Bi-Objective Optimization Model Based on Profit and CO2 Emissions for Pig Deliveries to the Abattoir
Abstract
:1. Introduction
- RQ1: Is the inclusion of CO emissions penalizing optimal decisions regarding the delivery of fattened pig to the abattoir?
- RQ2: What is a reasonable margin of profit reduction in favor of a greener production?
- RQ3: Are the policy of deliveries to the abattoir affected by the inclusion of CO emissions?
- RQ4: Is there room for additional gains in reducing CO reduction preserving pig production efficiency?
2. Literature Review
3. Mathematical Modeling
3.1. The Optimal Delivery Problem
3.2. The Optimization Model
3.2.1. Indices and Sets
- t ∈ T,
- Index (in weeks) the fattening period is divided into, .
- i ∈ P,
- Index of partitions to cluster pigs into growth categories .
- k ∈ K,
- Index of types of truck .
3.2.2. Parameters
- N,
- Batch size representing the number of pigs moved to the fattening farms.
- ni,
- Cluster of growth category i, in which the initial batch was partitioned.
- ,
- Mean value of the live weight of pigs (kg) in the growth category i at week t. We assume the live weight of the batch follows a normal distribution, ).
- ω,
- Selling price, € per kg of carcass weight.
- ,
- Cumulative feed intake average (kg) by a pig in growth category i until week t.
- ,
- Bonus given by the abattoir (€/kg of carcass weight) as a function of growth category i at week t.
- δ,
- cost in Euros per kg of feed intake.
- λk,
- Fixed cost in Euros for trucks of type k sent to the abattoir.
- αi,
- Cost in Euros for other expenses in the system for growth category i, such as vets and medicines.
- ξ,
- Cost in Euros per young pig purchased.
- ψk,
- Capacity of trucks of type k in number of animals.
- τk,
- Capacity of trucks of type k in kilograms of load.
- ϱit,
- Carcass weight per growth category i at week t.
- κ,
- kg CO -eq per kg of meat produced.
- v,
- Euros per kg of CO .
- γk,
- Emissions kg CO per trip and k-truck type
- φ,
- Weight for the bi-objective function ().
3.2.3. Decision Variables
- xit,
- Number of pigs from partition i to be sent to the abattoir in fattening week t.
- ykt,
- Integer variable with the number of trucks of type k needed at week t to ship pigs.
- zit,
- Inventory of pigs for partition i at the beginning of the fattening week t.
- hit,
- Binary variable with a value of one when pigs from two consecutive partitions (, i) are sent to the abattoir, zero otherwise.
- dit,
- Binary variable with a value of one when pigs from partition i at week t are sent to the abattoir, zero otherwise.
- wit,
- Live weight when animals are sent to abattoir.
3.2.4. Objective Function
3.2.5. Constraints
4. Results and Discussion
4.1. Default Parameters
4.2. Maximizing Revenues and Minimizing CO Emissions
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Age (Week) | Weight (kg) Mean | SD | Intake (kg) Mean | SD |
---|---|---|---|---|
1 | 29.7 | 3.9 | 5.1 | 5.5 |
2 | 33.4 | 4.6 | 12.1 | 8.5 |
3 | 37.8 | 5.4 | 20.5 | 12.1 |
4 | 42.6 | 6.3 | 30.2 | 15.9 |
5 | 47.9 | 7.4 | 41.3 | 19.7 |
6 | 53.5 | 8.4 | 53.4 | 23.6 |
