?????LINGO????

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??????(2008?7?,??) ?????LINGO????
??? ????????? Tel [phone] Email
jxie_at_math.tsinghua.edu.cn http//faculty.math.tsi
nghua.edu.cn/jxie/lindo
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????

• 1. ??????
• 2. LINGO????
• 3. ???????

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1. ??????
4
??????????????
(?)????????,???????(?)???

• OR/MS/DS???OR(???,Operations/-al Research)
  
• MS(????,Management Science)
  
• DS(????,Decision Science)
• ????/????/????/?????????

????/???????

• ???,???

• ????,????

• ??????(????),?????(??)

CUMCM??50?????,???,?????
5
?????????
???????????????????

• ???(????)????(??????)
• ???(????/??????)

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??????????????
?????? f(x),?? x ?? f(x)??,?
?????
?????
?????????????????????????
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????? ????
????
????

• ????(LP) ???????????
• ?????(NLP) ?????????????
• ????(QP) ?????????????
• ????(IP) ????(?????)???
• ??????(ILP),???????(INLP)
• ?????(PIP), ??????(MIP)
• ??????,0-1(??)??

????
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??(Optimization), ??(Programming)
?????
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?????
?????
????
????
????
????
????
????
????
????
???????
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Optimization Tree http//www-fp.mcs.anl.gov/otc/G
uide/OptWeb/
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?????????

• ??1????,????
• ---- ????????????????
• ---- ???????,??????
• ---- ????/????,??????/????
• ----
• ??2????,????
• ---- ????????????????
• ---- ????????,??????????
• ---- ??????? / ??
• ----

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??????????????
1?????????,??????????? 2?????????,??????????
??????????????????????/?????????????? 3????????
?,???????????????? (?x/y lt5
??xlt5y) 4??????????,?????????? 5???????????????
(???103)
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??????

• 1. LINGO??
• 2. MATLAB?????
• 3. EXCEL???????
• 4. SAS(????)???????
• 5. ??

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MATLAB?????????????
?????3.0 (MATLAB 7.0 R14)
?0-1?? bintprog ??IP(??)
????
????
?????
????
??? ?? fminunc
???(?? ?)?? fminsearch
???? linprog
???? quadprog
??? ??(?) fzero fsolve
?? ?? ??
??? ???? lsqnonlin lsqcurvefit
????? fmincon fminimax fgoalattain fseminf
????? fminbnd fmincon lsqnonlin lsqcurvefit
???? ???? lsqnonneg lsqlin
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• 2. LINGO????

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LINDO ??????????
?????(Chicago)???Linus Schrage???1980?????, ????
LINDO????(LINDO Systems Inc.), ??http//www.lindo
.com
LINGO Linear INteractive General Optimizer
(V11.0) LINDO API LINDO Application
Programming Interface (V4.0) Whats Best!
(SpreadSheet e.g. EXCEL)
(V8.0)
??(??)????????????????????? (???????????)
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LINDO?LINGO??????????
????
????(IP)
????

LINGO
LINDO(????)
???? (LP)
???? (QP)
????? (NLP)
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LINGO????
LINGO?????

• ?????(???) / ??(??) ????
• ??????
• ?????? / ??????
• ??????????(?????),????????
• ????????????(?TEXT, EXCEL, ODBC?????)
• ????????????
• LINDO API ???????

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LINGO???????
LINGO?????
1. ???? 2. ????
LP QP NLP IP ????(?)
ILP
IQP INLP

????????
????????
?????????
1????????(SLP) 2????????(GRG) (?)
3?????(Multistart) (?)
1. ????? 2. ????(?)
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LINGO?????6??

• ??????
• ???(SETS ENDSETS)
• ???(DATA ENDDATA)
• ???(INIT ENDINIT)
• ???(CALC ENDCALC)---- 9.0
• ???(SUBMODEL ENDSUBMODEL)
• 
  ---- 10.0

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LINGO???????
LINGO?????
1. ???? 2. ????
LP QP NLP IP ????(?)
ILP
IQP INLP

????????
????????
?????????
1????????(SLP) 2????????(GRG) (?)
3?????(Multistart) (?)
1. ????? 2. ????(?)
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LINGO?? ?????
????6?????,?????(ai, bi) (????),?????di (???)
??????????????
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????ci j (??j???i???)12?
??????
???????,????
??????136.2
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????NLP
2)???????,?????????(xj,yj)???cij
,?????????????????
???? ci j,(xj,yj)16?
???????
??Location.lg4
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LINGO?????4??
???(SETS ENDSETS)
???(DATA ENDDATA)
???(INIT ENDINIT)
LP?????
??? ???
????89.8835(??? )
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??
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?????
setname(parent_set_list) /member_list/
attribute_list
setname /member_list/ attribute_list
??
???? ????
???? ???? ????? ????? ?????
?????
SETS CITIES /A1,A2,A3,B1,B2/ ROADS(CITIES,
CITIES)/ A1,B1 A1,B2 A2,B1 A3,B2/D
ENDSETS
SETS STUDENTS /S1..S8/ PAIRS( STUDENTS,
STUDENTS) 2 GT 1 BENEFIT, MATCH ENDSETS
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?????????
?? ?????? ?? ???????
??? 1..n 1..5 1, 2, 3, 4, 5
??-??? stringM..stringN Car101..car208 Car101, car102, , car208
??? dayM..dayN MON..FRI MON, TUE, WED, THU, FRI
??? monthM..monthN OCT..JAN OCT, NOV, DEC, JAN
??-??? monthYearM..monthYearN OCT2001..JAN2002 OCT2001, NOV2001, DEC2001, JAN2002
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???????
????? ????? ????? ?????
??? ???
?? NOT (??)

