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Ically mathematical programuvannya - Nakonechny S.І.
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Ically mathematical programuvannya - Nakonechny S.І.
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Nakonechny S. I., Savіna SS H-22 ically mathematical programuvannya: Navch. posіb. - K .: KNEU, 2003. - 452 p. ISBN 966-574-538-7 The Teaching posіbnik vіdpovіdno written to prog course "ically mathematical programuvannya" for pіdgotovki bakalavrіv s Economy. In posіbniku rozglyadayutsya osnovnі matematichnі methodical that modelі doslіdzhennya ekonomіchnih systems that protsesіv scho Yea the basis of acceptance for obґruntovanih upravlіnskih rіshen in real minds. Rozdіli s Perche on p'yaty prisvyachenі tasks lіnіynogo programuvannya, teorії dvoїstostі, ekonomіchnomu analіzu planіv optimally. W Shostya on odinadtsyaty rozdіli rozglyadayutsya skladnіshі zadachі ically mathematical programuvannya: tsіlochislovі, Nonlinear, dinamіchnі, stohastichnі, shot-lіnіynі, zadachі teorії Igor. Theoreticity materіal іlyustruєtsya numeric ekonomіko-ically mathematical models adequately SSMSC vіdobrazhayut osnovnі virobnicho-ekonomіchnі processes. In kіlkoh rozdіlah imposed ponadprogramny materіal. Rekomenduєtsya for bakalavrіv unіversitetіv s napryamku "Ekonomіka i pіdpriєmnitstvo" she studentіv іnshih The Teaching zakladіv, SSMSC vivchayut course "ically mathematical programuvannya" that "Doslіdzhennya operatsіy" and takozh for sluhachіv rіznih kursіv i shkіl pіdvischennya kvalіfіkatsії for ekonomіstіv. BBK 22.18 |
ZMІST
PEREDMOVA
ROZDІL 1. SUBJECT, SCOPE TA OSOBLIVOSTІ ZASTOSUVANNYA ically mathematical PROGRAMUVANNYA In EKONOMІTSІ. KLASIFІKATSІYA PROBLEMS
1.1. The subject is the ob'єkti ically mathematical programuvannya
1.2. Ically mathematical formulation zadachі ically mathematical programuvannya
1.3. Butt-ekonomіko matematichnoї modelі
1.4. Bagatokriterіalna optimіzatsіya
1.5. Іstorichna dovіdka
1.6. Klasifіkatsіya ically mathematical tasks programuvannya
1.7. Butt ekonomіchnih ically mathematical tasks programuvannya
2. OBJECTIVE ROZDІL ZAGALNA LІNІYNOGO PROGRAMUVANNYA TA DEYAKІ W METODІV ЇЇ ROZV'YAZUVANNYA
2.1. Butt pobudovi ekonomіko-ically mathematical models ekonomіchnih protsesіv that yavisch
2.2. Zagalna ekonomіko-ically mathematical model zadachі lіnіynogo programuvannya
2.3. Form of writing tasks lіnіynogo programuvannya
2.4. Geometric іnterpretatsіya zadachі lіnіynogo programuvannya
2.5. Osnovnі vlastivostі rozv'yazkіv zadachі lіnіynogo programuvannya
2.6. Grafіchny method rozv'yazuvannya tasks lіnіynogo programuvannya
2.8. Simplex method rozv'yazuvannya tasks lіnіynogo programuvannya
2.8.1. Pochatkova support program
2.8.2. Perehіd od one support plan to іnshogo
2.8.3. Optimally rozv'yazok. Kriterіy optimalnostі plan
2.8.4. Rozv'yazuvannya zadachі lіnіynogo programuvannya simplex method
2.8.6. The method of block basis
2.8.7. Fixated in problems lіnіynogo programuvannya
2.8.8. Іnterpretatsіya geometric simplex method
2.9. Modifіkatsії simplex method
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
3. ROZDІL TEORІYA DVOЇSTOSTІ TA DVOЇSTІ OTSІNKI have LІNІYNOMU PROGRAMUVANNІ
