Processes 2021 , 9 , 274
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will increase the pressure on work-in-process inventory. However, a short interval time is likely to cause frequent downtime of the machine in the conversion stage. Therefore, it is important to determine the optimal interval time in the production scheduling. The scheduling of a tissue paper mill, which is two-stage flexible flow shop scheduling, is composed of the pulping and papermaking stage and the conversion stage. Each job is processed by a production line in the pulping and papermaking stage and a production line in the conversion stage. The energy consumption in the processing stage accounts for the vast majority of energy consumption in tissue paper mills. Product characteristics can deter- mine the processing energy consumption. Different product characteristics mean different process parameters, and the energy consumed by machines under different process parame- ters varies significantly. For example, the products with high grammage will consume more energy in the papermaking stage, and vice versa. Under TOU electricity tariffs, the energy cost can be reduced in two ways: (i) arranging the job to the production line with low processing energy consumption; and (ii) arranging the job with high grammage production in the off-peak or mid-peak period and the job with low grammage production in the on-peak period. When there are two different consecutive jobs, production changeover will occur in tissue paper mills. The parameters of the machine should be adjusted to process the new later job, which will consume a lot of energy in the setup stage. In general, the setup energy cost can be reduced by arranging jobs with lower setup energy consumption processed consecutively. Under TOU electricity tariffs, the setup energy cost can be further reduced by arranging the jobs with higher setup energy consumption processed in the off-peak or mid-peak period and the jobs with lower setup energy consumption processed in the on-peak period. The parent rolls produced in the pulping and papermaking stage should be transported to the conversion stage for further processing. The transport energy consumption is related to the distance between the papermaking line and the conversion line. Similarly, the transportation distance can be shortened to decrease the transport energy cost. Moreover, the transport energy cost can be further reduced by arranging the jobs with high transportation energy consumption in the off-peak or mid-peak period and the jobs with low transportation energy consumption in the on-peak period. Tissue paper mills can decrease the energy cost by utilizing the TOU electricity pricing scheme in job scheduling. Table 1 shows the TOU electricity tariffs in Guangdong, China.
Table1. Time-of-use (TOU) electricity tariffs implemented in Guangdong.
Period Type
Time Periods
Electricity Price (CNY/kWh)
Off-peak Mid-peak On-peak
00:00–08:00
0.3351 0.6393 1.0348
08:00–09:00; 12:00–19:00; 22:00–24:00
09:00–12:00; 19:00–22:00
2.1. Energy Cost Modeling According to the characteristics of energy consumption in tissue paper mills, this study mainly considers energy cost from three aspects: processing energy cost, setup energy cost, and transportation energy cost. Processing energy cost is related to processing energy consumption and electricity price. Under the TOU electricity pricing scheme, different electricity prices are set for different periods in a day. This study establishes a processing energy cost model combined with the TOU electricity pricing scheme and the processing energy consumption. The processing energy cost model is as below.
m ∑ j = 1 n ∑ i = 1 ( EP 1 + EP 2 + EP 3 + EP 4 ) ∗ O i , j
(1)
EP =
EP 1 = MIN CEIL S i , j − S i , j , FG CEIL S i , j + T i , j , CEIL S i , j × U i , j × P FLOOR ( MOD ( S i , j , K ))
(2)
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