# Energy-Efficient Hybrid Flow-Shop Scheduling under Time-of-Use and Ladder Electricity Tariffs
## 1 Introduction
To build a green manufacturing model and realize energy conservation and emission reduction, a distributed two-stage reentrant hybrid flow-shop bi-level scheduling model was established, which takes the makespan, total carbon emissions, and total energy consumption costs as the optimization objectives [53]. The optimal scheduling scheme is determined using the upper model to minimize the time between jobs. Specifically, the lower model aims to minimize the overall carbon emissions and the overall energy costs by allocating the power supply among distributed energy resources (DERs), energy storage systems (ESSs), and the primary grid. An improved hybrid salp swarm (SSA) and NSGA-III algorithm was proposed to solve this problem. Furthermore, aiming to minimize the makespan and total energy cost in capital-intensive manufacturing industries, [PERSON] and [PERSON] [54] addressed flexible job-shop scheduling under time-of-use pricing and scheduled downtime. First, an integer linear programming model was proposed. Second, a constraint programming model was discussed. Third, managerial insights were derived. A model under a sequential-dependent single machine scheduling problem was proposed to minimize energy costs and reduce carbon footprint emissions [55]. A Low Energy-Carbon Cost Sequence Dependent Job Scheduling optimization model (LEC-SDJS) was developed. Comparing the model to classical scheduling optimization approaches shows the model to be useful. Considering a mixture of job-shop and flow-shop production scheduling problems with a speed-scaling policy and no-idle time strategy, a multi-objective Q-learning-based hyper-heuristic with Bi-criteria selection (QHH-BS) was developed. This can result in the production of a set of high-quality Pareto frontier solutions [56]. The manufacturing sequence of job-shop and flow-shop goods was represented by this method, which employed a novel three-layer encoding. Our study considers a HFSP depending on electricity price and energy-saving measures to reach the goal of minimization of total energy consumption without effect the maximum complete time. The proposed mathematical programming model focuses on the characteristic of HFSP and electricity price scheme, while right-shift approach is geared toward the Pareto solution through the adoption of an improved NSGA-II algorithm. However, the purpose of research is to integrate multiple algorithms for a new problem, without a large degree innovation for the existing algorithms. Thus, we can verify its feasibility based on a general multi-objective algorithm. For these reasons, we adopt NSGA-II as the original algorithm, which is proven to be a useful method to solve multi-objective problems. The contributions of the paper can be summarized as follows. 1. A new scenario containing energy-intensive industries under punitive electricity price is considered. 2. In response to problems, several low-carbon strategies are integrated into a multi-objective algorithm framework. 3. Experimental results show that the proposed framework reduces carbon reduction effectively without affecting make span. In this work, the background, research significance, article contribution, and article structure are described in Section 1. Furthermore, the research problem is described in Section 2. Section 3 introduces an improved NSGA-II algorithm with a right-shift procedure. Section 4 reports the experimental results and compares them with the original NSGA-II algorithm. Finally, some conclusions and future work are provided in Section 5.