3.1. Ekonomichna іnterpretatsіya pryamoї that dvoїstoї tasks lіnіynogo programuvannya
3.2. Rules pobudovi dvoїstih tasks
3.3. Osnovnі theorem dvoїstostі that їh ekonomіchny zmіst
3.3.1. Persha theorem dvoїstostі
3.3.2. Another theorem dvoїstostі
3.3.3. Third theorem dvoїstostі
3.4. Butt zastosuvannya teorії dvoїstostі for znahodzhennya optimally planіv pryamoї that dvoїstoї tasks
3.5. Pіslyaoptimіzatsіyny analіz tasks lіnіynogo programuvannya
3.5.1. Analіz dіapazonu zmіni vector components obmezhen
3.5.2. Analіz dіapazonu zmіni koefіtsієntіv tsіlovoї funktsії
3.5.3. Analіz dіapazonu zmіni koefіtsієntіv matritsі obmezhen
3.6. Dvoїsty simplex method
3.7. the parame- programuvannya
3.7.1. Parametrichnі zmіni vector obmezhen
3.7.2. Parametrichnі zmіni vector koefіtsієntіv tsіlovoї funktsії
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
4. ROZDІL ANALІZ LІNІYNIH MODELS EKONOMІCHNIH PROBLEMS
4.1. Butt ekonomіchnoї іnterpretatsії bet conjugation tasks
4.2. Analіz rozv'yazkіv conjugation ekonomіko-ically mathematical problems
4.3. Otsіnka rentabelnostі produktsії, yak viroblyaєtsya, i novoї produktsії
4.4. Analіz obmezhen defіtsitnih i nedefіtsitnih resursіv
4.5. Analіz koefіtsієntіv tsіlovoї funktsії
4.6. Analіz koefіtsієntіv matritsі obmezhen
4.7. Butt practical vikoristannya dvoїstih otsіnok in analіzі ekonomіchnoї zadachі
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
5. ROZDІL transport problems
5.1. Ekonomichna i ically mathematical formulation transportnoї zadachі
5.2. Vlastivostі reference planіv transportnoї zadachі
5.3. Metodi pobudovi support plan transportnoї zadachі
5.4. Vipadok virodzhennya support plan transportnoї zadachі
5.5. Metodi rozv'yazuvannya transportnoї zadachі
5.5.1. The task dvoїsta to transportnoї
5.5.2. Method potentsіalіv rozv'yazuvannya transportnoї zadachі
5.5.3. Monotonnіst i skіnchennіst method potentsіalіv
5.5.4. Butt rozv'yazuvannya transportation problem by potentsіalіv
5.5.5. Ugorsky method rozv'yazuvannya transportnoї zadachі
5.6. Transport problems dodatkovimi s minds
5.7. Two-stage transport problems
5.8. Transportation problem for kriterієm hour
5.9. Rozv'yazuvannya transportnoї zadachі on MEREZHI
5.9.1. Transport problems in merezhevіy formі
5.9.2. Potentsіalіv method for MEREZHI
5.10. Butt ekonomіchnih tasks scho zvodyatsya to transport model
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
6. ROZDІL TSІLOCHISLOVІ ZADACHІ LІNІYNOGO PROGRAMUVANNYA. OSNOVNІ Method ЇH ROZV'YAZUVANNYA TA ANALІZU
6.1. Ekonomichna i ically mathematical formulation tsіlochislovoї zadachі lіnіynogo programuvannya
6.2. Geometric іnterpretatsіya rozv'yazkіv tsіlochislovih tasks lіnіynogo programuvannya on ploschinі
6.3. Zagalna characteristic metodіv rozv'yazuvannya tsіlochislovih tasks lіnіynogo programuvannya
6.4. Metodi vіdtinannya. Gomorі method
6.5. Kombіnatornі methods. Gіlok method that between
6.6. Nablizhenі methods. Method recession vector
6.7. Butt zastosuvannya tsіlochislovih tasks lіnіynogo programuvannya in planuvannі that upravlіnnі virobnitstvom
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
7. ROZDІL ZADACHІ shot-LІNІYNOGO PROGRAMUVANNYA. OSNOVNІ Method ЇH ROZV'YAZUVANNYA TA ANALІZU
7.1. Ekonomichna i ically mathematical formulation zadachі shot-lіnіynogo programuvannya
