Weninger D (2016)
Publication Language: English
Publication Type: Thesis
Publication year: 2016
Pages Range: 150
In the light of increasing globalization and ongoing rapid developments in information technology, software systems for planning production and supply networks play an important role for companies to remain competitive in future markets. Most planning systems use optimization methods for determining an efficient and economical production or supply network plan. In particular, mixed-integer optimization plays an important role in this context. It can be observed that the size of the arising mixed-integer programs has constantly increased over recent decades. The challenge is to ensure a high scalability of running time and solution quality even for very large instances anticipated in future. To address this challenge, we pursue three different approaches.
In the first part of the work, we initially describe presolving methods known from literature and practice. Based on these methods, we develop eight new presolving techniques for mixed-integer programming and confirm their benefit by computational results on real-world instances.
Decomposition methods are well suited for achieving a high scalability of running time and solution quality. Therefore, we examine a decomposition approach in the second part of this thesis. Our algorithm splits the original problem into mixed-integer subproblems and solves the subproblems alternately to determine an optimal solution. By presenting computational results, we show that our method performs significantly better than a standard decomposition approach.
In the last part, we describe an aggregation scheme for solving discrete lot-sizing problems. Starting with a coarsened formulation of the original problem, the formulation gets refined until an optimal solution is determined. Test results demonstrate that our approach usually accomplishes a better running time than a state-of-the-art mixed-integer solver.
Weninger, D. (2016). Solving mixed-integer programs arising in production planning (Dissertation).
Weninger, Dieter. Solving mixed-integer programs arising in production planning. Dissertation, 2016.