7 | 59.3 | 9.5 | 66.4 | 27.5 |
8 | 65.3 | 10.6 | 80.3 | 31.4 |
9 | 71.3 | 11.8 | 94.9 | 35.3 |
10 | 77.4 | 12.9 | 110.1 | 39.2 |
11 | 83.4 | 14.0 | 125.7 | 43.2 |
12 | 89.2 | 15.2 | 141.6 | 47.1 |
13 | 94.8 | 16.3 | 157.6 | 51 |
14 | 100 | 17.5 | 173.7 | 54.9 |
15 | 104.8 | 18.7 | 189.6 | 58.9 |
16 | 109.1 | 19.8 | 205.3 | 62.8 |
17 | 112.8 | 21.0 | 220.6 | 66.7 |
T1 | T2 | T3 | T4 | |
---|---|---|---|---|
Capacity () | 50 | 220 | 440 | 550 |
Cost per trip () | 125 | 475 | 900 | 1000 |
Emissions kg CO /trip () | 28.25 | 66.30 | 57.99 | 79.14 |
S | E | U | R | O | P | Live Weight (kg) | Carcass Weight (kg) |
---|---|---|---|---|---|---|---|
0.57 | 0.28 | 0.12 | 0.03 | 0.00 | 0.00 | 50 | 39.4 |
0.55 | 0.27 | 0.14 | 0.04 | 0.00 | 0.00 | 55 | 43.4 |
0.53 | 0.26 | 0.15 | 0.05 | 0.01 | 0.00 | 60 | 47.4 |
0.50 | 0.28 | 0.16 | 0.05 | 0.01 | 0.00 | 65 | 51.4 |
0.49 | 0.27 | 0.17 | 0.05 | 0.01 | 0.00 | 70 | 55.5 |
0.49 | 0.28 | 0.17 | 0.06 | 0.01 | 0.00 | 75 | 59.5 |
0.45 | 0.27 | 0.18 | 0.08 | 0.01 | 0.00 | 80 | 63.6 |
0.44 | 0.26 | 0.19 | 0.09 | 0.03 | 0.01 | 85 | 67.6 |
0.43 | 0.25 | 0.18 | 0.09 | 0.03 | 0.01 | 90 | 71.7 |
0.41 | 0.24 | 0.19 | 0.10 | 0.04 | 0.01 | 95 | 75.8 |
0.40 | 0.23 | 0.19 | 0.11 | 0.05 | 0.02 | 100 | 79.9 |
0.39 | 0.23 | 0.19 | 0.12 | 0.05 | 0.02 | 105 | 84.0 |
0.38 | 0.22 | 0.19 | 0.12 | 0.06 | 0.03 | 110 | 88.1 |
0.38 | 0.21 | 0.19 | 0.13 | 0.07 | 0.04 | 115 | 92.3 |
0.37 | 0.2 | 0.18 | 0.13 | 0.07 | 0.04 | 120 | 96.4 |
% Profit Decrease | % CO emission Decrease | Profit (€) | CO Cost (€) | |
---|---|---|---|---|
1 | 23,891 | 6051 | ||
0.68 | 0.00 | 0.00 | 23,891 | 6051 |
0.38 | 0.33 | 2.65 | 23,812 | 5891 |
0.22 | 0.50 | 3.44 | 23,684 | 5843 |
0.20 | 0.87 | 3.44 | 23,684 | 5843 |
0.16 | 1.189 | 4.35 | 23,440 | 5788 |
0.12 | 4.48 | 6.05 | 22,821 | 5685 |
0.10 | 15.30 | 11.36 | 20,237 | 5364 |
0.08 | 15.88 | 11.59 | 20,098 | 5350 |
0.04 | 16.63 | 11.82 | 19,919 | 5336 |
0 | 26.68 | 13.31 | 17,516 | 5246 |
13 | 14 | 15 | 16 | 17 | |
---|---|---|---|---|---|
0 | 1,000 | 0 | 0 | 0 | 0 |
0.04 | 600 | 400 | 0 | 0 | 0 |
0.08 | 550 | 450 | 0 | 0 | 0 |
0.1 | 500 | 500 | 0 | 0 | 0 |
0.12 | 200 | 0 | 600 | 200 | 0 |
0.16 | 180 | 0 | 220 | 600 | 0 |
0.20 | 50 | 220 | 0 | 730 | 0 |
0.22 | 50 | 180 | 0 | 770 | 0 |
0.38 | 0 | 200 | 50 | 750 | 0 |
0.68 | 0 | 200 | 0 | 0 | 800 |
1 | 0 | 200 | 0 | 0 | 800 |
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Nadal-Roig, E.; Pagès-Bernaus, A.; Plà-Aragonès, L.M. Bi-Objective Optimization Model Based on Profit and CO2 Emissions for Pig Deliveries to the Abattoir. Sustainability 2018, 10, 1782. https://doi.org/10.3390/su10061782
Nadal-Roig E, Pagès-Bernaus A, Plà-Aragonès LM. Bi-Objective Optimization Model Based on Profit and CO2 Emissions for Pig Deliveries to the Abattoir. Sustainability. 2018; 10(6):1782. https://doi.org/10.3390/su10061782
Chicago/Turabian StyleNadal-Roig, Esteve, Adela Pagès-Bernaus, and Lluís M. Plà-Aragonès. 2018. "Bi-Objective Optimization Model Based on Profit and CO2 Emissions for Pig Deliveries to the Abattoir" Sustainability 10, no. 6: 1782. https://doi.org/10.3390/su10061782