We consider power system expansion planning under
uncertainty. In our approach, integer programming and stochastic
programming provide a basic framework. We develop a multistage
stochastic programming model in which some of the variables are
restricted to integer values. By utilizing the special property of the
problem, called block separable recourse, the problem is transformed
into a two-stage stochastic program with recourse. The electric power
capacity expansion problem is reformulated as the problem with first
stage integer variables and continuous second stage variables. The
L-shaped algorithm to solve the problem is proposed.
 J. R. Birge, Decomposition and partitioning methods for multistage
stochastic linear programs. Operations Research, 33(1985) 989-1007.
 J. R. Birge, Stochastic programming computation and applications. INFORMS
Journal on Computing, 9(1997) 111-133.
 J. R. Birge and F. Louveaux, Introduction to Stochastic Programming.
 J. R. Birge, C. J. Donohue, D. F. Holmes and O. G. Svintsitski, A parallel
implementation of the nested decomposition algorithm for multistage
stochastic linear programs. Mathematical Programming, 75(1996) 327-
 R. Fourer, D. M. Gay and B. W. Kernighan, AMPL: A Modeling Langage
for Mathematical Programming. Scientific Press, 1993.
 F. V. Louveaux, A solution method for multistage stochastic programs
with recourse, with application to an energy investment problem. Operations
Research, 28(1980) 889-902.
 F. V. Louveaux, Multistage stochastic programs with block-separable
recourse. Mathematical Programming Study, 28(1986) 48-62.
 T. Shiina, L-shaped decomposition method for multi-stage stochastic
concentrator location problem. Journal of the Operations Research Society
of Japan, 43(2000) 317-332.
 T. Shiina, Stochastic programming model for the design of computer
network (in Japanese). Transactions of the Japan Society for Industrial
and Applied Mathematics, 10(2000) 37-50.
 R. Van Slyke and R. J.-B. Wets, L-shaped linear programs with applications
to optimal control and stochastic linear programs. SIAM Journal
on Applied Mathematics, 17(1969) 638-663.