(wǎng)膜疾2008-7-2008-8-2008-8-12008-8-3/病198視網(wǎng)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-白內(nèi)障2008-8-12008-8-4/197外傷2008-7-2008-7-22008-7-2/2008-7-66676869707172737475761901252008-7-2008-8-白內(nèi)障2008-8-22008-8-4/1982008-7-2008-8-青光眼2008-8-22008-8-5/1916視網(wǎng)膜疾2008-7-2008-8-2008-8-22008-8-5/病20132008-7-2008-8-白

15、內(nèi)障2008-8-22008-8-4/208白內(nèi)障（雙2008-7-2008-8-2008-8-2008-8-22008-8-4眼）20692008-7-2008-8-白內(nèi)障2008-8-22008-8-4/2072008-7-2008-8-白內(nèi)障2008-8-22008-8-4/2072008-7-2008-7-22008-7-22008-7-外傷/2012292008-7-2008-7-22008-7-22008-7-外傷/201228視網(wǎng)膜疾2008-7-2008-8-2008-8-22008-8-5/病2014視網(wǎng)膜疾2008-7-2008-8-22008-8-5/2008-8-200

16、8-7-2008-8-77白內(nèi)障2008-8-32008-8-4/2162008-7-2008-7-22008-7-22008-7-78外傷/212329白內(nèi)障（雙2008-7-2008-8-2008-8-792008-8-32008-8-4眼）2169白內(nèi)障（雙2008-7-2008-8-2008-8-802008-8-32008-8-4眼）21692008-7-2008-7-22008-7-22008-7-81外傷/2123272008-7-2008-8-82白內(nèi)障2008-8-32008-8-4/216白內(nèi)障（雙2008-7-2008-8-2008-8-832008-8-32008-8-

17、4眼）2169白內(nèi)障（雙2008-7-2008-8-2008-8-842008-8-32008-8-4眼）2169白內(nèi)障（雙2008-7-2008-8-12008-8-2008-8-852008-8-4眼）21113162008-7-2008-7-22008-7-22008-7-86外傷/22342887青光眼2008-7-2008-8-42008-8-7/2008-8-病201622162008-7-2008-8-88白內(nèi)障2008-8-42008-8-6/2292008-7-2008-8-89白內(nèi)障2008-8-42008-8-6/22102008-7-2008-8-90白內(nèi)障2008-8

18、-42008-8-6/229視網(wǎng)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外傷/234512008-7-2008-8-94白內(nèi)障2008-8-52008-8-6/23102008-7-2008-8-95白內(nèi)障2008-8-52008-8-6/2392008-7-2008-7-22008-7-22008-7-96外傷/2345302008-7-2008-8-97白內(nèi)障2008-8-52008-8-6/23998白內(nèi)障

19、（雙2008-7-2008-8-62008-8-12008-8-2008-8-99100101102103104105106107108109眼）2311317視網(wǎng)膜疾2008-7-2008-8-2008-8-62008-8-8/病23182008-7-2008-8-12008-8-白內(nèi)障2008-8-6/23113視網(wǎng)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視網(wǎng)膜疾2008-7-2008-8-2008-8-62008-8-8/病2317視網(wǎng)膜疾2008-7-2008-8-2008-

20、8-62008-8-8/病2319白內(nèi)障（雙2008-7-2008-8-12008-8-2008-8-2008-8-6眼）23113152008-7-2008-8-12008-8-白內(nèi)障2008-8-6/23115視網(wǎng)膜疾2008-7-2008-8-2008-8-72008-8-9/病2323視網(wǎng)膜疾2008-7-2008-8-2008-8-72008-8-9/病2419視網(wǎng)膜疾2008-7-2008-8-72008-8-9/2008-8-病24222008-7-2008-8-12008-8-110白內(nèi)障2008-8-7/241152008-7-2008-8-111青光眼2008-8-7200

