運籌學(xué)課程設(shè)計分析機械產(chǎn)品生產(chǎn)計劃問題

1、食油生產(chǎn)問題（案例一）分析報告一、實踐性質(zhì)及目的運籌學(xué)作為一門必修課，是學(xué)生們在學(xué)習(xí)了運籌學(xué)課程后，進行的一次綜合性的設(shè)計和分析。通過這次設(shè)計，能夠提高學(xué)生的建模能力，提高學(xué)生的綜合分析能力，提高學(xué)生對于軟件的應(yīng)用能力。最后由于課程設(shè)計是團隊進行的，因此通過這次設(shè)計，還能提高學(xué)生的團隊協(xié)作能力。二、組織方式每小組由1-2人組成?？捎尚〗M成員自行安排分配工作內(nèi)容。三、時間和主要內(nèi)容安排1.進行案例整體分析和建模（時間為11.5天）2.應(yīng)用lino或lingo求解數(shù)學(xué)模型（時間為1.5天）3.對解的具體分析和討論（1.5天）4.課程設(shè)計小組答辯（0.5天）四、分析機械產(chǎn)品生產(chǎn)計劃問題 機械加工廠生

2、產(chǎn)1種產(chǎn)品（從產(chǎn)品1產(chǎn)品7）。該廠有以下設(shè)備：4臺磨床、3臺立式鉆床、3臺水平鉆床、2臺鏜床和2臺刨床。每種產(chǎn)品的利潤（元/件，這里利潤定義為銷售價格與原料成本之差）以及生產(chǎn)單位產(chǎn)品需要的各種設(shè)備的工時（小時）如下表。表中的短劃表示這種產(chǎn)品不需要相應(yīng)的設(shè)備加工。表1產(chǎn)品利潤和需要的設(shè)備工時產(chǎn)品1234567利潤10634195磨床0.50.70.30.20.5立鉆0.10.20.30.6水平鉆0.260.80.6鏜床0.050.020.70.10.08刨床0.010.050.05總工時0.856.920.8110.450.81.23從一月到六月，每個月中需要檢修的設(shè)備是（在檢修的月份中，被檢修

3、的設(shè)備全月不能用于生產(chǎn)）：表2 設(shè)備檢修計劃月份計劃檢修設(shè)備及臺數(shù)月份計劃檢修設(shè)備及臺數(shù)1月1臺磨床4月1臺立式鉆床2月1臺立式鉆床5月1臺磨床和1臺立式鉆3月1臺鏜床6月1臺刨床和1臺水平鉆每個月各種產(chǎn)品的銷售量上限是：表3產(chǎn)品的市場銷售量上限（件/月）產(chǎn)品12345671月50010003003008002001002月40050020004003001503月300600005004001004月20030040050020001005月0100500100100030006月500500100300110050060表4 各月設(shè)備可用情況 月份設(shè)備1月2月3月4月5月6月磨床34443

4、4立式鉆床323223水平鉆床333332鏜床221222刨床222221每種產(chǎn)品的最大庫存量為100件，庫存費用為每件每月0.1元，在一月初，所有產(chǎn)品都沒有庫存；而要求在六月底，每種產(chǎn)品都有50件庫存。工廠每天開2班，每班工作8小時，為簡單起見，假定每月都工作24天。每月總時間=2×8×24=384小時。生產(chǎn)過程中，各種工序沒有先后次序的要求。建立利潤最大化的生產(chǎn)計劃優(yōu)化模型，編制這7種產(chǎn)品六個月的生產(chǎn)庫存銷售計劃。并利用模型分析評價制約該工廠利潤進一步增加的各種瓶頸因素。例如，可以討論以下問題：1）在最優(yōu)生產(chǎn)計劃中，提高哪幾個月中哪些產(chǎn)品的市場銷售量上限可以增加利潤？其

