Minimizing Total Idle Energy Consumption in the Permutation Flow Shop Scheduling Problem

In this paper, we investigate the well-known permutation flow shop (PFS) scheduling problem with a particular objective, the minimization of total idle energy consumption of the machines. The problem considers the energy waste induced by the machine idling, in which the idle energy consumption is evaluated by the multiplication of the idle time and power level of each machine. Since the problem considered is NP-hard, theoretical results are given for several basic cases. For the two-machine case, we prove that the optimal schedule can be found by employing a relaxed Johnson's algorithm within O(n(2)) time complexity. For the cases with multiple machines (not less than 3), we propose a novel NEH heuristic algorithm to obtain an approximate energy-saving schedule. The heuristic algorithms are validated by comparison with NEH on a typical PFS problem and a case study for tire manufacturing shows an energy consumption reduction of approximately 5% by applying the energy-saving scheduling and the proposed algorithms.