21、8-8-9/2417視網(wǎng)膜疾2008-7-2008-8-1122008-8-72008-8-9/病24192008-7-2008-8-12008-8-113白內(nèi)障2008-8-7/24114視網(wǎng)膜疾2008-7-2008-8-12008-8-1142008-8-8/病240172008-7-2008-8-12008-8-115白內(nèi)障2008-8-8/25114視網(wǎng)膜疾2008-7-2008-8-12008-8-1162008-8-8/病25022白內(nèi)障（雙2008-7-2008-8-12008-8-2008-8-1172008-8-8眼）2511315視網(wǎng)膜疾2008-7-2008-8-120

22、08-8-1182008-8-8/病25020白內(nèi)障（雙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-白內(nèi)障2008-8-8/261142008-7-2008-8-12008-8-白內(nèi)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、外傷/278922008-7-2008-8-12008-8-青光眼2008-8-8/270192008-7-2008-8-12008-8-白內(nèi)障2008-8-8/27114白內(nèi)障（雙2008-7-2008-8-12008-8- 2008-8-2008-8-8眼）27113152008-7-2008-8-12008-8-白內(nèi)障2008-8-9/27113視網(wǎng)膜疾2008-7-2008-8-12008-8-2008-8-9/病272222008-7- 2008-7-22008-7-22008-8-外傷/27895視網(wǎng)膜疾2008-7- 2008-8-92008-8-1/2008-8-1321331

24、34135136137138139140141142病27223白內(nèi)障（雙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視網(wǎng)膜疾2008-7-2008-8-12008-8-2008-8-9/病282252008-7-2008-7-22008-7-32008-8-外傷/289062008-7-2008-8-12008-8-青光眼2008-8-9/282192008-7-2008-7-22008-7-32008-8-外傷/28905視網(wǎng)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視網(wǎng)膜疾2008-7-2008-8-12008-8-2008-8-9/病28224白內(nèi)障（雙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視網(wǎng)膜疾2008-7-2008-8-12008-8-2008-8-9/病28224視網(wǎng)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白內(nèi)障（雙2008-7-2008-8-12008-8-2008-8-2008-8-9眼）2911316視網(wǎng)膜疾2008-7-2008-8-12008-8-2008-8-9/病292242008-7-2008-8-12008-8-白內(nèi)障2008-8-9/291142008-7-2008-8-12008-8-青光眼2008-8-9/292222008-7-2008-8-12008-8-12008-8-白內(nèi)障/300115視網(wǎng)膜疾2008-7-2008-8-12008-8-12008-8-/病3002202008-

27、7-2008-8-12008-8-12008-8-白內(nèi)障/300113外傷2008-7-2008-7-32008-8-1/2008-8-15415515615715815916016116216316430111白內(nèi)障（雙2008-7-2008-8-12008-8-12008-8-2008-8-眼）30011316外傷2008-7-302008-7-312008-8-1/2008-8-6外傷2008-7-312008-8-12008-8-2/2008-8-7青光眼2008-7-312008-8-102008-8-12/2008-8-18視網(wǎng)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白內(nèi)障（雙2008-7-2008-8-12008-8-12008-8-2008-8-眼）31011315視網(wǎng)膜疾病2008-7-312008-8-112008-8-14/2008-8-28外傷2008-7-312008-8-12008-8-2/2008-8-9視網(wǎng)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視網(wǎng)膜疾2008-7-2008-8-12008-8-12008-8-166/病3114272008-8-2008-8-167 外傷2008-8-22008-8-3/110視網(wǎng)膜疾2008-8-2008-8-12008-8-12008-8-168/病12429白內(nèi)障（雙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白內(nèi)障（雙2008-8-2008-8-12008-8-12008-8- 2008-8-171眼）1382023白內(nèi)障（雙2008

30、-8-2008-8-12008-8-12008-8- 2008-8-172眼）1382024視網(wǎng)膜疾2008-8-2008-8-12008-8-12008-8-173/病13523視網(wǎng)膜疾2008-8-2008-8-12008-8-12008-8-174/病13522175 外傷2008-8-2008-8-22008-8-3/2008-8-19176外傷2008-8-12008-8-22008-8-3/2008-8-8白內(nèi)障（雙2008-8-2008-8-12008-8-12008-8-2008-8-177眼）1382023視網(wǎng)膜疾2008-8-2008-8-12008-8-12008-8-1

