Multiperiod Production-Distribution Planning Problems
Model-Based Approaches and Network-Based Algorithms
Industrial Engineering, PhD Dissertation, 2014
Assoc. Prof. Tonguç Ünlüyurt (Thesis Advisor),
Assoc. Prof. Güvenç Şahin (Thesis Co-Advisor),
Prof. Şevket İlker Birbil, Assoc. Prof. Hüsnü Yenigün,
Assist. Prof. Erhun Kundakçıoğlu
Date & Time: December 30th, 2014 – 9:30 AM
Place: FENS L067
Keywords : Linear and Non-Linear Optimization, Matrix Decomposition, Network Programming, Approximation Algorithms, Scaling Algorithms
Multiperiod dynamic 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. The efficiency of the proposed approaches is demonstrated through numerical experiments. Then, scaling and δ-optimality together with penalty function methods are used to develop some network-based scaling approximation algorithms to cope with minimum cost and feasibility multiperiod multiproduct flow problems (or multiperiod planning problems with side constraints).
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.