Weak and Strong Machine Dominance in a Nonpreemptive Flowshop

Flowshop scheduling deals with processing a set of jobs through a set of machines, where all jobs have to pass among machines in the same order. With the exception of minimizing a makespan on two machines, almost all other flowshop problems in a general setup are known to be computationally intractable. In this paper we study a special case of flowshop defined by additional machine dominance constraints. The main result of this paper shows that the flowshop problem with a dominant machine (where dominance can be defined in several ways) can be solved in a polynomial time for a broad class of objective functions. This result is achieved by providing a general recipe how to obtain polynomial time optimization algorithms for particular objective functions from the corresponding algorithms for single machine problems.