Algorithms and Linear Programming Relaxations for Scheduling Unrelated Parallel Machines

Since the early days of combinatorial optimization, algorithms and techniques from the closely related area of mathematical programming have played a pivotal role in solving combinatorial optimization problems. This holds both for ‘easy’ problems that can be solved efficiently in polynomial time, such as, e. g., the weighted matching problem [3], as well as for NP-hard problems whose solution might take exponential time in the worst case, such as, e. g., the traveling salesperson problem [1].