Flow Shop

The jobs of a set N = 1, 2,…, n are processed in a system consisting of M sequential machines. A job i ∈ N is available at time d _i ≥ 0. The routes (machine processing orders) are identical for all jobs of set N and are determined by the sequence of machines 1, 2,…, M. The processing times t _iL ≥ 0 of each job i ∈ N on each machine L, 1 ∈ L ∈ M, are given. Simultaneous processing of any job on several machines is not allowed. Moreover, each machine processes no more than one job at a time. Such a processing system is called a flow shop.