No-Wait Flowshop Scheduling Is as Hard as Asymmetric Traveling Salesman Problem

In this paper we study the classical no-wait flowshop scheduling problem with makespan objective (F|no-wait| C-max in the standard three-field notation). This problem is well-known to be a special case of the asymmetric traveling salesman problem (ATSP) and as such has an approximation algorithm with logarithmic performance guarantee. In this work we show a reverse connection, we show that any polynomial time a-approximation algorithm for the no-wait flowshop scheduling problem with makespan objective implies the existence of a polynomial-time alpha(1+epsilon)-approximation algorithm for the ATSP, for any epsilon > 0. This in turn implies that all non-approximability results for the ATSP (current or future) will carry over to its special case. In particular, it follows that no-wait flowshop problem is APX-hard, which is the first non-approximability result for this problem.