5、中對利潤影響最大的銷售量是哪些？在保持最優(yōu)生產(chǎn)計劃不變的前提下，這些市場銷售量上限提高的幅度是多大？2）哪幾個月中哪些產(chǎn)品的最大庫存量對增加利潤構(gòu)成限制？庫存費用的變化是否會導(dǎo)致最優(yōu)生產(chǎn)庫存銷售計劃的變化？3）哪幾個月哪些設(shè)備的能力是緊缺的，哪些設(shè)備的能力是冗余的？列出設(shè)備能力的優(yōu)先順序？4）現(xiàn)有的設(shè)備檢修計劃是否合理？列出其中不合理的因素根據(jù)分析結(jié)果，寫出綜合性的分析報告。分析報告要用文字和表格，對該工廠7種產(chǎn)品6個月的生產(chǎn)庫存銷售量、產(chǎn)品倉庫的容量、設(shè)備利用和檢修、產(chǎn)品銷售價格、產(chǎn)品市場容量等相關(guān)因素作出詳細描述，并對其中值得注意的問題進行討論。五、模型構(gòu)造5.1變量設(shè)置設(shè)7種產(chǎn)品代號分別

6、為（代表產(chǎn)品）。每種產(chǎn)品的生產(chǎn)（prouct）、銷售（use and sale）和儲存（store）量分別在產(chǎn)品的代號前加p、u和s表示。16月份7種產(chǎn)品的生產(chǎn)、銷售和儲存量分別在代號后面加16表示。第一種產(chǎn)品六個月的生產(chǎn)量、銷售量、月末儲存量共有17變量，其中，六月末的存儲量為50件。ph11，ph12，ph13，ph14，ph15，ph16；uh11，uh12，uh13，uh14，uh15，uh16；sh11，sh12，sh13，sh14，sh15；第二種產(chǎn)品六個月的生產(chǎn)量、銷售量、月末儲存量共有17變量，其中，六月末的存儲量為50件。ph21，ph22，ph23，ph24，ph25，ph

7、26；uh21，uh22，uh23，uh24，uh25，uh26；sh21，sh22，sh23，sh24，sh25；第三種產(chǎn)品六個月的生產(chǎn)量、銷售量、月末儲存量共有17變量，其中，六月末的存儲量為50件。ph31，ph32，ph33，ph34，ph35，ph36；uh31，uh32，uh33，uh34，uh35，uh36；sh31，sh32，sh33，sh34，sh35；第四種產(chǎn)品六個月的生產(chǎn)量、銷售量、月末儲存量共有17變量，其中，六月末的存儲量為50件。ph41，ph42，ph43，ph44，ph45，ph46；uh41，uh42，uh43，uh44，uh45，uh46；sh41，sh42

8、，sh43，sh44，sh45；第五種產(chǎn)品六個月的生產(chǎn)量、銷售量、月末儲存量共有17變量，其中，六月末的存儲量為50件。ph51，ph52，ph53，ph54，ph55，ph56；uh51，uh52，uh53，uh54，uh55，uh56；sh51，sh52，sh53，sh54，sh55；第六種產(chǎn)品六個月的生產(chǎn)量、銷售量、月末儲存量共有17變量，其中，六月末的存儲量為50件。ph61，ph62，ph63，ph64，ph65，ph66；uh61，uh62，uh63，uh64，uh65，uh66；sh61，sh62，sh63，sh64，sh65；第七種產(chǎn)品六個月的生產(chǎn)量、銷售量、月末儲存量共有17

9、變量，其中，六月末的存儲量為50件。ph71，ph72，ph73，ph74，ph75，ph76；uh71，uh72，uh73，uh74，uh75，uh76；sh71，sh72，sh73，sh74，sh75；這樣,一共有7×17=119個變量。5.2 模型構(gòu)建這個問題的建?？梢苑譃閮刹?，首先建立單期問題模型，然后建立多期問題模型。5.2.1單期模型以一月份的模型為例，如果產(chǎn)品沒有庫存，一月份的生產(chǎn)量和銷售量相等，生產(chǎn)計劃線性規(guī)劃模型如下，其中有5個約束條件：產(chǎn)品1 產(chǎn)品2產(chǎn)品3產(chǎn)品4產(chǎn)品5產(chǎn)品6產(chǎn)品7利潤max10uh11+6uh21-0.1 sh21+3uh31-0.1 sh31+4

