Two-stage Stochastic Programming for Engineering Problems

The purpose of the paper is to present existing and discuss modified optimization models and solution techniques which are suitable for engineering decision-making problems containing random elements with emphasis on two decision stages. The developed approach is called two-stage stochastic programming and the paper links motivation, applicability, theoretical remarks, transformations, input data generation techniques, and selected decomposition algorithms for generalized class of engineering problems. The considered techniques have been found applicable by the experience of the authors in various areas of engineering problems. They have been applied to engineering design problems involving constraints based on differential equations to achieve reliable solutions. They have served for technological process control e.g. in melting, casting, and sustainable energy production. They have been used for industrial production technologies involving related logistics, as e.g. fixed interval scheduling under uncertainty. The paper originally introduces several recent improvements in the linked parts and it focuses on the unified two-stage stochastic programming approach to engineering problems in general. It utilizes authentic experience and ideas obtained in certain application areas and advises their fruitful utilization for other cases. The paper follows the paper published in 2010 which deals with the applicability of static stochastic programs to engineering design problems. Therefore, it refers to the basic concepts and notation introduced there and reviews only the principal ideas in the beginning. Then, it focuses on motivation of recourse concepts and two decision stages from engineering point of view. The principal models are introduced and selected theoretical features are reviewed. They are also accompanied by the discussion about difficulties caused by real-world cases. Scenario-based approach is detailed as the important one for the solution of engineering problems, discussion in data input generation is added together with model transformation remarks. Robust algorithms suitable for engineering problems involving nonlinearities and integer variables are selected and scenario-based decomposition is preferred. An original experience with using heuristics is shared. Several postprocessing remarks are added at the end of the paper, which is followed by an extensive literature review.