A Logic-Based Decomposition for the Global Optimization of the Multiperiod Blending Problem Using Symmetry-Breaking Cuts

High Resolution Image Download MS PowerPoint Slide The multiperiod blending problem (MPBP) extends the classical pooling problem by incorporating scheduling operations across multiple time periods, where blending pools operate dynamically rather than in a steady-state manner. Various formulations and algorithmic approaches have been developed to tackle this problem, but existing decomposition methods suffer from symmetry-related inefficiencies. In this work, we present an improved decomposition approach based on Generalized Disjunctive Programming (GDP) that addresses a key symmetry issue present in existing GDP-based decomposition methods from literature. By eliminating the possibility of exploring an exponential number of redundant symmetric solutions, our method significantly enhances algorithmic efficiency. Additionally, it reduces significantly the number of bilinear constraints in the subproblems, leading to a two-order-of-magnitude decrease in subproblem solution times. Computational results demonstrate that our approach outperforms previously proposed GDP-based decomposition methods and well-established monolithic formulations solved with state-of-the-art solvers such as Gurobi. Additionally, we introduce a novel library of 60 benchmark instances, providing the research community with a diverse and challenging dataset for evaluating MPBP models and solution techniques.