Effectively approximating Pareto frontiers by patch representations - with applications to supply chain optimization

Trade-offs between conflicting objectives are required in most real-world optimization problems. Decision-makers require an approximation of the Pareto frontier which illustrates the corresponding optimal compromises. This thesis develops algorithms that can provide these approximations effectively with provable quality guarantees. In the first part, an algorithm for bicriteria mixed-integer problems is developed. Based on the concept of patches, it is shown that the algorithm obtains an almost-optimal convergence rate. The second part starts with a discussion of algorithms for computing an approximation quality measure for Pareto frontiers. On this basis, a new multicriteria optimization algorithm for an arbitrary number of objectives is developed. Finally, models for multicriteria robust optimization are studied with a focus on supply chains. In various case studies, the proposed algorithms are applied to supply chain models, in particular regarding the objectives of costs and risks. The results show the large practical applicability of the approaches in this thesis.