A Multi-Objective Model for Sustainable Perishable Food Distribution Considering the Impact of Temperature on Vehicle Emissions and Product Shelf Life
Abstract
:1. Introduction
2. Literature Review
3. Problem Statement and Model Formulation
3.1. Temperature Prediction Based on Heat Transfer
3.1.1. Temperature Prediction during Unloading
3.1.2. Temperature Prediction during Transportation
3.2. CO2 Emissions
3.3. Food Product Freshness Based on Shelf Life Prediction
3.4. Mathematical Model
4. Solution Procedure
Algorithm 1 NSGA-II main loop pseudocode |
p = population of randomly generated chromosomes with size pops for i = 1 to Max number of iterations do for j =1 to (pc ÷ 2) do c1 = 1st randomly chosen parent chromosome c2 = 2nd randomly selected parent chromosome popc = append crossover (c1, c2) for k = 1 to pm do m = a randomly chosen parent chromosome popm = append mutate (m) pop = merge (p, popc, popm) function (non-dominated sorting (input: pop)) return: Rank of chromosomes function (crowding distance (input: pop, rank)) return: crowding distance value for each chromosome function (sort population (input: pop, rank, crowding distance)) return: sorted pop based on 1) rank, 2) crowding distance pop = store only the top pop and truncate the others function (non-dominated sorting (input: pop)) return: Rank of chromosomes function (crowding distance (input: pop, rank)) return: crowding distance value for each chromosome function (sort population (input: pop, rank, crowding distance)) return: sorted pop based on 1) rank, 2) crowding distance Pareto_frontier = chromosomes with rank 1 Go to the next iteration if the stopping criteria are not met |
5. Computational Results and Discussion
5.1. Performance of the Solution Method
5.2. Optimality Analysis
5.3. Sensitivity to Shelf Life
5.4. Sensitivity to Temperature Setting
6. Conclusions and Future Research
Author Contributions
Funding
Conflicts of Interest
Appendix A
References
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Literature | Quality Degradation Changes | Method of Addressing Perishability | Objectives | Temperature Effect on Quality | Emission | Temperature Effect on Emissions | Temperature Prediction | Solution Method | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Linear over Time | Linear over Temperature | Nonlinear over Time | Nonlinear over Temperature | Economic | Perishability | Emissions | Transportation | Refrigeration | Exact | Heuristic | Metaheuristic | |||||
Hsu et al. [31] | x | The predicted amount of spoiled products are added to the shipment to ensure orders are filled | x | x | x | x | x | |||||||||
Osvald & Stirn [10] | x | Minimize delivery time | x | x | ||||||||||||
Chen et al. [26] | x | Minimize product deterioration, assuming a constant rate | x | x | ||||||||||||
Wang et al. [43] | Does not address perishability | x | x | x | x | |||||||||||
Ahumada & Villalobos [29] | x | Minimize product decay | x | x | ||||||||||||
Farahani et al. [30] | x | Minimize time between production and delivery | x | x | ||||||||||||
Amorim et al. [34] | x | x | Maximize fractional remaining shelf life | x | x | x | ||||||||||
Hsu et al. [35] | Does not address perishability | x | x | x | ||||||||||||
Govindan et al. [41] | Does not address perishability | x | x | x | x | |||||||||||
Molina et al. [42] | Does not address perishability | x | x | x | x | |||||||||||
Amorim & Almada-Lobo [33] | x | Maximize average freshness | x | x | x | x | ||||||||||
Khalili-Damghani et al. [45] | x | Constrain delivery of products to occur before they expire | x | x | x | |||||||||||
Bortolini et al. [32] | x | Minimize delivery time | x | x | x | x | x | |||||||||
Wang et al. [22] | x | x | Maximize freshness | x | x | x | ||||||||||
Ghezavati et al. [27] | x | Minimize quality degradation and disposal costs | x | x | ||||||||||||
Devapriya et al. [44] | x | Constrain delivery of products to occur before they expire | x | x | ||||||||||||
Hsiao et al. [36] | x | x | Minimize loss in shelf life as product-related costs | x | x | |||||||||||
