Johnson's algorithm: A key to solve optimally or approximately flow shop scheduling problems with unavailability periods

Johnson's algorithm (JA) is perhaps the most classical algorithm in the scheduling area. JA gives the optimal solution to the two machine flow shop to minimize the makespan in polynomial time. Researchers have tried to extend this notorious result to obtain polynomial time algorithms for more general cases. Such importance motivated us to devote this paper to JA applied to three flow shop problems with unavailability periods to minimize the makespan. First we focus on the optimality condition of JA. Then we propose a modification of JA. After we calculate new performances of JA as a heuristic. Last we deal with an extension of JA.