Stochastic decomposition: an algorithm for two-state linear programs with recourse
Mathematics of Operations Research
Decomposition methods in stochastic programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence
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Abstract: Biomass feedstock production is an important component of the biomass based energy sector. Seasonal and distributed collection of low energy density material creates unique challenges, and optimization of the complete value chain is critical for cost-competitiveness. BioFeed is a mixed integer linear programming (MILP) problem model that has been developed and successfully applied to optimize bioenergy feedstock production system. It integrates the individual farm design and operating decisions with transportation logistics to analyze them as a single system. However, this integration leads to a model that is computationally demanding, leading to large simulation times for simplified case studies. Given these challenges, and in wake of the future model extensions, this work proposes a new computational approach that reduces computational demand, maintains result accuracy, provides modeling flexibility and enables future model enhancements. The new approach, named the Decomposition and Distributed Computing (DDC) approach, first decomposes the model into two separate optimization sub-problems: a production problem, focusing on on-farm activities such as harvesting, and a provision problem, incorporating the post-production activities such as transportation logistics. An iterative scheme based on the concepts from agent based modeling is adapted to solve the production and provision problems iteratively until convergence had been achieved. The computational features of the approach are further enhanced by enabling distributed computing of the individual farm optimization models. Simulation studies comparing the performance of the DDC approach with the rigorous MILP solution approach illustrated an order of magnitude reduction in computational time using the proposed DDC approach. Moreover, the solution obtained using the DDC approach was within +/-5% of the rigorous MILP solution. This approach can be a valuable tool to solve complex supply chain optimization problems in other sectors where similar challenges are encountered.