COMPLEXITY OF FLOWSHOP AND JOBSHOP SCHEDULING.

NP-complete problems form an extensive equivalence class of combinatorial problems for which no nonenumerative algorithms are known. The first result shows that determining a shortest-length schedule in an m-machine flowshop is NP-complete for m greater than equivalent to 3. (For m equals 2, there is an efficient algorithm for finding such schedules). The second result shows that determining a minimum mean-flow-time schedule in an m-machine flowshop is NP-complete for every m greater than equivalent to 2. Finally, it is shown that the shortest-length schedule problem for an m-machine jobshop is NP-complete for every m greater than equivalent to 2. The results are strong in that they hold whether the problem size is measured by number of tasks, number of bits required to express the task lengths, or by the sum of the task lengths.