Efficient algorithms for flexible job shop scheduling with parallel machines

Job shop scheduling with a bank of machines in parallel is important from both theoretical and practical points of view. Herein we focus on the scheduling problem of minimizing the makespan in a flexible two‐center job shop. The first center consists of one machine and the second has k parallel machines. An easy‐to‐perform approximate algorithm for minimizing the makespan with one‐unit‐time operations in the first center and k‐unit‐time operations in the second center is proposed. The algorithm has the absolute worst‐case error bound of k − 1, and thus for k = 1 it is optimal. Importantly, it runs in linear time and its error bound is independent of the number of jobs to be processed. Moreover, the algorithm can be modified to give an optimal schedule for k = 2.