User’s guide to ddsip.vSD – A C Package for the Dual Decomposition of Stochastic Programs with Dominance Constraints Induced by Mixed-Integer Linear Recourse

ddsip.vSD is a C-implementation of a number of scenario decomposition algorithms for stochastic linear programs with firstor second-order stochastic dominance constraints induced by mixed-integer linear recourse. The program is based on a previous implementation of scenario decomposition algorithms for mean-risk models of A. Märkert [20]. Main idea of the decomposition algorithms is the Lagrangean relaxation of unavoidable scenario coupling second stage constraints and of (some) nonanticipativity constraints. A branch-and-bound algorithm to reestablish nonanticipativity is employed. The original scenario decomposition algorithm for stochastic linear programs with mixed-integer recourse has been developed in [5]. Extensions including the treatment of mean-risk models have been made in [19]. The algorithms focussing stochastic dominance have been elaborated in [10, 11]. For the dual optimization we use ConicBundle – a C++ implementation provided by C. Helmberg, see [12]. We use the CPLEX callable library to solve the mixed-integer subproblems in the branch-and-bound tree, see [14]. The current version of ddsip.vSD relies on CPLEX 9.1.3. Unfortunately, we did not yet have the chance to debug and optimize the code in a sufficient way. We ask the user to support fixing bugs by reporting them to us as they occur. This manual describes the format of the input files and the data contained in the output files of ddsip.vSD. We try to provide all necessary information on the input parameters.