Unregulated Cap-and-Trade Model for Sustainable Supply Chain Management
<p>Emissions <math display="inline"><semantics> <msub> <mi>E</mi> <mi>t</mi> </msub> </semantics></math> for instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>3</mn> </msub> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>.</p> "> Figure 2
<p>Emissions <math display="inline"><semantics> <msub> <mi>E</mi> <mi>t</mi> </msub> </semantics></math> for instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>10</mn> </msub> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>.</p> "> Figure 3
<p>Emission chart over time for instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>3</mn> </msub> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: comparison between models <tt>UM</tt> and <tt>UM′</tt>.</p> "> Figure 4
<p>Emission chart over time for instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>10</mn> </msub> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>: comparison between models <tt>UM</tt> and <tt>UM′</tt>.</p> "> Figure 5
<p>Emission chart over time for instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>10</mn> </msub> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: comparison between models <tt>UM</tt> and <tt>UM′</tt>.</p> "> Figure 6
<p>Emissions <math display="inline"><semantics> <msub> <mi>E</mi> <mi>t</mi> </msub> </semantics></math> for instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>3</mn> </msub> </semantics></math> (model <tt>UM′</tt>) for different <math display="inline"><semantics> <mi>η</mi> </semantics></math> values.</p> "> Figure 7
<p>Emissions <math display="inline"><semantics> <msub> <mi>E</mi> <mi>t</mi> </msub> </semantics></math> for instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>10</mn> </msub> </semantics></math> (model <tt>UM′</tt>) for different <math display="inline"><semantics> <mi>η</mi> </semantics></math> values.</p> "> Figure 8
<p>Pareto front for instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>10</mn> </msub> </semantics></math>; (<b>a</b>) Pareto front for model <math display="inline"><semantics> <mrow> <mi>U</mi> <mi>M</mi> </mrow> </semantics></math>, Instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>10</mn> </msub> </semantics></math>; (<b>b</b>) Pareto front for model <math display="inline"><semantics> <mrow> <mi>U</mi> <msup> <mi>M</mi> <mo>′</mo> </msup> </mrow> </semantics></math>, instance <math display="inline"><semantics> <msub> <mi>I</mi> <mn>10</mn> </msub> </semantics></math>.</p> ">
Abstract
:1. Introduction and Literature Review
2. Problem Definition and Mathematical Formulations
- Trade emissions, receiving carbon quotas from or providing carbon quotas to other facilities;
- An increase in the technology level owned at to a level in order to reduce emissions for a unit or worked product; this implies an investment by facility j. Trivially, if the technology level of j at time t remains unchanged w.r.t. we have .
- T:
- the set of time periods indexed by t;
- F:
- the set of facilities indexed by j and ;
- S:
- the set of suppliers indexed by s;
- L:
- the set of technology levels indexed by l and ;
- :
- CO2 emissions per unit of product manufactured in plant with technology level [ton/unit]; with ;
- :
- CO2 emissions per unit of product transported from supplier to plant [ton/unit];
- :
- unit production cost in facility using technology level ;
- :
- unit transportation cost from supplier to facility ;
- D:
- market demand within the time horizon;
- B:
- the overall budget that facilities can use to invest in (green) technologies;
- : installation cost of technology level in plant assuming a negligible level of technology in j;
- :
- capacity of a facility ;
- :
- capacity of a supplier ;
- :
- weighting value for the emissions term in the objective function.
- : holds 1 if plant works with a technological level at time and 0 otherwise;
- : amount of production in plant at time ;
- : amount of products moved from supplier to plant at time ;
- : amount of CO2 exchanged from plant to plant at time ;
- : supply chain global emissions at time ;
- : net CO2 emissions of facility at time (takes into account also carbon quotas traded).
- The term which, based on the technological level l chosen for plant j at time t, calculates the product between the unit emission cost associated with technology level l, i.e., , times the flow of products manufactured in j at time t, and
- The total CO2 exchanged among plant j and the other facilities.