10、uh41-0.1 sh41+uh51-0.1 sh51+9uh61-0.1 sh61+5uh71-0.1 sh71生產(chǎn)時間s.t.0.85ph11+6.92ph21+0.81ph31+ph41+0.45ph51+0.8ph61+1.23ph71£384磨床0.5ph11+0.7ph21+0.3ph51+0.2ph61+0.5ph71£3×384立式鉆床0.1 ph11+0.2ph21+0.3ph41+0.6ph61£3×384水平鉆床0.2ph11+6ph21+0.8ph31+0.6ph71£3×384鏜床0.05ph11+

11、0.02ph21+0.7ph41+0.1ph51+0.08ph71£2×384刨床0.01ph31+0.05ph51+0.05ph71£2×384變量非負約束uh11,ph11，sh11，uh21,ph21，sh21，uh31,ph31，sh31，uh41,ph41，sh41，uh51,ph51，sh51，uh61,ph61，sh61，uh71,ph71，sh71，³0二月份的生產(chǎn)計劃模型與以上模型的結(jié)構(gòu)完全相同，不同的是模型中的變量全部換成7種產(chǎn)品二月份的。二月份的生產(chǎn)計劃模型如下：產(chǎn)品1 產(chǎn)品2產(chǎn)品3產(chǎn)品4產(chǎn)品5產(chǎn)品6產(chǎn)品7利潤max10u

12、h12+6uh22-0.1 sh22+3uh32-0.1 sh32+4uh42-0.1 sh42+uh52-0.1 sh52+9uh62-0.1 sh62+5uh72-0.1 sh72生產(chǎn)時間s.t.0.85ph12+6.92ph22+0.81ph32+ph42+0.45ph52+0.8ph62+1.23ph72£384磨床0.5ph12+0.7ph22+0.3ph52+0.2ph62+0.5ph72£4×384立式鉆床0.1 ph12+0.2ph22+0.3ph42+0.6ph62£2×384水平鉆床0.2ph12+6ph22+0.8ph32

13、+0.6ph72£3×384鏜床0.05ph12+0.02ph22+0.7ph42+0.1ph52+0.08ph72£2×384刨床0.01ph32+0.05ph52+0.05ph72£2×384變量非負約束uh12,ph12，sh12，uh22,ph22，sh22，uh32,ph32，sh32，uh42,ph42，sh42，uh52,ph52，sh52，uh62,ph62，sh62，uh72,ph72，sh72，³0類似地，可以建立三月份生產(chǎn)計劃線性規(guī)劃模型：產(chǎn)品1 產(chǎn)品2產(chǎn)品3產(chǎn)品4產(chǎn)品5產(chǎn)品6產(chǎn)品7利潤max10uh1

14、3+6uh23-0.1 sh23+3uh33-0.1 sh33+4uh43-0.1 sh43+uh53-0.1 sh53+9uh63-0.1 sh63+5uh73-0.1 sh73生產(chǎn)時間s.t.0.85ph13+6.92ph23+0.81ph33+ph43+0.45ph53+0.8ph63+1.23ph73£384磨床0.5ph13+0.7ph23+0.3ph53+0.2ph63+0.5ph73£4×384立式鉆床0.1 ph13+0.2ph23+0.3ph43+0.6ph63£3×384水平鉆床0.2ph13+6ph23+0.8ph33+0

15、.6ph73£3×384鏜床0.05ph13+0.02ph23+0.7ph43+0.1ph53+0.08ph73£384刨床0.01ph33+0.05ph53+0.05ph73£2×384變量非負約束uh13,ph13，sh13，uh23,ph23，sh23，uh33,ph33，sh33，uh43,ph43，sh43，uh53,ph53，sh53，uh63,ph63，sh63，uh73,ph73，sh73，³0四月份生產(chǎn)計劃線性規(guī)劃模型：產(chǎn)品1 產(chǎn)品2產(chǎn)品3產(chǎn)品4產(chǎn)品5產(chǎn)品6產(chǎn)品7利潤max10uh14+6uh24-0.1 sh24+

