6. Building and Solving Stochastic Linear Programming Models with SLP-IOR

Abstract

This chapter describes the capabilities and the usage of SLP-IOR, our interactive model management system for stochastic linear programming (SLP). The main features of SLP-IOR are the following: the system is intended to support the entire life cycle of a model, including model formulation, analysis of the model instance, solving it, and analyzing the solution. A main design characteristic is keeping connection to an algebraic modeling system; we have chosen GAMS [3,4]. This approach has the following advantages: on the one hand, the powerful general-purpose solvers connected to GAMS are available for solving deterministic equivalents of SLP problems; on the other hand, deterministic linear programs (LPs) formulated in the algebraic modeling language of GAMS can be imported into SLP-IOR to develop stochastic variants of these. However, the use of GAMS is optional; with the exception of the above-mentioned GAMS-related features, SLP-IOR can be fully utilized without having access to GAMS.From the functional point of view, SLP-IOR integrates three main groups of facilities. The core part serves for dealing with SLP model instances. The workbench component supports working with test problem batteries and performing test runs with them. The third component consists of a solver library organized as a solver description database and a collection of executables of solvers. Besides some general-purpose LP solvers, the solver library contains several solvers specialized to the various SLP model classes.The system runs under Windows 32. SLP-IOR itself has been developed in Borland Delphi 6 in an object-oriented style. The majority of our own solvers have been developed in Fortran using Compaq Visual Fortran 6.1.

Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition

“…In the algorithm below we assume that the set X is compact, and that we know a lower bound η min for the optimal value of problem (17).…”

“…In the next algorithm we assume that the set X is compact, and that we know a lower bound η min for the optimal value of problem (17), as well as lower bounds [w min ] i on the optimal values of the second-stage problems (19). The method extends to the risk-averse case the idea of the multicut method for risk-neutral problems, developed in [4,26].…”

“…We complete this section by formulating optimality conditions for problem (17). The theorem below is an immediate consequence of standard optimality conditions in convex optimization (see, e.g., [28,Thm.…”

“…Particularly relevant for us are the duality theory [2,8,11,12,13,18,24,30,31], and the theory of conditional and dynamic risk measures [3,6,7,9,10,14,15,22,34,23,30,32]. The optimization part generalizes and extends decomposition approaches to riskneutral two-stage stochastic linear programming problems (see [5,17,27] and the references therein).…”

Stability and Scenario Trees for Multistage Stochastic Programs

“…We refer to the pioneering work of Dantzig [5,6], and to the recent books [39], [44] and the monograph [27] for the state-of-the-art of the theory and solution methods for multistage models and for a variety of applications.…”