7.2. Geometric іnterpretatsіya zadachі shot-lіnіynogo programuvannya
7.3. Rozv'yazuvannya shot-lіnіynoї zadachі Institution to zadachі lіnіynogo programuvannya
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
8. ROZDІL ZADACHІ NELІNІYNOGO PROGRAMUVANNYA. OSNOVNІ Method ЇH ROZV'YAZUVANNYA TA ANALІZU
8.1. Ekonomichna i ically mathematical formulation zadachі nelіnіynogo programuvannya
8.2. Geometric іnterpretatsіya zadachі nelіnіynogo programuvannya
8.3. Osnovnі trudnoschі rozv'yazuvannya tasks nelіnіynogo programuvannya
8.4. Klasichny optimіzatsії method. The method of Lagrange mnozhnikіv
8.4.1. Umovny that bezumovny ekstremumi funktsії
8.4.2. The method of Lagrange mnozhnikіv
8.5. Neobhіdnі minds іsnuvannya sіdlovoї point
8.6. Kuhn-Tucker theorem
8.6.1. Opuklі th ugnutі funktsії
8.7. Opukle programuvannya
8.8. quadratic programuvannya
8.8.1. Quadratic forms that її vlastivostі
8.8.2. Method rozv'yazuvannya tasks quadratic programuvannya
8.9. Ekonomichna іnterpretatsіya Lagrange mnozhnikіv
8.10. Gradієntny method
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
9. ROZDІL DINAMІCHNE PROGRAMUVANNYA
9.1. Ekonomichna sutnіst tasks dinamіchnogo programuvannya
9.2. The problem about rozpodіl kapіtalovkladen mіzh EYAD pіdpriєmstvami by n rokіv
9.2.1. Method recurrently spіvvіdnoshen
9.3. The problem about rozpodіl kapіtalovkladen mіzh pіdpriєmstvami
9.4. optimalnostі principle
9.5. Bagatokrokovy processes of acceptance rіshen
9.6. Butt rozv'yazuvannya tasks dinamіchnogo programuvannya
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
ROZDІL 10. stochasticity PROGRAMUVANNYA
10.1. Zagalna ically mathematical formulation zadachі stochasticity programuvannya
10.2. Osoblivostі matematichnoї tasking stochasticity programuvannya
10.3. Butt ekonomіchnih tasks stochasticity programuvannya
10.4. Odnoetapnі zadachі stochasticity programuvannya
10.5. Dvohetapnі zadachі stochasticity programuvannya
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
ROZDІL 11. TEORІYA Igor
11.1. Osnovnі ponyattya teorії Igor
11.2. Klasifіkatsіya Igor
11.3. Matrichnі іgri dvoh osіb
11.4. Gras Zi zmіshanimi strategіyami
11.5. Geometric іnterpretatsіya gris 2 x 2
11.6. Institution matrichnoї gris to zadachі lіnіynogo programuvannya
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
RECOMMENDED literature
ROZDІL 1. SUBJECT, SCOPE TA OSOBLIVOSTІ ZASTOSUVANNYA ically mathematical PROGRAMUVANNYA In EKONOMІTSІ. KLASIFІKATSІYA PROBLEMS
1.1. The subject is the ob'єkti ically mathematical programuvannya
1.2. Ically mathematical formulation zadachі ically mathematical programuvannya
1.3. Butt-ekonomіko matematichnoї modelі
1.4. Bagatokriterіalna optimіzatsіya
1.5. Іstorichna dovіdka
1.6. Klasifіkatsіya ically mathematical tasks programuvannya
1.7. Butt ekonomіchnih ically mathematical tasks programuvannya
2. OBJECTIVE ROZDІL ZAGALNA LІNІYNOGO PROGRAMUVANNYA TA DEYAKІ W METODІV ЇЇ ROZV'YAZUVANNYA
2.1. Butt pobudovi ekonomіko-ically mathematical models ekonomіchnih protsesіv that yavisch
2.2. Zagalna ekonomіko-ically mathematical model zadachі lіnіynogo programuvannya
2.3. Form of writing tasks lіnіynogo programuvannya
