Complexity of flowshop scheduling problems with a new blocking constraint

This article deals with makespan minimization in the flowshop scheduling problem under the condition of no intermediate storage between machines. A new blocking constraint met in several industrial problems is introduced, and several complexity results are presented from two to five machines. Some problems with four machines in which the new and the classical blocking constraints are mixed, are polynomial. Problems with only the new blocking constraint are polynomial for up to three machines. Although the complexity of the problem with four machines is left open, several cases are shown to be polynomial. Finally the problem with five machines is NP-hard.