# Energy-Efficient Hybrid Flow-Shop Scheduling under Time-of-Use and Ladder Electricity Tariffs
## 1 Introduction
[17] systematically analyzed the manufacturing process and described the relationship of process variables in energy consumption by constructing a mathematical model, while the parameters was optimized through an artificial bee colony algorithm. Additionally, [PERSON] et al. [18] conducted research in an unrelated parallel machine environment to minimize costs and consume energy. Their study developed a few dominance rules and valid inequalities in the mixed-integer linear programming model. As a typical scheduling problem, HFSP widely exists in the actual manufacturing process [19]. Several studies have considered energy consumption and emphasized the importance of energy conservation as an environmental issue [20]. [PERSON] and [PERSON] [21] considered the production costs and energy consumption in a flexible flow shop scheduling problem. The problem was described as a numeric example with machine dependent processing stages. To find the optimal or close to optimal solution, a new approach was introduced based on the NSGA-II. It is possible to reduce total energy consumption (TEC) during the manufacturing process through adjustments and technical upgrades [22]. Furthermore, the electricity price mechanism has played an important role in energy conservation. The time-of-use (TOU) price strategy is a very useful one in green scheduling, by adjusting processing time from peak periods to off-peak periods effectively [23]. TOU applications in many filed, such as Household, Logistics and Manufacturing. In order to minimize electricity cost and earn the relevant incentive, residential demand response was studied through the scheduling of typical home appliances as per the electricity price [24]. A practical optimization model for a household to determine the optimal scheduling of home appliances under TOU electricity prices is formulated and a mixed integer nonlinear optimization model was built. A case study showed that a household is able to shift consumption in response to the varying prices and incentives, through which the consumer may realize an electricity cost saving of more than 25%. To provide a comprehensive overview of the research that aim to achieve energy efficiency for sustainable and green ports, a systematic literature review was conducted to analyze operational strategies, technology usage and energy management systems [25]. As an operational strategy, peak shaving aimed to reduce the peak energy consumption of the port. A number of different methods using the load profile curves where (1) Power sharing: Using any stored energy in the case of peak energy demand periods; (2) Load shifting: Shifting the energy demand in the peak period to non-peak periods; (3) Load Shedding: Turning off non-critical loads during peak periods. Aiming at minimizing the overall electricity related cost as well as the potential penalty cost due to the failure of timely fulfillment of target production, a methodology was proposed to help the manufacturing enterprises identify a cost-effective reservation capacity by optimal production scheduling under Critical Peak Pricing (CPP) program, a typical price-driven electricity demand response program [26]. A Mixed Integer Nonlinear Programming (MINLP) is used to formulate the problem and approximate method is used to obtain a near optimal solution. The results of the case study show that a cost reduction of 31.42% and 11.04% can be achieved for a billing cycle compared with the simple method. To minimize total lateness cost of operations and total energy costs considering hourly energy price with energy selling back option under uncertain renewable energy generation, an energy management and operations planning problem for next generation green ports was addressed [27]. In this paper, energy management matches energy demand and supply considering different energy pricing schemes and bidirectional energy trading between energy sources and energy storage systems. A mixed integer linear programming model was suggested and the model finds optimal results in short computational times.