Hiking in the scheduling landscape: exact and approximation algorithms for parallel machines

This thesis investigates different optimization problems in the field of scheduling. Scheduling problems model situations in which limited resources have to be assigned to tasks over time as to minimize costs, maximize profits, balance workloads among resources or improve the efficiency of the usage of resources. The goal is to develop algorithms, which can find optimal solutions in an efficient amount of time. However, many scheduling problems turn out to be computationally difficult such that we cannot hope to accomplish this goal. To overcome this, we consider approximation algorithms, which offer a trade-off by computing solutions provably close to an optimal solution in an efficient amount of time. In this thesis both exact and approximation algorithms are studied for a variety of scheduling problems. To achieve this, this research investigates the structure and properties of optimal solutions to find solutions that are provably close.