16、3uh34-0.1 sh34+4uh44-0.1 sh44+uh54-0.1 sh54+9uh64-0.1 sh64+5uh74-0.1 sh74生產(chǎn)時間s.t.0.85ph14+6.92ph24+0.81ph34+ph44+0.45ph54+0.8ph64+1.23ph74£384磨床0.5ph14+0.7ph24+0.3ph54+0.2ph64+0.5ph74£4×384立式鉆床0.1 ph14+0.2ph24+0.3ph44+0.6ph64£2×384水平鉆床0.2ph14+6ph24+0.8ph34+0.6ph74£3

17、5;384鏜床0.05ph14+0.02ph24+0.7ph44+0.1ph54+0.08ph74£2×384刨床0.01ph34+0.05ph54+0.05ph74£2×384變量非負約束uh14,ph14，sh14，uh24,ph24，sh24，uh34,ph34，sh34，uh44,ph44，sh44，uh54,ph54，sh54，uh64,ph64，sh64，uh74,ph74，sh74，³0五月份生產(chǎn)計劃線性規(guī)劃模型：產(chǎn)品1 產(chǎn)品2產(chǎn)品3產(chǎn)品4產(chǎn)品5產(chǎn)品6產(chǎn)品7利潤max10uh15+6uh25-0.1 sh25+3uh35-0.1

18、sh35+4uh45-0.1 sh45+uh55-0.1 sh55+9uh65-0.1 sh65+5uh75-0.1 sh75生產(chǎn)時間s.t.0.85ph15+6.92ph25+0.81ph35+ph45+0.45ph55+0.8ph65+1.23ph75£384磨床0.5ph15+0.7ph25+0.3ph55+0.2ph65+0.5ph75£3×384立式鉆床0.1 ph15+0.2ph25+0.3ph45+0.6ph65£2×384水平鉆床0.2ph15+6ph25+0.8ph35+0.6ph75£3×384鏜床0.0

19、5ph15+0.02ph25+0.7ph45+0.1ph55+0.08ph75£2×384刨床0.01ph35+0.05ph55+0.05ph75£2×384變量非負約束uh15,ph15，sh15，uh25,ph25，sh25，uh35,ph35，sh35，uh45,ph45，sh45，uh55,ph55，sh55，uh65,ph65，sh65，uh75,ph75，sh75，³0六月份的生產(chǎn)計劃模型如下：產(chǎn)品1 產(chǎn)品2產(chǎn)品3產(chǎn)品4產(chǎn)品5產(chǎn)品6產(chǎn)品7利潤max10uh16+6uh26-0.1 sh26+3uh36-0.1 sh36+4uh46-

20、0.1 sh46+uh56-0.1 sh56+9uh66-0.1 sh66+5uh76-0.1 sh76生產(chǎn)時間s.t.0.85ph16+6.92ph26+0.81ph36+ph46+0.45ph56+0.8ph66+1.23ph76£384磨床0.5ph16+0.7ph26+0.3ph56+0.2ph66+0.5ph76£4×384立式鉆床0.1 ph16+0.2ph26+0.3ph46+0.6ph66£3×384水平鉆床0.2ph16+6ph26+0.8ph36+0.6ph76£2×384鏜床0.05ph16+0.02p

21、h26+0.7ph46+0.1ph56+0.08ph76£2×384刨床0.01ph36+0.05ph56+0.05ph76£384變量非負約束uh16,ph16，sh16，uh26,ph26，sh26，uh36,ph36，sh36，uh46,ph46，sh46，uh56,ph56，sh56，uh66,ph66，sh66，uh76,ph76，sh76，³0以上6個單期模型，共有個約束條件。5.2.2 多期模型以上6個單期模型中，目標函數(shù)中的變量是當(dāng)月各種產(chǎn)品的銷售量和儲存量，而約束條件中的變量是當(dāng)月產(chǎn)品的生產(chǎn)量。但根據(jù)題意，每一種產(chǎn)品上月末的存儲量、本月

