Processes 2021 , 9 , 274
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Mouzon and Yildirim are the pioneers that regard energy consumption as the objec- tive of production scheduling [3]. Energy-efficiency scheduling mainly improves energy efficiency in two ways: reducing energy consumption and reducing energy cost by schedul- ing. The existing research on energy-efficiency scheduling focuses on how to decrease energy consumption in different stages, such as decreasing the energy consumption in the processing stage, the setup stage, and the standby stage [4–9]. Recently, energy-efficiency scheduling decreases energy cost considering both energy consumption and energy price. Energy-efficiency scheduling under TOU electricity tariffs is an efficient way to reduce energy cost. Scholars have carried out a lot of research on energy-efficiency scheduling under TOU electricity tariffs in different generic manufacturing systems. Simple manu- facturing systems, such as single machine and parallel machine, have been studied by many researchers [10–13]. However, there are few reports on complex manufacturing systems, such as flow shop, flexible flow shop, job shop, flexible job shop, etc. [14–16]. The generic manufacturing systems are different from the real manufacturing systems. In order to study the energy-efficiency scheduling models in line with the actual manufacturing system, some scholars have investigated energy-efficiency scheduling in the actual pro- duction and manufacturing system, such as hardware manufacturing and iron and steel industry [17–22]. According to different production stages, the energy cost mainly consists of processing energy cost, setup energy cost, standby energy cost, etc. [23]. Many studies discuss process- ing energy cost, which accounts for the largest proportion of the total energy cost [24,25]. Setup energy cost cannot be ignored in many industries, especially in the processing indus- try. In addition, transport energy cost may be negligible in many industries, but it cannot be ignored in heavy industry. Setup time and transportation time may span multiple time periods, leading to different electricity prices in the same setup stage or transportation stage. Consequently, it is difficult to build an efficient energy cost model. Many research studies on energy-efficiency scheduling under TOU electricity tariffs fails to consider the setup energy cost and the transportation energy cost. The feasibility of reducing material wastage and energy consumption in tissue pa- per mills has been proved through production scheduling [26]. Energy consumption in tissue paper mills can be decreased by combining process optimization and production scheduling [27]. However, the previous research fails to consider TOU electricity tariffs. This study investigates the energy-efficiency scheduling under TOU electricity tariffs for tissue paper mills. There are three main contributions in this paper: First, a new mathe- matical model of energy-efficiency scheduling under TOU electricity tariffs is established for tissue paper mills. Energy cost includes processing energy cost, setup energy cost and transportation energy cost. Second, a novel Multi-Objective Evolutionary Algorithm based on Decomposition and Teaching–Learning-Based Optimization (MOEA/DTL) is proposed, which further improves the performance of the MOEA/DTL by Variable Neighborhood Search (IMOEA/DTLB). Third, the effectiveness of the proposed IMOEA/DTL is verified by carrying out a case study. Lastly, the energy-saving potential of the IMOEA/DTL is evaluated based on a practical scheduling problem in a tissue paper mill. This paper is structured as follows. In Section 2, the production process and the energy-efficiency scheduling of tissue paper mills under electricity tariffs are described. Moreover, an energy cost model under TOU electricity tariffs is built, and the energy- efficiency scheduling model under TOU electricity tariffs is built. Section 3 introduces the proposed IMOEA/DTL method. Section 4 verifies the feasibility of the study and the effectiveness of the proposed algorithm by carrying out a case study. Finally, Section 5 summarizes the study and proposes the future research direction. 2. Problem Description and Modeling As shown in Figure 1, the production of a tissue paper mill mainly includes two stages, namely the pulping and papermaking stage and the conversion stage. In the pulping and papermaking stage, the first production unit is the stock preparation system, which is
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