1d1405理工學院2011高教社杯全國生數(shù)學建模競賽

2011高教社杯大學生數(shù)學建模競賽區(qū)評閱編號（由賽區(qū)評閱前進行編號賽區(qū)評閱記錄（可供賽區(qū)評閱時使用統(tǒng)一編號（由賽區(qū)送交前編號評閱編號（ 評閱前進行編號長度及各類原料數(shù)量限制為約束，對各類原料單獨。利用lingo軟件進行對186見表六，給出了搭lingo3-3.410192將每一類原料中的編號為1到4的原料定為短材料，目標函數(shù)： max(Nixijmk為模型一中得到的第kk1,2,3 jLINGO（見附錄3-3.4151930-1zij

原料盡可能集中， zij最小，考慮到zij0時xij0;而zij1時,xij可用sgnzijxijMsgnzi,

M為足夠大的正數(shù)：腸衣搭配、遞減搜索、降級使用、最優(yōu)方案、0-1規(guī)一、問題重表1成品規(guī)格表378∞5表2原料描述表3-3.5-4-4.5-5-5.5-6-6.5-7-7.5-8-8.5-9-9.5-20600010.5米的誤差，總根數(shù)允許比標為了食品保鮮,要求在30要求我們建立上述問題的數(shù)學模型，并給出求解方法，并對表1、表2二、問題分，其次，考慮到原料使用率，題中允許每捆總長度有0.5的誤差，但是實際生產中廠家會盡可能節(jié)約成本，考慮到廠家的利益總長度控制在88.5m，89.5m之間，總根數(shù)允許比標準少1根，節(jié)約成本。因此，對每一類原料級處理后最多能裝出的成品捆數(shù)其作為模型一即成品捆數(shù)最多模型。三、符號說 ：i j 表示第ijLi：i1.....8;i1.....14;i 表示第iNi：i1.....8;i1.....14;i 表示第ink:k表示第kx'：i jijN'：i iix"：i j表示第二類降至一類后第ij次取出的根數(shù)N":i i表示第二類降至一類后第i種材料的Nyi:i1....14;i 原料中的第ii種原料j次被選取nk：k1,2,3第kmk：k第kMZ0xij 1x 表示第i種原料庫中第j次取原料為1，四、模型假1234、每捆總長度允許有0.51568910五、數(shù)據預第一類：3米6.9第二類：713.9第三類：14-14.425.5-編長度區(qū)根長度取①3-3②3.5-③4-4④4.5-⑤5-5⑥5.5-⑦6-6⑧6.5-合最大捆最大捆1305.5/89表二：編長度區(qū)根長度取7-77.5-8-88.5-9-99.5-10-10.5-11-11.5-12-12.5-13-.5-合按長度捆表三：編號14-14.5-15-15.5-16-16.5-17-17.5-18-18.5-19-19.5-20-20.5-21-21.5-22-22.5-223-0023.5-624-0024.5-0025-0025.5-1對于第三類原料最大長度的確

378∞5因此我們通過網上搜索資料（見參考文獻），了解到一些生產廠家生產的腸①②③④⑤⑥⑦⑧⑨m9914--32m3785六、模型的建立與求品捆數(shù)最多搭配考慮到原料使用率，題中允許每捆總長度有0.588.5m89.5m1各類材料的最大值，以此最大值作為成品捆數(shù)目標值，利用lingo軟件試探此目標值是否通過模型前準備粗略知道第一類原料進行成品捆數(shù)不會超過14捆，第二類原料進行成品捆數(shù)不會超過41捆，第三類原料進行成品捆數(shù)不會超過137ni表示第kn114n2n3137xij表示每類原料中的第ij次取出的根數(shù)，Li表示每類原料中第種材料的長度，

表示每類原料中第i種材料的根數(shù),對于第一類i1,2,,8j1,2,,n1對于第i1,2,,14j1,2,n2，對于第三類i1,2,,24j1,2,n3

88xij

第一類原料搭配要求

88

xijNi，每種材料根數(shù)限制 xijN; 7

xij

88.5

xij

xij xij 4 xij i88.524xi第三類原料搭配要求

xij xij利用LINGO軟件把目標進行遞減搜索(程序見附錄)求解得第一類材料成品捆最14第二類材料成品捆數(shù)37三類材料成品捆數(shù)最多135取編長度區(qū)剩余根最數(shù)31（8，653111252高等級剩余原料降級使用優(yōu)化模將第三類剩余降級到第二類考慮1原料最多可以的成品捆數(shù)n'61yix'表示降級后第ijL'表示第iN 降級后第ixx 7 88.5x'L' n'1

ijx'x

N'iiLINGO

yi201060000501001000將第二類剩余原料降級到第一類考慮x表示第二類降級后第ijL ii種材料的長度，N"表示降級后第i種材料的根數(shù)。我們根據表七中第二類剩余量結合第一類的剩余量降級估算出剩余的第一類原料最多可 的成品捆in2'3n2

8 198x8x

"88.5x"L" n'

ij22ii

N"LINGO解得如（表八

x"8 yi8 第二063007010002000000070最多獲取數(shù)N141713533192捆模型二剩余原料最小化模1923—4.9材料中長度為7—8.9米的定為短材料第三類材料中長度為14—15.9米的定為短材料，即取i1,2

