OPERACIJU TYRIMAS, LOSIMU IR RINKOS TEORIJA

Prof., hab.dr. J.Mockus - 45 akademines valandos paskaitu
                        - 22.5 val. laboratoriniu darbu

15 savaiciu semestras

Santrauka

Nagrinejami  praktiskai svarbus operaciju tyrimo, losimu ir rinkos teorijos uzdaviniai  bei ju sprendimo
metodai:
- Losimu teorija
- Naudingumo teorija
- Sprendimu teorija 
- Tvarkarasciu teorija

Sie klausimai iliustruojami nagrinejant astuonis 
specifinius matematinius modelius 
- Konkurencijos modelis (Nash'o pusiausvyra)
- Konkurencijos modelis ivertinant resursu kainas (Walras'o pusiausvyra)
- Portfelio uzdavinys (optimalus investavimas)
- Vertybiniu popieriu kurso modelis (ARMA) 
- Inspektoriaus modelis (daugiazingsnis losimas)
- Dvikovos modelis (diferencialinis losimas)
- Nuotakos uzdavinys (nuoseklus statististiniai sprendimai)
- Tvarkarascio modelis (Bayes'o heuristinis poziuris)

Panasus modeliai buvo nagrineti optimizavimo metodu kurse kaip  optimizavimo pavyzdziai. Siame kurse sie uzdavinai bus tiriami
kaip charakteringi operaciju tyrimo bei losimu ir rinkos teorijos modeliai iliustruojant praktines teorijos galimybes.

Kiekvienas studentas isprendzia bent viena savo pasirinkta uzdavini naudodami priemones ir pavyzdzius pateiktus mokymo tinklapyje
http://soften.ktu.lt/~mockus

LITERATURA

J. Rosenmuller, 
"The Theory of Games and Markets", 
North-Holand, Amsterdam, 1981

J. Mockus et al.,
"Bayesian Heuristic Approach to Discrete and Global Optimization"
Kluwer Academic Publishers, Boston, 1997,
eletronic archive 'bookps.tgz' in ftp anonymous:
pit.ktu.lt/pub/optimum

J. Mockus, "A Set of Examples of Global and Discrete Optimization: Application of Bayesian Heuristic Approach",
Kluwer Academic Publishers, Dordrecht-Boston-London, 2000 ,
electronic version 'stud2.pdf' in the web-site:
http://soften.ktu.lt/~mockus


A.Zilinskas, V.Saltenis,
"Poisk optimuma", 
Hauka, Moskva, 1989

V.Saltenis, A.Zilinskas, 
"Techniniu optimizavimo uzdaviniu sprendimas", 
Vilnius, Mokslas, 1986

A. Zilinskas
"Naujieji projektavimo metodai"
Vilnius, Mokslas, 1990

F. Peldschus, E.K. Zavadskas
"Matriciniai losimai technologijoje ir vadyboje"
Vilnius, Technika, 1997

E.S. Ventcel, 
"Issledovanioe operacii"
Sovetskoe Radio, Moskva, 1972.

E.S. Ventcel, 
"Issledovanioe operacii"
Sovetskoe Radio, Moskva, 1972.

D. Himmelblau, 
"Prikladnoe nelineinoe programmirovanie", 
Mir, Moskva, 1975

G. Owen, 
"Teorija igr", 
Mir", Moskva, 1971.

M. De Groot, 
"Optimalnye statisticeskie resenija", 
Mir, Moskva, 1974.

Ju. M. Ermoljev, 
"Metody stochasticeskovo programmirovanija", 
Hauka, Moskva, 1976.

B.V. Gnedenko, I.N.Kovalenko, 
"Vvedenie v teoriju massovovoobsluzivanija", 
Nauka, Moskva, 1987.

James O. Berger, 
"Statistical Decision Theory and Bayesian Analysis",
Springer-Verlag, New York, 1985

Yu. Ermoljev, R. Wets, 
"Numerical Techniques for StochasticOptimization", 
Springer-Verlag, Berlin,1980.

E.G.Davydov, 
"Issledovanie Operacii", 
Vyssaja skola, Moskva, 1990.

Michael J. Tod, 
"The Computation of Fixed Points and Applications",
Springer-Verlag, Berlin, 1976.

J. Mockus, Optimization Problems in Simple Competitive Model,
INFORMATICA, vol 5, No 1-2, 1994, p. 167-174

A. Mockus, J. Mockus, L. Mockus, Bayesian Approach Adapting Stochastic and Heuristic Methods of Global and Discrete Optimization,
INFORMATICA, vol 5, N0 1-2, 1994, p. 123-165. 

J. Mockus,
"A set of examples of global and discrete optimization: application of Bayesian heuristic approach I",
Informatica, 
vol 8,
p 237-264,
num 2, 1997

J. Mockus,
"A set of examples of global and discrete optimization: application of Bayesian heuristic approach II",
Informatica, 
vol 8,
p 495-526,
num 4, 1997


EGZAMINAI:  1 (po 15 savaiciu)

KONTROLINIAI DARBAI: 1 (po 8 savaiciu)


Resume

The following important topics of operations research are regarded.
- Games theory
- Decision theory
- Utility theory
- Queuing theory
- Scheduling theory

These topics are illustrated considering eight specific mathematical models.
- Competition model (Nash equilibrium)
- Competition model including resource prices (Walras equilibrium)
- Portfolio problem (optimal investment)
- Exchange rate model (ARMA)
- Inspection model (multi-stage game)
- Duel model (differential game)
- Bride's problem (sequential statistical decisions)
- Scheduling model (Bayesian heuristic approach)

Each student solves by computer at least one example of his\her choice using the software system available in the web-site
http://soften.ktu.lt/~mockus