Software tools for the investigation of stochastic programming problems

Stochastic Programming (SP) has become synonymous with optimum decision making under uncertainty. However, modelling and solving stochastic programming problems are challenging tasks. Many factors affect the complexity of SP models with respect to their deterministic counterparts: (i) the need for capturing the random behaviour of the models parameters, (ii) the difficulties in solving the model instances (which are usually very large), and (iii) the requirements for advanced analysis of the model results through simulation techniques. This research focuses on the investigation of stochastic programming problems using software tools, and the outcomes of this work address some of the aforementioned difficulties. The well known classes of stochastic programming models and their properties are first reviewed, and a critical analysis of the use of algebraic modelling languages and their extensions for the formulation of SP models is presented. The insight gained into the interaction of models of randomness with optimisation models has led to the design of a novel approach to extending algebraic modelling languages for SP modelling. This approach has been successfully applied to the AMPL and MPL language to incorporate new SP language constructs. The resulting languages SAMPL and SMPL support the formulation of scenario-based SP problems in a natural and concise way. The integration of modelling systems with specialised solvers for SP has also been investigated. The use of decomposition methods for solving recourse problems has been analysed in terms of scale-up properties; alternative formulations of chance-constrained problems, which can be formulated as deterministic mixed integer programs, are also illustrated. Computational and conceptual issues related to the value of stochastic solutions (VSS) have been analysed and discussed. A Stochastic Programming Integrated Environment (SPInE), which supports the SMPL and SAMPL extended modelling languages and embodies a stochastic solver has been designed and developed in this research. The features of the system include the integration with scenario generators and the analysis of the SP model solutions and validation through the use of simulation. A case study is presented to illustrate how the SPInE system provides practitioners with a powerful platform for the analysis of real life problems using stochastic programming techniques.