22、的生產(chǎn)量、本月銷售量，本月末存儲量有以下關(guān)系：（上月末存儲量）+（本月生產(chǎn)量）-（本月銷售量）-（本月末存儲量）=0對于一月份，有：（一月份生產(chǎn)量）-（一月份銷售量）-（一月末存儲量）=50對于六月份，有：（五月末存儲量）+（六月份生產(chǎn)量）-（六月份銷售量）=50用以上的變量代號表示，第一種產(chǎn)品h1一月份到六月份的生產(chǎn)量、銷售量和存儲量有以下約束：ph11-uh11-sh11=-50sh11+ph12-uh12-sh12= 0sh12+ph13-uh13-sh13= 0sh13+ph14-uh14-sh14= 0sh14+ph15-uh15-sh15= 0sh15+ph16-uh16=50第二

23、種產(chǎn)品h2一月份到六月份的生產(chǎn)量、銷售量和存儲量有以下約束： ph21-uh21-sh21=-50sh21+ph22-uh22-sh22= 0sh22+ph23-uh23-sh23= 0sh23+ph24-uh24-sh24= 0sh24+ph25-uh25-sh25= 0sh25+ph26-uh26=50第三種產(chǎn)品h3一月份到六月份的生產(chǎn)量、銷售量和存儲量有以下約束： ph31-uh31-sh31=-50sh31+ph32-uh32-sh32= 0sh32+ph33-uh33-sh33= 0sh33+ph34-uh34-sh34= 0sh34+ph35-uh35-sh35= 0sh35+ph

24、36-uh36=50第四種產(chǎn)品h4一月份到六月份的生產(chǎn)量、銷售量和存儲量有以下約束： ph41-uh41-sh41=-50sh41+ph42-uh42-sh42= 0sh42+ph43-uh43-sh43= 0sh43+ph44-uh44-sh44= 0sh44+ph45-uh45-sh45= 0sh45+ph46-uh46=50第五種產(chǎn)品h5一月份到六月份的生產(chǎn)量、銷售量和存儲量有以下約束： ph51-uh51-sh51=-50sh51+ph52-uh52-sh52= 0sh52+ph53-uh53-sh53= 0sh53+ph54-uh54-sh54= 0sh54+ph55-uh55-sh

25、55= 0sh55+ph56-uh56=50第六種產(chǎn)品h6一月份到六月份的生產(chǎn)量、銷售量和存儲量有以下約束： ph61-uh61-sh61=-50sh61+ph62-uh62-sh62= 0sh62+ph63-uh63-sh63= 0sh63+ph64-uh64-sh64= 0sh64+ph65-uh65-sh65= 0sh65+ph66-uh66=50第七種產(chǎn)品h7一月份到六月份的生產(chǎn)量、銷售量和存儲量有以下約束： ph71-uh71-sh71=-50sh71+ph72-uh72-sh72= 0sh72+ph73-uh73-sh73= 0sh73+ph74-uh74-sh74= 0sh74+

26、ph75-uh75-sh75= 0sh75+ph76-uh76=50以上七組反映七種不同的產(chǎn)品一月到六月的生產(chǎn)量、銷售量、存儲量之間平衡關(guān)系的約束稱為耦合約束。以上七組耦合約束條件共有7×6=42個，連同6個月單期模型的54個約束條件，總體模型共有96個約束條件。由于庫存容量的限制，每個月7種產(chǎn)品的存儲量不能超過100件，35個存儲變量的上界為100；銷售量上限7×6=42，42個存儲變量的上限見表3。變量的上界限制在實際問題中一般不用約束條件表示，在lino中有為變量設(shè)定上界的語句。形式為：sub變量名上界值如subsh1100這樣，119個變量，96個約束條件的總體線性

27、規(guī)劃模型的結(jié)構(gòu)如下：二、lino模型和求解結(jié)果2.1、lino模型title 生產(chǎn)問題!-!目標函數(shù)=六個月產(chǎn)品（h1-h7）的銷售利潤減去六個月7種產(chǎn)品的成本max10uh11+6uh21-0.1 sh21+3uh31-0.1 sh31+4uh41-0.1 sh41+uh51-0.1 sh51+9uh61-0.1 sh61+5uh71-0.1sh71+10uh12+6uh22-0.1 sh22+3uh32-0.1 sh32+4uh42-0.1 sh42+uh52-0.1 sh52+9uh62-0.1 sh62+5uh72-0.1sh72+10uh13+6uh23-0.1 sh23+3uh33

