运筹学资料多目标规划

多目标规划的单纯形算法

多目标规划问题与线性规划问题相似，可用单纯形算法求解。注意：在比较检验数大小时，要先比较较高级别的系数，再比较较低级别的系数。例4-9（例4-6）目标函数：MinS=P1d1-+P2(5d2++d3+)约束方程：6X1+4X2+d1--d1+=2802X1+3X2+d2--d2+=1004X1+2X2+d3--d3+=120X1,X2,di-,di+0(i=1,2,3)标准型目标函数：MaxS’=-P1d1--P2(5d2++d3+)约束方程：6X1+4X2+d1--d1+=2802X1+3X2+d2--d2+=1004X1+2X2+d3--d3+=120X1,X2,di-,di+0(i=1,2,3)初撞始薯单汤纯借形置表首座先狭满苏足徐第随一誉目前标冠P1进肿基慌变哀量乳X1，番出那基脆变怕量麦y3-主割元仗（岸4暗）主留元坡运碑算赚：阔第病三慢行与除掠以岛4主烘元忍运钢算座：加第渗一辨行哑加误上认第虚三走行女（朝-照6倦）钩倍主姜元射运萄算享：球第副二练行胆加驻上幅第拼三贯行坏（泛-净2盛）倒倍重猴新功计歉算州检呆验拢数第基二糕行慈除腥以坊2第激一席行夹加卡上猛第增二萝行庙（路-猎1觉）第避三气行妙加艰上蜜第为二有行晋（扑-国1朱/壮2挺）计精算喊检监验啄数计剪算泉检柿验革数第辞一趴行疏乘还上钞4杰/派5第疾三灶行绣加荣上症第物一孙行首（配3峰/宫8闯）计央算窗检逼验摊数最骡后坑变陷量孙y1-的宿检拉验腊数拒为搂-咬P1+朵(嚼4染/凯5心)梦P2由碧于匆假狱定灵P1》昆P2巴，所狐以身此禾检城验魂数随也诉小颠于柿零佛。该死问课题狭的效最浓优怀方腥案盖为还生绒产冤A税产采品辟4如4撤个跟单笑位萝，事B球产幅品邻4股个梦单库位术，筝利豪润驰为华2京8醉0夏百势元致。层此码时祥，醉原然料怖正犬好给用闭了纸1巴0怪0串吨弄，昂工旧时陷比寸原常计茎划郑超扫了骡6伯4坟小北时锁。例椅4语-张1膏0设季某旨工足厂迷生锅产登两叔种冠产帜品豆，还都号要排经栗过腐两脸道搂工揪序刚，债有爹关叹资鹿料框如群下任表易。搁假挤如荣工份序谨1抓，际2杂都羡允亭许成加默班械，樱使狐得套利烈润控不丛少态于秆1隙0康0桑0宰元尚作竞为扰目弟标毒。请又倡以烧：秋第换1包，缠2东工茄序楼的命加话班它工找时病之量和柄尽朗可否能科在早1廉6筑0筛之繁内赚为患第揉一保目娃标损；斥产简品店乙摄必亮须择严观格质控穷制排在疫7国0芦公躺斤蕉之淹内养为片第碑二煎目膨标餐；暂该启厂超的铺利湿润叙越递高昏越夺好恐为葡第究三完目浇标患；呼尽巩量览减乱少沉工骡序鹅1徐，觉2根加骗班升工问时忙为鹿第脏四润目毙标刑.册试兰问叫：唯在秋上梯述彩条滨件垦下察，挽该旗厂陪应详如贝何行生榜产刻？小时/公斤甲乙能提供的工时工序121100工序21180产量上界(kg)不限70利润（元/kg)64解腊：示设廉X1，赢X2为蝴甲习，划乙窄两昆种俩产皱品猛的吩生但产骄公械斤蝇数抚，d1-，役d1+分稠别席为静低仍于甜或畅超裹过是利遗润云1赤0校0裳0恳元俘的决偏较差d2-，广d2+分毯别宽为抢第征1删道份工删序籍剩探余珠和侮加骆班级的尸工棚时需数d3-，荡d3+分俭别盐为雹第沃2投道杂工酿序悟剩雪余吓和锹加岩班隐的仗工雷时截数d4-，隐d4+为桨加路班扬工怒时安之扭和厘低畅于粪或全超耳过梁1漂6痕0享工禽时饺数由薪于同产屑品坊X烫2泥必侄须雪严壤格境控剪制料在歪7陈0竖公写斤茶之袜内叫为挺第淹一厉目重标铺，阻则监可李取扶d5-为钥实奶际南公辆斤士数蔽不城到魔7届0怎的旁偏迈差太，语且溪d5+=不0足。目呢标赴函笑数亏：共M炼i窗n戴Z词=栗P1d4++病P2d5-+啄P3d1-+悔P4(粮d2++宗d3+)约学束浊方惩程蝇：蹦6龟X1+那4戒X2+胶d1--端d1+=般1劲0烧0筹02伐X1+灾X2+栏d2--蹄d2+=酬1致0王0X1+如X2+供d3--农d3+=辈8兆0d2++踩d3++d4–-乱d4+=驶1音6多0X2+d5–=青7趁0X1,却X2,池di-,见di+,d5–0泥(冲i吊=吨1息,尊2哲,竹3盲,混4菠)目监标很函循数衰：隐M猜a姻x锡s租=恼-巴P1d4+-线P2d5--沉P3d1--料P4(姻d2++么d3+)约腥束华方盒程建：注6敞X1+叨4聋X2+扑d1--款d1+=师1素0省0渗02忧X1+宇X2+眯d2--损d2+=背1场0寇0X1+捕X2+持d3--渠d3+=竭8乳0d2++督d3++d4–d4+=拍1铸6那0X2+d5–=胞7耳0X1,薯X2,衔di-,秩di+,d5–0梢(蜜i垦=催1绸,脉2犯,哲3蝴,桐4津)表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-641-1000000010000d2-21001-1000001000d3-1100001-1000800d4-000001011-10160-p2d5-0100000000170Óp400000-10-10000p3640-100000001000p20100000000070p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-641-1000000010000d2-21001-1000001000d3-1100001-1000800d4-000001011-10160-p2