31、78/病24629視網(wǎng)膜疾2008-8-2008-8-12008-8-12008-8-179/病24625視網(wǎng)膜疾2008-8-2008-8-12008-8-12008-8-180/病246272008-8-2008-8-12008-8-12008-8-181白內(nèi)障/24822視網(wǎng)膜疾2008-8-2008-8-12008-8-12008-8-182/病24628白內(nèi)障（雙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白內(nèi)障（雙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視網(wǎng)膜疾2008-8-2008-8-12008-8-1/2008-8-病35726白內(nèi)障（雙2008-8-2008-8-12008-8-12008-8-2008-8-眼）35820232008-8-2008-8-12008-8-12008-8-白內(nèi)障358/21白內(nèi)障（雙2008-8-2008-8-12008-8-12008-8-2008-8-眼）3582023視網(wǎng)膜疾2008-8-2008-8-12008-8-1/2008-8-病35726視網(wǎng)

33、膜疾2008-8-2008-8-12008-8-1/2008-8-病35729視網(wǎng)膜疾2008-8-2008-8-12008-8-1/2008-8-病35730視網(wǎng)膜疾2008-8-2008-8-12008-8-1/2008-8-病36928白內(nèi)障（雙2008-8-2008-8-12008-8-12008-8-2008-8-眼）4682024視網(wǎng)膜疾2008-8-2008-8-12008-8-1/2008-8-病46927187188189190191192193194195196197白內(nèi)障（雙 2008-8- 2008-8-1 2008-8-1 2008-8- 2008-8-眼）46820

34、232008-8-2008-8-外傷42008-8-52008-8-6/13白內(nèi)障（雙2008-8-2008-8-12008-8-12008-8-2008-8-眼）46820232008-8-2008-8-12008-8-12008-8-白內(nèi)障468/21視網(wǎng)膜疾2008-8-2008-8-12008-8-1/2008-8-病56929視網(wǎng)膜疾2008-8-2008-8-12008-8-1/2008-8-病569242008-8-2008-8-12008-8-12008-8-白內(nèi)障568/212008-8-2008-8-12008-8-12008-8-白內(nèi)障568/202008-8-2008-

35、8-12008-8-12008-8-青光眼569/25視網(wǎng)膜疾2008-8-2008-8-12008-8-1/2008-9-病66912008-8-2008-8-12008-8-12008-8-白內(nèi)障668/21198199200201202203204205206207208白內(nèi)障（雙 2008-8- 2008-8-1 2008-8-1 2008-8- 2008-8-眼）67820232008-8-2008-8-12008-8-12008-8-209 白內(nèi)障/67820視網(wǎng)膜疾2008-8-2008-8-12008-8-12008-8-210/病679292008-8-2008-8-1200

36、8-8-12008-8-211 白內(nèi)障/67820白內(nèi)障（雙2008-8-2008-8-12008-8-12008-8-2008-8-212眼）6782024白內(nèi)障（雙2008-8-2008-8-12008-8-22008-8-2008-8-213眼）68527302008-8-2008-8-214 外傷2008-8-72008-8-8/615視網(wǎng)膜疾2008-8-2008-8-12008-8-22008-9-215/病69112008-8-2008-8-12008-8-22008-8-216 白內(nèi)障/69023白內(nèi)障（雙2008-8-2008-8-12008-8-22008-8-2008-8-217眼）6952730白內(nèi)障（雙2008-8-2008-8-12008-8-22008-8-2008-8-218眼）6952730219 視網(wǎng)膜疾2008-8-2008-8-12008-8-2/2008-9-病6911視網(wǎng)膜疾病2008-8-72008-8-202008-8-22/2008-9-2視網(wǎng)膜疾病2008-8-72008-8-202