28、-0.1 sh33+4uh43-0.1 sh43+uh53-0.1 sh53+9uh63-0.1sh63+5uh73-0.1 sh73+10uh14+6uh24-0.1 sh24+3uh34-0.1 sh34+4uh44-0.1 sh44+uh54-0.1 sh54+9uh64-0.1 sh64+5uh74-0.1 sh74+10uh15+6uh25-0.1 sh25+3uh35-0.1 sh35+4uh45-0.1 sh45+uh55-0.1 sh55+9uh65-0.1 sh65+5uh75-0.1 sh75+10uh16+6uh26-0.1 sh26+3uh36-0.1 sh36+4uh

29、46-0.1 sh46+uh56-0.1 sh56+9uh66-0.1 sh66+5uh76-0.1 sh76st!-!一月份生產(chǎn)線的生產(chǎn)時間約束（jan-time）!一月份生產(chǎn)線的磨床約束（jan-moc）!一月份立式鉆床（jan-lis）!一月份水平鉆床（jan-shu）!一月份鏜床約束（jan-tan）!一月份刨床約束（jan-bao）jan-time) 0.85ph11+6.92ph21+0.81ph31+ph41+0.45ph51+0.8ph61+1.23ph71<384jan-moc) 0.5ph11+0.7ph21+0.3ph51+0.2ph61+0.5ph71<11

30、52jan-lis) 0.1ph11+0.2ph21+0.3ph41+0.6ph61<1152jan-shu) 0.2ph11+6ph21+0.8ph31+0.6ph71<1152jan-tan) 0.05ph11+0.02ph21+0.7ph41+0.1ph51+0.08ph71<768jan-bao) 0.01ph31+0.05ph51+0.05ph71<768!-!二月份生產(chǎn)線的生產(chǎn)時間約束（feb-time）!二月份磨床約束（feb-moc）!二月份立式鉆床（feb-lis）!二月份水平鉆床約束（feb-shu）!二月份鏜床約束（feb-tan）!二月份刨床約束

31、（feb-bao）feb-time) 0.85ph12+6.92ph22+0.81ph32+ph42+0.45ph52+0.8ph62+1.23ph72<384feb-moc) 0.5ph12+0.7ph22+0.3ph52+0.2ph62+0.5ph72<1536feb-lis) 0.1 ph12+0.2ph22+0.3ph42+0.6ph62<768feb-shu) 0.2ph12+6ph22+0.8ph32+0.6ph72<1152feb-tan) 0.05ph12+0.02ph22+0.7ph42+0.1ph52+0.08ph72<768feb-bao)

32、0.01ph32+0.05ph52+0.05ph72<768!-!三月份硬質(zhì)油生產(chǎn)線的生產(chǎn)能力約束（mar-time）!三月份磨床約束（mar-moc）!三月份立式鉆床（mar-lis）!三月份水平鉆床約束（mar-shu）!三月份鏜床約束（mar-tan）!三月份刨床約束（mar-bao）mar-time) 0.85ph13+6.92ph23+0.81ph33+ph43+0.45ph53+0.8ph63+1.23ph73<384mar-moc) 0.5ph13+0.7ph23+0.3ph53+0.2ph63+0.5ph73<1536mar-lis) 0.1ph13+0.2p

33、h23+0.3ph43+0.6ph63<1152mar-shu)0.2ph13+6ph23+0.8ph33+0.6ph73<1152mar-tan)0.05ph13+0.02ph23+0.7ph43+0.1ph53+0.08ph73<384mar-bao) 0.01ph33+0.05ph53+0.05ph73<768!-!四月份硬質(zhì)油生產(chǎn)線的生產(chǎn)能力約束（apr-time）!四月份磨床約束（apr-moc）!四月份立式鉆床（apr-lis）!四月份水平鉆床約束（apr-shu）!四月份鏜床約束（apr-tan）!四月份刨床約束（apr-bao）apr-time) 0.8