d5-0100000000170Óp400000-10-10000p3640-100000001000p20100000000070p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-641-1000000010000d2-21001-1000001000d3-1100001-1000800d4-000001011-10160-p2d5-0100000000170Óp400000-10-10000p3640-100000001000p20100000000070p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-601-1000000-47200d2-21001-1000001000d3-1100001-1000800d4-000001011-10160-p2d5-0100000000170Óp400000-10-10000p3640-10000000720p20100000000070p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-601-1000000-47200d2-20001-10000-1300d3-1100001-1000800d4-000001011-10160-p2d5-0100000000170Óp400000-10-10000p3640-10000000720p20100000000070p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-601-1000000-47200d2-20001-10000-1300d3-1000001-100-1100d4-000001011-101600X20100000000170Óp400000-10-10000p3600-1000000-4720p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-100-660026600d2-20001-10000-1300d3-1000001-100-1100d4-000001011-101600X20100000000170Óp400000-10-10000p3600-1000000-4660p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-100-660026600d2-00001-1-22001100X11000001-100-1100d4-000001011-101600X20100000000170Óp400000-10-10000p3600-1000000-4660p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-100-660026600d2-00001-1-22001100X11000001-100-1100d4-000001011-101600X20100000000170Óp400000-10-10000p3000-100-66002660p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-100-660026600d2-00001-1-22001100X11000001-100-1100d4-000001011-101600X20100000000170Óp400000-10-10000p3000-100-66002660p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-100-660026600d2-00001/2-1/2-11001/250X11000001-100-1100d4-000001011-101600X20100000000170Óp400000-10-10000p3000-100-66002660p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-330000-16300d2-00001/2-1/2-11001/250X11000001-100-1100d4-000001011-101600X20100000000170Óp400000-10-10000p3000-100-66002630p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-330000-16300d2-00001/2-1/2-11001/250X110001/2-1/2-1000-1/2150d4-000001011-101600X20100000000170Óp400000-10-10000p3000-100-66002630p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-330000-1630-p4d3+00001/2-1/2-11001/250X110001/2-1/2-1000-1/2150d4-0000-1/23/2101-1-1/21550X20100000000170Óp400001/2-3/2-10001/25p3000-1-330000-1630p