2.4. Geometric іnterpretatsіya zadachі lіnіynogo programuvannya
2.5. Osnovnі vlastivostі rozv'yazkіv zadachі lіnіynogo programuvannya
2.6. Grafіchny method rozv'yazuvannya tasks lіnіynogo programuvannya
2.8. Simplex method rozv'yazuvannya tasks lіnіynogo programuvannya
2.8.1. Pochatkova support program
2.8.2. Perehіd od one support plan to іnshogo
2.8.3. Optimally rozv'yazok. Kriterіy optimalnostі plan
2.8.4. Rozv'yazuvannya zadachі lіnіynogo programuvannya simplex method
2.8.6. The method of block basis
2.8.7. Fixated in problems lіnіynogo programuvannya
2.8.8. Іnterpretatsіya geometric simplex method
2.9. Modifіkatsії simplex method
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
3. ROZDІL TEORІYA DVOЇSTOSTІ TA DVOЇSTІ OTSІNKI have LІNІYNOMU PROGRAMUVANNІ
3.1. Ekonomichna іnterpretatsіya pryamoї that dvoїstoї tasks lіnіynogo programuvannya
3.2. Rules pobudovi dvoїstih tasks
3.3. Osnovnі theorem dvoїstostі that їh ekonomіchny zmіst
3.3.1. Persha theorem dvoїstostі
3.3.2. Another theorem dvoїstostі
3.3.3. Third theorem dvoїstostі
3.4. Butt zastosuvannya teorії dvoїstostі for znahodzhennya optimally planіv pryamoї that dvoїstoї tasks
3.5. Pіslyaoptimіzatsіyny analіz tasks lіnіynogo programuvannya
3.5.1. Analіz dіapazonu zmіni vector components obmezhen
3.5.2. Analіz dіapazonu zmіni koefіtsієntіv tsіlovoї funktsії
3.5.3. Analіz dіapazonu zmіni koefіtsієntіv matritsі obmezhen
3.6. Dvoїsty simplex method
3.7. the parame- programuvannya
3.7.1. Parametrichnі zmіni vector obmezhen
3.7.2. Parametrichnі zmіni vector koefіtsієntіv tsіlovoї funktsії
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
4. ROZDІL ANALІZ LІNІYNIH MODELS EKONOMІCHNIH PROBLEMS
4.1. Butt ekonomіchnoї іnterpretatsії bet conjugation tasks
4.2. Analіz rozv'yazkіv conjugation ekonomіko-ically mathematical problems
4.3. Otsіnka rentabelnostі produktsії, yak viroblyaєtsya, i novoї produktsії
4.4. Analіz obmezhen defіtsitnih i nedefіtsitnih resursіv
4.5. Analіz koefіtsієntіv tsіlovoї funktsії
4.6. Analіz koefіtsієntіv matritsі obmezhen
4.7. Butt practical vikoristannya dvoїstih otsіnok in analіzі ekonomіchnoї zadachі
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
5. ROZDІL transport problems
5.1. Ekonomichna i ically mathematical formulation transportnoї zadachі
5.2. Vlastivostі reference planіv transportnoї zadachі
5.3. Metodi pobudovi support plan transportnoї zadachі
5.4. Vipadok virodzhennya support plan transportnoї zadachі
5.5. Metodi rozv'yazuvannya transportnoї zadachі
5.5.1. The task dvoїsta to transportnoї
5.5.2. Method potentsіalіv rozv'yazuvannya transportnoї zadachі
5.5.3. Monotonnіst i skіnchennіst method potentsіalіv
5.5.4. Butt rozv'yazuvannya transportation problem by potentsіalіv
5.5.5. Ugorsky method rozv'yazuvannya transportnoї zadachі
5.6. Transport problems dodatkovimi s minds
5.7. Two-stage transport problems
5.8. Transportation problem for kriterієm hour
5.9. Rozv'yazuvannya transportnoї zadachі on MEREZHI
5.9.1. Transport problems in merezhevіy formі
5.9.2. Potentsіalіv method for MEREZHI
5.10. Butt ekonomіchnih tasks scho zvodyatsya to transport model
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
6. ROZDІL TSІLOCHISLOVІ ZADACHІ LІNІYNOGO PROGRAMUVANNYA. OSNOVNІ Method ЇH ROZV'YAZUVANNYA TA ANALІZU
