@misc{CaroeeSchultz1996, author = {Car{\"o}e, Claus C. and Schultz, R{\"u}diger}, title = {Dual Decomposition in Stochastic Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2560}, number = {SC-96-46}, year = {1996}, abstract = {We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and Lagrangian relaxation. The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. \%We outline a branch-and-bound algorithm for obtaining primal feasible and \%possibly optimal solutions. Numerical experience is presented for some two-stage test problems.}, language = {en} } @misc{CaroeeSchultz1998, author = {Car{\"o}e, Claus C. and Schultz, R{\"u}diger}, title = {A Two-Stage Stochastic Program for Unit Commitment Under Uncertainty in a Hydro-Thermal Power System}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3543}, number = {SC-98-11}, year = {1998}, abstract = {We develop a two-stage stochastic programming model with integer first-stage and mixed-integer recourse for solving the unit commitment problem in power generation in the presence of uncertainty of load profiles. The solution methodology rests on a novel scenario decomposition method for stochastic integer programming. This method combines Lagrangian relaxation of non-anticipativity constraints with branch-and-bound. It can be seen as a decomposition algorithm for large-scale mixed-integer linear programs with block-angular structure. With realistic data from a German utility we validate our model and carry out test runs. Sizes of these problems go up to 20.000 integer and 150.000 continuous variables together with up to 180.000 constraints.}, language = {en} }