Abstract
A two-step problem of quintile optimization with linear constraints, discrete distribution of the vector of random parameters, and the first stage scalar strategy is studied. An algorithm for finding the exact solution to the problem, and its convergence condition are suggested. As an example, a logistic problem of optimization of a freight reserved by a company engaged in cargo delivering is considered.
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References
Birge, J.R. and Louveaux, F., Introduction to Stochastic Programming, New York: Springer-Verlag, 1997.
Yudin, D.B., Zadachi i metody stokhasticheskogo programmirovaniya (Problems and Methods of Stochastic Programming), Moscow: Sovetskoe Radio, 1979.
Kall, P., Stochastic Linear Programming, New York: Springer-Verlag, 1976.
Kibzun, A.I. and Kan, Yu.S., Stochastic Programming Problems with Probability and Quantile Functions, Chichester: Wiley, 1996.
Kibzun, A.I. and Naumov, A.V., Two-Stage Problems of Quintile Linear Programming, Avtom. Telemekh., 1995, no. 1, pp. 83–93.
Kibzun, A.I., Naumov, A.V., and Ulanov, S.V., A Stochastic Algorithm to Control the Aircraft Fleet of an Air Company, Avtom. Telemekh., 2000, no. 8, pp. 126–136.
Naumov, A.V. and Bogdanov, A.B., Research on a Two-Step Integral Problem of Quintile Optimization, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2003, no. 5, pp. 62–69.
Malyshev, V.V. and Kibzun, A.I., Analiz i sintez vysokotochnogo upravleniya letatel’nymi apparatami (Analysis and Design of a Precision Control for Flying Vehicles), Moscow: Mashinostroenie, 1987.
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Original Russian Text © A.B. Bogdanov, A.V. Naumov, 2006, published in Avtomatika i Telemekhanika, 2006, No. 12, pp. 36–42.
This work was supported by the Russian Foundation for Basic Research, project no. 05-08-17963.