(Nixij jmk為模型一中算出的第kj1,2.....14j1,2,37j1,2,,135。 19xij

xijNi，每種材料根數(shù)限制xijN; 7 xij i88.514xi第二類原料搭配要求：

xij xij 4 xij

ij xij xij對于第二類的剩余的放到第一類中，長度按第一類計算。將第三類剩余降級到第二類考慮1原料最多可以的成品捆數(shù)n'61yi：表示高級原料剩余量降級放到低級原料中的第ix'表示降級后第ijL'表示第iN 降級后第ixx 7 88.5x'L' n'1

ijx'x

N'ii yi LINGO0000605130200100520010190最多獲取數(shù)將第二類剩余原料降級到第一類考慮x表示第二類降級后第ijL ii種材料的長度，N"表示降級后第i種材料的根數(shù)。我們根據表七中第二類剩余量結合第一類的剩余量降級估算出剩余的第一類原料最多可 的成品捆in2'3n2

8 198x8x

"88.5x"L" n'

ij22ii

N" x"8 yi8 LINGO第二0000000000000100000030最多獲取數(shù)N141713543193捆193模型三：搭配時間最優(yōu)化模0,xij0-1zij

目1,x zijsgn0x0

1,xxij第i種材料的第j次所取得的根數(shù)目標函數(shù)： 對于第一類i 8，對于第二類i1,2,14,對于第三類i1,2,,24。 0xij1 zij1

xijsgnzijxijMsgn xij 模型的優(yōu)

七、模型的評價與推總長度允許有±0.51了最優(yōu)方案。模型的缺模型的推八、參考文【1】謝金星《數(shù)學模型（第三版，：高等教育【2】數(shù)學建模與數(shù)學實驗：高等教育【3】通《最優(yōu)化模型與實驗》同濟大 【4】編寫組《運籌學（第三版【5】,實用數(shù)學建模與軟件應用,西北工業(yè)大學【6】腸衣價格腸衣到網腸衣頻道 【附錄模型一程序L=33.544.555.56N=43593941272834L=77.588.599.51010.51111.51212.513N=24242025212321183123225918L=1414.51515.51616.51717.51818.51919.52020.52121.522.5 23.52424.525N=3529304228424549506452634935;w=2424650000000000L=77.588.599.51010.51111.51212.513w=163010000L=33.544.555.56L=33.544.555.56N=43593941272834L=77.588.599.51010.51111.51212.513 242025212321183123225918L=1414.51515.51616.51717.51818.51919.52020.52121.522.5 23.52424.525N=3529304228424549506452634935;w=24231112000010501L=77.588.599.51010.51111.51212.513cailiao2/1..8/:z;w=220000100L=33.544.555.56根數(shù)12345678每捆4-5-6-1100080122335100530000610021剩余編捆123456789每根0001100282000010005100108300100003010300840000103011000285000011020020000004210010880001010030030089000012000203008000000302200000000128001000300101103020010500108020308003008003001103008400008000200100104008002000100005008000000500002000012208000300001002028000300001002028001100002004008010002000005008001100000060008000300000004007000300010000100122008000011021002007000040000001128001003000002028000000000010337000030000023008000001006000007剩余12151123456789111022222每012901234捆1010000004000000000000005200300000000002000000000530002000020001000000000054000010040000000000000005500020000030000000000000560200000000300000000000050000001003000000100000000050002001000000200000000005000200000200010000000000500100010010200000000000050000004000000010000000005000200010000020000000000500030000000000050002000000000005000100110000000040000000000000050002000000000005002100000000000500120000000000050001100000300000000000005200000000000030000000000501100000002000001000000050000030000100010000000005110000000000300000000000520000000001000200000000051000000003010000000000005000101002000001000000000520001020000110000000000050000010031000000000000005891011122021222324252627282900000000000010000000030000400001000220000000000000050000010030100000000000005010000003000001000000000500100000202000000000000050000030000020000000000005000003000100010000000000500200000000300000000000050000000000000300000000005000000220001000000000000500010020000200000000000050000101002100000000000005000002101000001000000000501100000100000200000000050000002020010000000000005020000000002010000000000520000000000003000000000051000100000200010000000005000200000020100000000000500010001102000000000000051001000000003000000000005010001000020000000000000403132333435363738394041424344454647484950511010001000000300000000000050010010000300000000000005001000200000200000000000500002000003000000000000050100100000030000000000005000001100300000000000000510100000000030000000000050010000100300000000000005000000000101000000000000400000000000005000000040000000000000000402000000000030000000000050101000000030000000000005000200000003000000000000500030000000000020000000050000002003000000000000005000100002110000000000000500000000100000001000000040000100103000000000000005000003000010001000000000510000000000003000000000040011000000021000000000005253545556575859606162636465666768697071727300000010030000000000000000411000000000021000000000052000000000000001010000004000001003010000000000000500010003000000010000000050000000000000000310000004010000000310000000000000500012000000001100000000050100000100210000000000005001000003000010000000000501001001000100100000000050000003000200000000000005010020000000000200000000500000400000000000001000050110000000020100000000005000011000030000000000000500000003110000000000000050003000000000101000000005000010030000100000000000501000000030100000000000050011000002000010000000005000001021001000000000000547576777879808182838485868788899091929394950000000003110000000000000050020000100000200000000005000200000003000000000000510000000200200000000000050200000000003000000000005110000000000120000000000500100020010000100000000050000002101100000000000005100100000010020000000000500020000100020000000