Fragkos, I; (2014) Large-Scale Optimisation in Operations Management: Algorithms and Applications. Doctoral thesis , UCL (University College London).

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Abstract

The main contributions of this dissertation are the design, development and application of optimisation methodology, models and algorithms for large-scale problems arising in Operations Management. The first chapter introduces constraint transformations and valid inequalities that enhance the performance of column generation and Lagrange relaxation. I establish theoretical connections with dual-space reduction techniques and develop a novel algorithm that combines Lagrange relaxation and column generation. This algorithm is embedded in a branch-and-price scheme, which combines large neighbourhood and local search to generate upper bounds. Computational experiments on capacitated lot sizing show significant improvements over existing methodologies. The second chapter introduces a Horizon-Decomposition approach that partitions the problem horizon in contiguous intervals. In this way, subproblems identical to the original problem but of smaller size are created. The size of the master problem and the subproblems are regulated via two scalar parameters, giving rise to a family of reformulations. I investigate the efficiency of alternative parameter configurations empirically. Computational experiments on capacitated lot sizing demonstrate superior performance against commercial solvers. Finally, extensions to generic mathematical programs are presented. The final chapter shows how large-scale optimisation methods can be applied to complex operational problems, and presents a modelling framework for scheduling the transhipment operations of the Noble Group, a global supply chain manager of energy products. I focus on coal operations, where coal is transported from mines to vessels using barges and floating cranes. Noble pay millions of dollars in penalties for delays, and for additional resources hired to minimize the impact of delays. A combination of column generation and dedicated heuristics reduces the cost of penalties and additional resources, and improves the efficiency of the operations. Noble currently use the developed framework, and report significant savings attributed to it.

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