{"title":"Stochastic Programming Model for Power Generation","authors":"Takayuki Shiina","volume":54,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":889,"pagesEnd":895,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/15305","abstract":"We consider power system expansion planning under\r\nuncertainty. In our approach, integer programming and stochastic\r\nprogramming provide a basic framework. We develop a multistage\r\nstochastic programming model in which some of the variables are\r\nrestricted to integer values. By utilizing the special property of the\r\nproblem, called block separable recourse, the problem is transformed\r\ninto a two-stage stochastic program with recourse. The electric power\r\ncapacity expansion problem is reformulated as the problem with first\r\nstage integer variables and continuous second stage variables. The\r\nL-shaped algorithm to solve the problem is proposed.","references":"[1] J. R. Birge, Decomposition and partitioning methods for multistage\r\nstochastic linear programs. Operations Research, 33(1985) 989-1007.\r\n[2] J. R. Birge, Stochastic programming computation and applications. INFORMS\r\nJournal on Computing, 9(1997) 111-133.\r\n[3] J. R. Birge and F. Louveaux, Introduction to Stochastic Programming.\r\nSpringer-Verlag, 1997.\r\n[4] J. R. Birge, C. J. Donohue, D. F. Holmes and O. G. Svintsitski, A parallel\r\nimplementation of the nested decomposition algorithm for multistage\r\nstochastic linear programs. Mathematical Programming, 75(1996) 327-\r\n352.\r\n[5] R. Fourer, D. M. Gay and B. W. Kernighan, AMPL: A Modeling Langage\r\nfor Mathematical Programming. Scientific Press, 1993.\r\n[6] F. V. Louveaux, A solution method for multistage stochastic programs\r\nwith recourse, with application to an energy investment problem. Operations\r\nResearch, 28(1980) 889-902.\r\n[7] F. V. Louveaux, Multistage stochastic programs with block-separable\r\nrecourse. Mathematical Programming Study, 28(1986) 48-62.\r\n[8] T. Shiina, L-shaped decomposition method for multi-stage stochastic\r\nconcentrator location problem. Journal of the Operations Research Society\r\nof Japan, 43(2000) 317-332.\r\n[9] T. Shiina, Stochastic programming model for the design of computer\r\nnetwork (in Japanese). Transactions of the Japan Society for Industrial\r\nand Applied Mathematics, 10(2000) 37-50.\r\n[10] R. Van Slyke and R. J.-B. Wets, L-shaped linear programs with applications\r\nto optimal control and stochastic linear programs. SIAM Journal\r\non Applied Mathematics, 17(1969) 638-663.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 54, 2011"}