Multi-period multi-product distribution planning problems: model-based and network-based approaches
Hosseini, Seyed Ahmad (2014) Multi-period multi-product distribution planning problems: model-based and network-based approaches. [Thesis]
Dynamic and multiperiod flow problems arise frequently in management applications, communication systems, and process systems engineering with important applications in large-scale production scheduling and time-varying distribution planning. This thesis investigates various multiperiod distribution planning problems, where all problem parameters may change over time and or products. First, matrix decomposition is exploited through index sets of the models to delineate block structures and to develop some methods that lead to linear programming problems comprising a set of sparse polyhedrals. Considering the sparsity and repeating structure of the polyhedrals algorithmic approaches based on decomposition techniques of block angular and block staircase are proposed aiming to reduce the computational resources required and/or getting rapid near-optimal solutions. The efficiency of the proposed approaches is demonstrated through numerical experiments. Then, we use scaling and approximate optimality together with penalty function method to develop some network-based scaling approximation algorithms. Our algorithms exploit different ideas including matrix transformation from linear algebra, graph partitioning from graph theory, penalty methods from nonlinear optimization, and scaling and approximation algorithms from network flow theory. Moreover, we analyze the algorithms from both theoretical and practical perspectives. The practical performances corresponding to some electricity transmission distribution networks support the theoretical properties.
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