6.1. Ekonomichna i ically mathematical formulation tsіlochislovoї zadachі lіnіynogo programuvannya
6.2. Geometric іnterpretatsіya rozv'yazkіv tsіlochislovih tasks lіnіynogo programuvannya on ploschinі
6.3. Zagalna characteristic metodіv rozv'yazuvannya tsіlochislovih tasks lіnіynogo programuvannya
6.4. Metodi vіdtinannya. Gomorі method
6.5. Kombіnatornі methods. Gіlok method that between
6.6. Nablizhenі methods. Method recession vector
6.7. Butt zastosuvannya tsіlochislovih tasks lіnіynogo programuvannya in planuvannі that upravlіnnі virobnitstvom
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
7. ROZDІL ZADACHІ shot-LІNІYNOGO PROGRAMUVANNYA. OSNOVNІ Method ЇH ROZV'YAZUVANNYA TA ANALІZU
7.1. Ekonomichna i ically mathematical formulation zadachі shot-lіnіynogo programuvannya
7.2. Geometric іnterpretatsіya zadachі shot-lіnіynogo programuvannya
7.3. Rozv'yazuvannya shot-lіnіynoї zadachі Institution to zadachі lіnіynogo programuvannya
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
8. ROZDІL ZADACHІ NELІNІYNOGO PROGRAMUVANNYA. OSNOVNІ Method ЇH ROZV'YAZUVANNYA TA ANALІZU
8.1. Ekonomichna i ically mathematical formulation zadachі nelіnіynogo programuvannya
8.2. Geometric іnterpretatsіya zadachі nelіnіynogo programuvannya
8.3. Osnovnі trudnoschі rozv'yazuvannya tasks nelіnіynogo programuvannya
8.4. Klasichny optimіzatsії method. The method of Lagrange mnozhnikіv
8.4.1. Umovny that bezumovny ekstremumi funktsії
8.4.2. The method of Lagrange mnozhnikіv
8.5. Neobhіdnі minds іsnuvannya sіdlovoї point
8.6. Kuhn-Tucker theorem
8.6.1. Opuklі th ugnutі funktsії
8.7. Opukle programuvannya
8.8. quadratic programuvannya
8.8.1. Quadratic forms that її vlastivostі
8.8.2. Method rozv'yazuvannya tasks quadratic programuvannya
8.9. Ekonomichna іnterpretatsіya Lagrange mnozhnikіv
8.10. Gradієntny method
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
9. ROZDІL DINAMІCHNE PROGRAMUVANNYA
9.1. Ekonomichna sutnіst tasks dinamіchnogo programuvannya
9.2. The problem about rozpodіl kapіtalovkladen mіzh EYAD pіdpriєmstvami by n rokіv
9.2.1. Method recurrently spіvvіdnoshen
9.3. The problem about rozpodіl kapіtalovkladen mіzh pіdpriєmstvami
9.4. optimalnostі principle
9.5. Bagatokrokovy processes of acceptance rіshen
9.6. Butt rozv'yazuvannya tasks dinamіchnogo programuvannya
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
ROZDІL 10. stochasticity PROGRAMUVANNYA
10.1. Zagalna ically mathematical formulation zadachі stochasticity programuvannya
10.2. Osoblivostі matematichnoї tasking stochasticity programuvannya
10.3. Butt ekonomіchnih tasks stochasticity programuvannya
10.4. Odnoetapnі zadachі stochasticity programuvannya
10.5. Dvohetapnі zadachі stochasticity programuvannya
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
Butts that zavdannya samostіynoї for robots
ROZDІL 11. TEORІYA Igor
11.1. Osnovnі ponyattya teorії Igor
11.2. Klasifіkatsіya Igor
11.3. Matrichnі іgri dvoh osіb
11.4. Gras Zi zmіshanimi strategіyami
11.5. Geometric іnterpretatsіya gris 2 x 2
11.6. Institution matrichnoї gris to zadachі lіnіynogo programuvannya
Zaklyuchnі zauvazhennya
Kontrolnі zapitannya
RECOMMENDED literature
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