Abstract: 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.
Abstract: Mathematical programming has been applied to various
problems. For many actual problems, the assumption that the parameters
involved are deterministic known data is often unjustified. In
such cases, these data contain uncertainty and are thus represented
as random variables, since they represent information about the
future. Decision-making under uncertainty involves potential risk.
Stochastic programming is a commonly used method for optimization
under uncertainty. A stochastic programming problem with recourse
is referred to as a two-stage stochastic problem. In this study, we
consider a stochastic programming problem with simple integer
recourse in which the value of the recourse variable is restricted to a
multiple of a nonnegative integer. The algorithm of a dynamic slope
scaling procedure for solving this problem is developed by using a
property of the expected recourse function. Numerical experiments
demonstrate that the proposed algorithm is quite efficient. The
stochastic programming model defined in this paper is quite useful
for a variety of design and operational problems.