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Title Page

Abstract

Contents

1. Introduction 11

2. Literature review 15

3. Methodology 17

3.1. Problem Statement 17

3.2. Notation 19

3.3. Fraction of Energy Cost Computation 19

3.4. Mathematical Formulation 21

3.5. Solution Approaches 22

4. Computational experiments 24

4.1. Data 24

4.1.1. Study area 24

4.1.2. Data description 25

4.2. Results and analysis 27

4.2.1. Result of normalized weighting method 27

4.2.2. Result of constraint method 28

4.2.3. Baseline experiment 30

4.3. Sensitivity analysis 35

4.3.1. Energy generation cost 35

4.3.2. Combination of energy sources 40

5. Conclusions 47

REFERENCES 49

List of Tables

Table 1. U.S. electricity generation costs and carbon emissions by energy sources. 12

Table 2. Partial lists of unproduced item data in June 2021. 25

Table 3. Partial lists of production time data for NC machines to produce items. 26

Table 4. Worldwide carbon emissions and electricity generation cost by energy source in 2021. 27

Table 5. Partial results obtained by the normalized weighting method. 28

Table 6. Partial results obtained by the constraint method. 29

Table 7. Trade-offs between weekly total cost and weekly total carbon emissions from the baseline experiment. 31

Table 8. Detailed results of a baseline experiment for carbon emissions limit at 2000 kg. 33

Table 9. Detailed results of a baseline experiment for carbon emissions limit at 4400 kg. 34

Table 10. Assignment results of various natural gas generation costs for Figure 6. 37

Table 11. Assignment results of various coal generation costs for Figure 7. 39

Table 12. Results of weekly total cost and weekly total carbon emissions from the combination of two energy sources from Figure 7. 43

Table 13. Results of weekly total cost and weekly total carbon emissions from the combination of three energy sources from Figure 8. 46

List of Figures

Figure 1. Structure of the proposed methodology. 18

Figure 2. Examples of energy cost growth functions. 21

Figure 3. Weekly total cost and total carbon emissions based on the normalized weighting method. 28

Figure 4. Weekly total cost based on weekly carbon emissions limit in the constraint method. 30

Figure 5. Results of a baseline experiment for weekly total cost and weekly total carbon emissions for different carbon emissions limits from Table 7. 31

Figure 6. Assignment results of various natural gas generation costs (the original generation cost, 40% increase, 80% increase, 40% decrease, 80% decrease). 36

Figure 7. Assignment results of various coal generation costs (the original generation cost, 40% increase, 80% increase, 40% decrease, 80% decrease). 38

Figure 8. Results of weekly total cost and weekly total carbon emissions from the combination of two energy sources. 42

Figure 9. Results of weekly total cost and weekly total carbon emissions from the combination of three energy sources. 45

초록보기

 This paper addresses the production scheduling problem with non-identical parallel machines in a high-mix, low-volume production environment with due dates, considering carbon emissions savings and diverse types of energy sources for machine operation. To this end, we present a bi-objective mixed-integer programming model that minimizes both the total production-related cost and the total carbon emissions in the production process to determine the optimal production strategy. For each machine, we consider various types of energy sources with different electricity generation costs and different amounts of carbon emissions. The proposed model is validated with an application to a manufacturer in Ulsan, the industrial capital of the Republic of Korea. Our results showcase the potential use of non-identical parallel machines to minimize the total cost and carbon emissions in green manufacturing. Furthermore, the results identify the trade-off between different energy sources and the total cost under different carbon emissions limits. Generally, as the carbon emissions limit increases, our proposed model tends to replace natural gas with coal to minimize the total cost. Also, we perform sensitivity analyses with respect to the energy price of different types of energy sources combined with nuclear and renewable energy sources. We find that coal provides more stability than natural gas in terms of the total cost, particularly when there are fluctuations in the price for coal and natural gas. Additionally, we determine the optimal combination of energy sources for various carbon emissions limits, aiming to minimize the total cost while simultaneously satisfying all production-related and environmental constraints.

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