# Energy-Efficient Hybrid Flow-Shop Scheduling under Time-of-Use and Ladder Electricity Tariffs
## 1 Introduction  
As a result of the increasing influence of climate change, green development has become an important trend. As a concept of economic growth and social development aiming at efficiency and sustainability, green manufacturing is an integral part of green development [1]. Green manufacturing involves the entire process of production, such as renewable energy power generation, saving raw materials, reducing energy consumption, green product redesign, and reducing pollution emissions [2]. According to a China Electricity Council (CEC) report, China's total electricity consumption reached 7511 TWh in 2020, with year-over-year growth of 3.1%. Specifically, the electricity consumption of the secondary industry was 5.121 TWh, accounting for 68.2% of the total electricity consumption [3]. Green development considers the environmental impact and resource efficiency while ensuring the economic and social benefits of the enterprise, especially in China [4]. Traditional workshop scheduling problems usually consider a single economic indicator, while green and economic indicator are both considered green manufacturing [5]. Green indicators usually contain minimizing the consumption of resources and minimizing the impact on the environment [6]. Due to most of the production methods of chemical, steel, and other high-profile production methods being flowing operations, the similar processing production processes can be abstracted as a hybrid flow-shop scheduling problem (HFSP) [7]. In industrial production, the flow shop scheduling problem (FSP) is ageneral problem model and a hot spot in the academic field [8]. As an extended form, HFSP is a popularization of the traditional workshop scheduling problem, which has the comprehensive characteristics of assembly-line work and parallel machines [9]. In the basic flowshop scheduling problem (FSP), n jobs must be processed on m machines in the same order, that is, the operations of each job follow the same route. It is commonly assumed that there is no job preemption, and all jobs are ready to be processed at the beginning. Therefore, if an operation of a job has begun on a machine, it cannot be interrupted until it is finished. All these assumptions are also valid for the permutation flowshop scheduling problem (PFSP). Considering the green PFSP that minimizes total flowtime and total energy consumption concurrently, a bi-objective mixed-integer linear programming (MILP) model and three effective heuristic algorithms were developed for the problem, employing a simple job-based speed-scaling strategy [10]. The study incorporated the energy concerns into the PFSP and analyzes the trade-off between total flowtime and energy consumption criteria in an efficient way to assist decision making in this environment. Environmental issues in green FSPs were proposed to capture both operational and tactical planning decisions, from an environmental policy-maker perspective [11]. Test instances were randomly generated and the optimal solution sets were derived for each of three carbon reduction policies. The outcome of evaluation in most cases has shown that an Emissions Trading (ET) policy yields a stronger market-based policy. Many scholars have the intensive study of the methods to reduce energy consumption for HFSP optimization in existing literature, including energy-saving measures [12] and energy saving strategies [13]. After sorting out a large number of relevant documents on energy requirements in the production process, [PERSON] et al. [14] put forward the concept of \"Energy Saving Scheduling\" (EES). They gave a research framework of EES, which classified the existing literature according to three dimensions of energy coverage, energy supply, and energy demand. Undoubtedly, it helped scholars understand this research problem more systematically [15]. So far, several studies have demonstrated that reducing energy consumption has become one of the hot spots in scheduling [16]. [PERSON] et al.