Twostage: A Code of a Basis Decomposition Method for Stochastic Programming

The experimental version of the TWOSTAGE code for solving the two stage stochastic linear programs with discretely distributed random right-hand-sides and/or technology matrix gives an alternate possibility to the existing software produced in SDS/ADO

An alternating method for stochastic linear programming with simple recourse

Stochastic linear programming with simple recourse arises naturally in economic problems and other applications. One way to solve it is to discretize the distribution functions of the random demands. This will considerably increase the number of variables and will involved discretization errors. Instead of doing this, we describe a method which alternates between solving some n-dimensional linear subprograms and some m-dimensional convex subprograms, where n is the dimension of the decision vector and m is the dimension of the random demand vector. In many cases, m is relatively small. This method converges in finitely many steps

Sublinear upper bounds for stochastic programs with recourse

Separable sublinear functions are used to provide upper bounds on the recourse function of a stochastic program. The resulting problem's objective involves the inf-convolution of convex functions. A dual of this problem is formulated to obtain an implementable procedure to calculate the bound. Function evaluations for the resulting convex program only require a small number of single integrations in contrast with previous upper bounds that require a number of function evaluations that grows exponentially in the number of random variables. The sublinear bound can often be used when other suggested upper bounds are intractable. Computational results indicate that the sublinear approximation provides good, efficient bounds on the stochastic program objective value.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47918/1/10107_2005_Article_BF01582286.pd