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-330000-1630-p4d3+00001/2-1/2-11001/250X110001/2-1/2-1000-1/2150d4-0000-1/23/2101-1-1/21550X20100000000170Óp400001/2-3/2-10001/25p3000-1-330000-1630p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-330000-1630-p4d3+00001/2-1/2-11001/250X110001/2-1/2-1000-1/215-p4d2+0000-1/312/302/3-2/3-1/31030X20100000000170Óp400001/2-3/2-10001/2108p3000-1-330000-1630p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-20-20-220320-p4d3+00001/2-1/2-11001/250X110001/2-1/2-1000-1/215-p4d2+0000-1/312/302/3-2/3-1/31030X20100000000170Óp400001/2-3/2-10001/2108p3000-1-330000-1320p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-20-20-220320-p4d3+00001/30-2/311/3-1/31/3570X110001/2-1/2-1000-1/215-p4d2+0000-1/312/302/3-2/3-1/31030X20100000000170Óp400001/2-3/2-10001/2160p3000-1-330000-1320p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-20-20-220320-p4d3+00001/30-2/311/3-1/31/3570X110001/2-1/2-1000-1/215-p4d2+0000-1/312/302/3-2/3-1/31030X20100000000170Óp400001/2-3/2-10001/2160p3000-1-330000-1320p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-20-20-220320-p4d3+00001/30-2/311/3-1/31/3570X110001/30-2/301/3-1/3-2/3200/3-p4d2+0000-1/312/302/3-2/3-1/31030X20100000000170Óp4000000001-10160p3000-1-20-20-220320p20000000000-10p1000000000-100表1C00-p300-p40-p40-p1-p2CBXBX1X2d1-d1+d2-d2+d3-d3+d4-d4+d5-b-p3d1-001-1-20-20-220320-p4d3+00001/30-2/311/3-1/31/3570X110001/30-2/301/3-1/3-2/3200/3-p4d2+0000-1/312/302/3-2/3-1/31030X20100000000170Óp4000000001-10160p3000-1-20-20-220320p20000000000-10p1000000000-100到滩目夕前他为阿止赤，敏已剂经利不红能拍再删进尖行筛下桑去爽，（耗2碎）弃（拘1碑）否故则暮会辫破术坏桐已升经勇满炉足序的肃条萄件镰。该丑题宾的轿解呢答切：摧X1=禽2趣0辟0效/缺3棋，沟X2=跃7遍0李，d1-=座3露2坚0染，叹d2+=坛3计1尼0适/长3正，代d3+=打1烧7爬0湖/穗3d4+=据d4-=乡丰d5-=麦0即钟该艰厂币生侮产数方纠案稻：吵生义产坐产召品稠甲梁2陆0做0踪蝶/价3倾公锻斤起，胞产症品抓乙供7融0涌公伶斤帖，载第雷1鬼道挣工零序扩加委班宪3奏1戒0驳/指3仰工氏时码，削第留2伪道刑工馋序钩加纵班型1碑7烦0凡/彻3絮工址时谊，送才旱能搬获眠利1粥0白0冬0仇-裁d1-=印1覆0船0哈0耐-不3址2拐0卵=宿6甜8相0姐元任。投背资球规展划招实引例某慕经偷济这区陶准个备船筹疮集肆资犯金及，手在蚁下冬个叠计带划窃期清内热投谦资墨建咽设金新幸项痛目正，竿有区轻层工稠业鱼、侧重瘦工孩业秀和周新回技茶术杰产协业舅三撤种然项捡目抹，开这倦些肾项装目纯能筑否绸如绿期扇建胃成那有洋一府定茧风缺险饼。梯在坊建毅成啄投座产汁后舞，窝其音收改入乎与沾投挥资踪蝶额丸有海关铸，久经锋过挑分早析好研臂究右，航各缺项肠目业的刊建摄设窑方亏案脱不笑能论如够期蓝投碰入继的榨风梦险狮因驱子千及偏投固产坦后啄可牵以举增猎加胀的剖经舟济使收保入苏的意资史金尤收焰益编率葱百课分诱数乎如绣下项目种类建设方案风险因子ri资金收益率gi(%)轻工业10.220轻工业20.220轻工业30.312轻工业40.316新技术产业50.430新技术产业60.216新技术产业70.530重工业80.720重工业90.64重工