Two-machine job shop problem with a single server and sequence-independent non-anticipatory set-up times

We address in this paper the two-machine job shop scheduling problem with a single server that sets up the jobs before they get processed on the machines. The server is only needed during the set-up and becomes free at the end of this phase. Moreover, the set-ups are non-anticipatory and the set-up times are sequence-independent. We seek a schedule that minimizes the overall completion time, also called the makespan. We propose several lower bounds to the problem and prove the $NP$-hardness in the strong sense of two restricted cases. In addition, we present a linear time algorithm for a special case. In order to solve the general problem, we develop a genetic and simulated annealing algorithms that use feasibility guaranteed procedures. An experimental study is carried out to analyze the performance of these meta-heuristic methods.