Energy-awareness in the industrial sectors has become a global consensus in recent decades. Green scheduling is acknowledged as an effective weapon to reduce energy consumption in the industrial sectors. Therefore, this paper is devoted to the green scheduling of flexible manufacturing cells (FMC) with auto-guided vehicle transportation, where conflict-free routing of the vehicles is considered. To deal with this problem, a bi-objective optimization model is proposed to achieve the minimization of the maximum completion time and the total energy consumption in an FMC. The studied problem is an extension of flexible job shop problem which is NP-hard. Thus, an improved bi-objective salp swarm algorithm based on decomposition (IMOSSA/D) is proposed and applied to the problem. The approach is based on the decomposition of the bi-objective problem. Salp swarm intelligence along with three stochastic-distribution-based operators are incorporated into the approach, to enhance and balance its exploring and exploiting ability. Computational experiments are performed to compare the proposed approach with two state-of-the-art algorithms. This study allows the decision makers to better trade-off between energy savings and production efficiency in flexible manufacturing cellular environment.