34、5ph14+6.92ph24+0.81ph34+ph44+0.45ph54+0.8ph64+1.23ph74<384apr-moc) 0.5ph14+0.7ph24+0.3ph54+0.2ph64+0.5ph74<1536apr-lis) 0.1 ph14+0.2ph24+0.3ph44+0.6ph64<768apr-shu)0.2ph14+6ph24+0.8ph34+0.6ph74<1152apr-tan)0.05ph14+0.02ph24+0.7ph44+0.1ph54+0.08ph74<768apr-bao) 0.01ph34+0.05ph54+0.05ph

35、74<768!-!五月份硬質(zhì)油生產(chǎn)線的生產(chǎn)能力約束（may-time）!五月份磨床約束（may-moc）!五月份立式鉆床（may-lis）!五月份水平鉆床約束（may-shu）!五月份鏜床約束（may-tan）!五月份刨床約束（may-bao）may-time) 0.85ph15+6.92ph25+0.81ph35+ph45+0.45ph55+0.8ph65+1.23ph75<384may-moc)0.5ph15+0.7ph25+0.3ph55+0.2ph65+0.5ph75<1152may-lis)0.1 ph15+0.2ph25+0.3ph45+0.6ph65<76

36、8may-shu)0.2ph15+6ph25+0.8ph35+0.6ph75<1152may-tan)0.05ph15+0.02ph25+0.7ph45+0.1ph55+0.08ph75<768may-bao) 0.01ph35+0.05ph55+0.05ph75<768!-!六月份硬質(zhì)油生產(chǎn)線的生產(chǎn)能力約束（jun-time）!六月份磨床約束（jun-moc）!六月份立式鉆床（jun-lis）!六月份水平鉆床約束（jun-shu）!六月份鏜床約束（jun-tan）!六月份刨床約束（jun-bao）jun-time) 0.85ph16+6.92ph26+0.81ph36+ph

37、46+0.45ph56+0.8ph66+1.23ph76<384jun-moc) 0.5ph16+0.7ph26+0.3ph56+0.2ph66+0.5ph76<1536jun-lis)0.1 ph16+0.2ph26+0.3ph46+0.6ph66<1152jun-shu)0.2ph16+6ph26+0.8ph36+0.6ph76<768jun-tan)0.05ph16+0.02ph26+0.7ph46+0.1ph56+0.08ph76<768jun-bao) 0.01ph36+0.05ph56+0.05ph76<384!-!第一種產(chǎn)品（h1）相鄰兩個月的

38、生產(chǎn)量，銷售量和存儲量的平衡h1-j ) ph11-uh11-sh11=-50h1-jf) sh11+ph12-uh12-sh12=0h1-fm) sh12+ph13-uh13-sh13=0h1-ma) sh13+ph14-uh14-sh14=0h1-am) sh14+ph15-uh15-sh15=0h1-mj) sh15+ph16-uh16-sh16=0!-!第二種產(chǎn)品（h2）相鄰兩個月的生產(chǎn)量，銷售量和存儲量的平衡h2-j ) ph21-uh21-sh21=-50h2-jf ) sh21+ph22-uh22-sh22=0h2-fm ) sh22+ph23-uh23-sh23=0h2-ma

39、) sh23+ph24-uh24-sh24=0h2-am ) sh24+ph25-uh25-sh25=0h2-mj ) sh25+ph26-uh26-sh26=0!-!第三種產(chǎn)品（h3）相鄰兩個月的生產(chǎn)量，銷售量和存儲量的平衡 h3-j ) ph31-uh31-sh31=-50h3-jf )sh31+ph32-uh32-sh32=0h3-fm )sh32+ph33-uh33-sh33=0h3-ma )sh33+ph34-uh34-sh34=0h3-am )sh34+ph35-uh35-sh35=0h3-mj )sh35+ph36-uh36-sh36=0!-!第四種產(chǎn)品（h4）相鄰兩個月的生產(chǎn)量