/
(??)
EQ NE GT GE LT LE
AND OR
?? lt() gt()
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??????
????????FOR?SUM ? MAX?MIN _at_function( setname (
set_index_list) condition expression_list)
Example
objective MAX _at_SUM( PAIRS( I, J) BENEFIT( I,
J) MATCH( I, J)) _at_FOR(STUDENTS( I)
constraints _at_SUM( PAIRS( J, K) J EQ I
OR K EQ I MATCH( J, K)) 1) _at_FOR(PAIRS( I,
J) _at_BIN( MATCH( I, J))) MAXB_at_MAX(PAIRS( I,
J) BENEFIT( I, J)) MINB_at_MIN(PAIRS( I, J)
BENEFIT( I, J))
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????
Model Class LP, QP,ILP, IQP,PILP,
PIQP,NLP,INLP,PINLP

• State
• Global Optimum
• Local Optimum
• Feasible
• Infeasible
• Unbounded
• Interrupted
• Undetermined

• Solver Type
• B-and-B
• Global
• Multistart

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7????(???80-90?????)
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????????

• Cut (or Copy) Paste ??
• _at_FILE ?????_at_TEXT????(????)
• _at_OLE?????????(?EXCEL)??
• _at_ODBC????????
• LINGO??????

???????

• LG4 (LONGO????)
• LNG (LONGO????)
• LTF (LONGO????)
• LDT (LONGO????)
• LRP (LONGO????)

? ? ? ?
??????
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• 3. ???????(??????)

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???????
????? ???? ???? DVD??
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? ?????
????T????
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?? ????????
VOR1 x764, y1393
?
161.20 (0.80)
DME x155, y987
864.3(2.0)
?? x?, y?
VOR3 x1571, y259
45.10 (0.60)
y
VOR2 x629, y375
x
309.00 (1.30)
0
??????(???????????????)
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????????
xi yi ??? (?d4)
VOR1 746 1393 161.20(2.81347??) 0.80(0.0140??)
VOR2 629 375 45.10 (0.78714??) 0.60(0.0105??)
VOR3 1571 259 309.00(5.39307??) 1.30(0.0227??)
DME 155 987 d4864.3(km) 2.0(km)
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?????????
?1??? ???????
?????,???????!
????! ?
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????????
?2??? ??????(?????)
?
?????
???????!
Min x Min y Max x Max y.
????????????,?
??????,????????(????) ???????,??????.
? ???????! ????????????!
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????????
?3??? ??????(?????) ????
???????????
??????????
????!
?????!
????????????
?????????,??? Matlab?atan2??, ??(-pi, pi)
shili0702.m
????(978.31,723.98), ?????0.6685 (ltlt 4)
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????????
??? LINGO???atan2??, ????
??????_at_tan??!
exam0507c.lg4
??????/??
exam0507d.lg4
?? ??????

• ????(980.21,727.30 ), ?????2.6
• ??????????, ???? ????????

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???????
??MRP(MRP-II)????????
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??????????
??N, T, s, h, d, r, a, C
Min s.t.
?? exam0502.lg4
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?DVD????
??DVD????,??????3? ??????100?DVD?????????????10
00????????(?????http//mcm.edu.cn/mcm05/problems20
05c.asp) ???????DVD????,??????????????
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EXCEL??????
DVD?? DVD?? D001 D002 D003 D004
DVD???? DVD???? 10 40 15 20
?????? C0001 6 0 0 0
?????? C0002 0 0 0 0
?????? C0003 0 0 0 3
?????? C0004 0 0 0 0
??????
???????????????,??0?????DVD????????????
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??
???sij?? ??,?sij 1-aij/11
(aij 0?sij 0)

,
,
,
?? Dvd_1000_100.lg4
? lt
,
?
0-1????10001001000101000
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CUMCM??????(??http//mcm.edu.cn)
?????? ?????? ?????? ?????? ??
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??????

• ???, ?? ?????LINDO/LINGO??,
• ???????, 2005?7???.
• http//faculty.math.tsinghua.edu.cn/jxie
  /lindo
• ???,???,???, ??? ??????,
• ???????, 2005?2???.
• http//mathexp.math.tsinghua.edu.cn
• ?????????
• ?????????????????(1992-2000)?????,2001.
• ????????(2000????)
• ?????? (2001????)

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Thank you for your attendance!
??,???
???????? ???????!
Thats all. Any Questions?
?????????? ???, 2008.