Linearization
3. Experimental Analysis of the Model
4. Theoretical Results and Further Experiments
Further Computational Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
CO2 | Carbon Dioxide |
ETS | Emissions Trading System |
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Reference | Problem | CO2 | Objective | Solution |
---|---|---|---|---|
[3] | lot-sizing | carbon price | min costs | analytical |
[4] | green investment | cap-and-trade | max profit | analytical |
[5] | inventory-routing | cap-and-trade | min costs | branch and price |
[6] | green investments | cap-and-trade | min total costs | analytical |
[7] | reverse logistics | cap-and-trade | max NPV | solver |
[8] | revenue sharing | cap-and-trade | max profit | analytical |
[14] | social welfare | carbon tax | min deviation | solver |
[15] | renewable energy | carbon credits | min credits | KKT & algorithm |
[16] | country incentives | carbon tax | max GDP | NSGA-II |
[17] | tax allocation | carbon tax | max GDP | analytical |
[18] | revenue sharing | cap-and-trade | max profit | analytical |
[19] | cooperation | cap-and-trade | max profit | analytical |
[20] | carbon mechanism | cap-and-trade | max profit | analytical |
Parameter | Baseline Value (bv) |
---|---|
[gCO2/unit] | |
1 [gCO2/unit] | |
[€/unit] | |
5 [€/unit] | |
D | 15,000 [units] |
B | [k€] |
[€] | |
[units] | |
[units] |
Parameter | Baseline Values (bv) |
---|---|
[gCO2/unit] | |
1 [gCO2/unit] | |
[€/unit] | |
5 [€/unit] | |
D | 1500 [units] |
B | [k€] |
[€] | |
[units] | |
[units] |
j | 2 | 3 | |
---|---|---|---|
1 | 0.00 | 2085.65 | 0.00 |
2 | 4377.40 | 0.00 | 0.00 |
3 | 2186.19 | 0.00 | 0.00 |
j | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|
1 | 0.00 | 408.47 | 161.47 | 56.94 | 0.00 | 0.00 | 49.20 | 0.00 | 0.00 | 166.53 |
2 | 107.94 | 0.00 | 124.33 | 112.42 | 0.00 | 0.00 | 177.66 | 0.00 | 106.94 | 0.00 |
3 | 0.00 | 0.00 | 0.00 | 63.25 | 0.00 | 0.00 | 60.65 | 0.00 | 52.59 | 55.55 |
4 | 242.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
7 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
8 | 0.00 | 0.00 | 0.00 | 298.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
9 | 271.86 | 220.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
10 | 242.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
j | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|
1 | −218.01 | −1920.51 | −100.54 | −2146.21 | −92.67 |
2 | 218.01 | 1920.51 | −2085.65 | 2146.21 | 92.67 |
3 | 0.00 | 0.00 | 2186.19 | 0.00 | 0.00 |
j | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|
1 | −64.65 | −70.17 | −56.98 | 231.49 | −61.85 |
2 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
3 | −4.23 | −30.10 | −0.00 | −11.97 | −7.46 |
4 | −54.06 | −63.25 | −58.36 | −56.94 | −56.44 |
5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
7 | −68.70 | −49.20 | −54.51 | −54.45 | −60.65 |
8 | 0.00 | 0.00 | 0.00 | 0.00 | 298.73 |
9 | −51.04 | 271.86 | 220.81 | −52.59 | −55.89 |
10 | 242.68 | −59.14 | −50.96 | −55.55 | −56.43 |
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Caramia, M.; Stecca, G. Unregulated Cap-and-Trade Model for Sustainable Supply Chain Management. Mathematics 2024, 12, 477. https://doi.org/10.3390/math12030477
Caramia M, Stecca G. Unregulated Cap-and-Trade Model for Sustainable Supply Chain Management. Mathematics. 2024; 12(3):477. https://doi.org/10.3390/math12030477
Chicago/Turabian StyleCaramia, Massimiliano, and Giuseppe Stecca. 2024. "Unregulated Cap-and-Trade Model for Sustainable Supply Chain Management" Mathematics 12, no. 3: 477. https://doi.org/10.3390/math12030477