40、，銷售量和存儲量的平衡 h4-j )ph41-uh41-sh41=-50h4-jf)sh41+ph42-uh42-sh42=0h4-fm)sh42+ph43-uh43-sh43=0h4-ma)sh43+ph44-uh44-sh44=0h4-am)sh44+ph45-uh45-sh45=0h4-mj)sh45+ph46-uh46-sh46=0!-!第五種產(chǎn)品（h5）相鄰兩個月的生產(chǎn)量，銷售量和存儲量的平衡h5-j) ph51-uh51-sh51=-50h5-jf)sh51+ph52-uh52-sh52=0h5-fm)sh52+ph53-uh53-sh53=0h5-ma)sh53+ph54-uh5

41、4-sh54=0h5-am)sh54+ph55-uh55-sh55=0h5-mj)sh55+ph56-uh56-sh56=0!-!第六種產(chǎn)品（h6）相鄰兩個月的生產(chǎn)量，銷售量和存儲量的平衡h6-j) ph61-uh61-sh61=-50h6-jf)sh61+ph62-uh62-sh62=0h6-fm)sh62+ph63-uh63-sh63=0h6-ma)sh63+ph64-uh64-sh64=0h6-am)sh64+ph65-uh65-sh65=0h6-mj)sh65+ph66-uh66-sh66=0!-!第七種產(chǎn)品（h7）相鄰兩個月的生產(chǎn)量，銷售量和存儲量的平衡h7-j) ph71-uh71

42、-sh71=-50h7-jf)sh71+ph72-uh72-sh72=0h7-fm)sh72+ph73-uh73-sh73=0h7-ma)sh73+ph74-uh74-sh74=0h7-am)sh74+ph75-uh75-sh75=0h7-mj)sh75+ph76-uh76-sh76=0!-!期末存儲量約束sh16=50sh26=50sh36=50sh46=50sh56=50sh66=50sh76=50!-end!存儲量的上限約束sub sh11 100sub sh12 100sub sh13 100sub sh14 100sub sh15 100sub sh16 100sub sh21 10

43、0sub sh22 100sub sh23 100sub sh24 100sub sh25 100sub sh26 100sub sh31 100sub sh32 100sub sh33 100sub sh34 100sub sh35 100sub sh36 100sub sh41 100sub sh42 100sub sh43 100sub sh44 100sub sh45 100sub sh46 100sub sh51 100sub sh52 100sub sh53 100sub sh54 100sub sh55 100sub sh56 100 sub sh61 100sub sh62 1

44、00sub sh63 100sub sh64 100sub sh65 100sub sh66 100sub sh71 100sub sh72 100sub sh73 100sub sh74 100sub sh75 100sub sh76 100!銷售量的上限約束sub uh11 500sub uh12 400sub uh13 300sub uh14 200sub uh15 0sub uh16 500sub uh21 1000sub uh22 500sub uh23 600sub uh24 300sub uh25 100sub uh26 500sub uh31 300sub uh32 200su

45、b uh33 0sub uh34 400sub uh35 500sub uh36 100sub uh41 300sub uh42 0sub uh43 0sub uh44 500sub uh45 100sub uh46 300sub uh51 800sub uh52 400sub uh53 500sub uh54 200sub uh55 1000sub uh56 1100 sub uh61 200sub uh62 300sub uh63 400sub uh64 0sub uh65 300sub uh66 500sub uh71 100sub uh72 150sub uh73 100sub uh7

46、4 100sub uh75 0sub uh76 602.2、lino求解結(jié)果 lp optimum found at step 67 objective function value 1) 25234.02variable valuereducedcostuh11500.000000-0.437500uh210.0000000.000000sh2150.0000000.000000uh3150.0000000.000000sh310.0000000.000000uh4150.0000000.000000sh410.0000000.000000uh510.0000000.000000sh5150

47、.0000000.000000uh6150.0000000.000000sh610.0000000.100000uh7150.0000000.000000sh710.0000000.100000uh12400.000000-0.437500uh220.0000000.100000sh2250.0000000.000000uh320.0000000.100000sh320.0000000.000000uh420.0000000.100000sh420.0000000.000000uh520.0000000.100000sh5250.0000000.000000uh6256.8750000.000000sh620.0000000.100000uh720.0000000.000000sh720.0000000.100000uh13300.000000-0.437500uh230.0000000.20000