Reduce-to-the-opt - A specialized search algorithm for contiguous task scheduling

A relevant class of real-world scheduling problems, e.g. for assembly lines, service centres but also for surgeries in operation rooms are characterised by contiguous tasks. These tasks are non-preemptive, non-overlapping, and especially without any time gaps. All tasks are performed without any breaks between any two tasks. Each task will start immediately after its direct predecessor, if there is any. For these contiguous task scheduling problems a specialised search algorithm called Reduce-To-The-Opt is presented and its correctness is proved. Applied to trivial problems, where any linear ordering of the tasks solves the problem, this search algorithm also performs in linear time with respect to the number of tasks. For practical optimization problems, where the tasks have to be ordered optimally with respect to an objective function, runtime comparisons have shown that Reduce-To-The-Opt performs much better than a well-known heuristic-based search algorithm often used for the more general job-shop scheduling problems and even better than simple depth-first search because only the minimal value of each variable has to be selected instead of all possible values.