A Linear Two-Stage Stochastic Programming Problem with Quantile Criterion: Its Discrete Approximation
- 34 Downloads
Algorithms for solving a linear two-stage stochastic programming problem with quantile criterion are designed. They are based on the reduction of the initial nonlinear problem to a sequence of linear programming problems. The first algorithm applies the simplex and Monte Carlo methods sequentially, whereas the second utilizes the simplex method and varies the confidence set. Their advantages are demonstrated by forming the budget of a hospital.
KeywordsMechanical Engineer Monte Carlo Method System Theory Programming Problem Nonlinear Problem
Unable to display preview. Download preview PDF.
- 1.Yudin, D.B., Zadachi i metody stokhasticheskogo programmirovaniya (Stochastic Programming Problems and Methods), Moscow: Sovetskoe Radio, 1979.Google Scholar
- 2.Kall, P. and Wallace, S.W., Stochastic Programming, Chichester: Wiley, 1994.Google Scholar
- 3.Kibzun, A.I. and Kan, Yu.S., Stochastic Programming Problems with Probability and Quantile Functions, Chichester: Wiley, 1996.Google Scholar
- 4.Kibzun, A.I. and Naumov, A.V., Two-Stage Linear Quantile Programming Problems, Avtom. Telemekh., 1995, no. 1, pp. 83-93.Google Scholar
- 5.Kibzun, A.I. and Lepp, R., Discrete Approximation in Quantile Problem of Portfolio Selection, in: Stochastic Optimization: Algorithms and Applications, Uryasev, S. and Pardalos, P.M., Eds., Dordrecht: Kluwer, 2001, pp. 119-133.Google Scholar
- 6.Lepp, R., Approximations to Stochastic Programs with Complete Recourse, SIAM J. Control Optimiz., 1990, vol. 28, no. 2, pp. 382-394.Google Scholar
- 7.Birge, J.R. and Wets, R.J.-B., Designing Approximation Schemes for Stochastic Optimization Problems, in Particular, for Stochastic Programs with Recourse, Math. Prog. Study, 1986, vol. 21, pp. 54-102.Google Scholar
- 8.Kibzun, A.I. and Naumov, A.V., A Guaranteeing Algorithm for Quantile Optimization, Kosm. Issled., 1995, no. 2, pp. 160-165.Google Scholar
- 9.Schrijver, A., Theory of Linear and Integer Programming, New York: Wiley, 1986. Translated under the title Teoriya lineinogo i tselochislennogo programmirovaniya, Moscow: Mir, 1991.Google Scholar
- 10.Naumov, A.V., Two-Stage Quantile Optimization of Hospital Budget, Teor. Sist. Upravlen., 1996, no. 2, pp. 87-90.Google Scholar