Gallo et al. [37] | x | x | Minimize energy consumed to cool down products spoiled in transportation | x | x | x | x | |||||||||
Musavi & Bozorgi-Amiri [25] | x | Maximize purchase probability | x | x | x | x | x | |||||||||
Albrecht & Steinrücke [28] | x | Maximize revenue from the grade of quality | x | x | ||||||||||||
Wang et al. [38] | x | Minimize product damage costs in the objective function | x | x | x | x | ||||||||||
Stellingwerf et al. [17] | Does not address perishability | x | x | x | x | x | ||||||||||
Rahbari et al. [23] | x | Maximize freshness | x | x | x | |||||||||||
This research | x | x | Maximize average freshness | x | x | x | x | x | x | x | x | x |
Sets: |
C = {1, …, n}: set of customers |
V = {1, …, v}: set of vehicles |
N = {0} C: set of depot and customers |
A = {(i, j): i, j N, and i ≠ j}: set of paths from node i to node j |
Parameters: |
cij: cost of traveling from node i to node j |
tij: travel time from node i to node j |
F: fixed dispatching cost |
Q: vehicle capacity |
di: customer i demand |
[ai, bi]: required time window for delivery to customer i |
ut: average unloading time for one unit of product |
ui: unloading time at customer i, where = and ui ≤ bi − ai |
Decision variables: |
: time that vehicle k arrives at node i |
: equals 1 if vehicle k travels from node i to node j, 0 otherwise |
: units of product carried by vehicle k between nodes i and j |
w-SA Parameters | Value | NSGA-II Parameters | Value | Test Problem Parameters | Value |
---|---|---|---|---|---|
Initial temperature | 20 | Population size | 30 | Vehicle speed (km h−1) | 15 |
Damping rate | 0.99 | Crossover rate | 0.7 | Product shelf life (h) | 2880 |
Mutation rate | 0.4 | Fixed cost per vehicle ($) | 1000 | ||
Transportation cost ($ km−1) | 1.5 | ||||
Service time (minute) | 10 * 90 ** | ||||
Vehicle capacity (kg) | 200 |
Test Problem | w-SA | NSGA-II | Gap | ||||||
---|---|---|---|---|---|---|---|---|---|
Costs ($) | Freshness (%) | CO2 (lbs × 103) | Costs ($) | Freshness (%) | CO2 (lbs × 103) | Costs ($) | Freshness (%) | CO2 (lbs × 103) | |
R101 (25) | 5233 | 89% | 4164 | 4,886 | 95% | 3848 | 6.6% | 4.8% | 17.5% |
R101 (100) | 13,450 | 90% | 48,042 | 12,356 | 94% | 45,026 | 8.1% | 2.3% | 6.3% |
C101 (25) | 3065 | 90% | 2452 | 2761 | 96% | 2305 | 9.9% | 6.7% | 6.0% |
C101 (100) | 10,655 | 92% | 39,787 | 9452 | 94% | 38,564 | 11.3% | 2.2% | 3.1% |
RC101 (25) | 3318 | 90% | 3,075 | 3027 | 92% | 2684 | 8.8% | 4.6% | 12.7% |
RC101 (100) | 11,569 | 91% | 47,666 | 10,335 | 93% | 42,597 | 10.7% | 4.5% | 2.4% |
Optimality | No. of Vehicles | Costs ($) | Freshness (%) | CO2 (lbs × 103) |
---|---|---|---|---|
Cost | 7 | 4886 (*) | 55% (42% gap) | 3997 (4% gap) |
Freshness | 8 | 112,123 (95% gap) | 95% (*) | 66,413 (94% gap) |
Emission | 7 | 5723 (14% gap) | 56% (41% gap) | 3848 (*) |
Final solution | 7 | 10,213 (52% gap) | 75% (21% gap) | 8892 (57% gap) |
Shelf Life (h) | Costs ($) | Freshness (%) | CO2 (lbs × 103) |
---|---|---|---|
168 | 13,522 | 62% | 12,916 |
1440 | 11,390 | 71% | 10,662 |
2880 | 10,213 | 75% | 8892 |
Temperature (°K) | Costs ($) | Freshness (%) | CO2 (lbs × 103) |
---|---|---|---|
263 | 10,213 | 75% | 8892 |
265 | 10,526 | 72% | 8556 |
267 | 11,013 | 68% | 8436 |
269 | 11,596 | 60% | 8301 |
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Gharehyakheh, A.; Krejci, C.C.; Cantu, J.; Rogers, K.J. A Multi-Objective Model for Sustainable Perishable Food Distribution Considering the Impact of Temperature on Vehicle Emissions and Product Shelf Life. Sustainability 2020, 12, 6668. https://doi.org/10.3390/su12166668
Gharehyakheh A, Krejci CC, Cantu J, Rogers KJ. A Multi-Objective Model for Sustainable Perishable Food Distribution Considering the Impact of Temperature on Vehicle Emissions and Product Shelf Life. Sustainability. 2020; 12(16):6668. https://doi.org/10.3390/su12166668
Chicago/Turabian StyleGharehyakheh, Amin, Caroline C. Krejci, Jaime Cantu, and K. Jamie Rogers. 2020. "A Multi-Objective Model for Sustainable Perishable Food Distribution Considering the Impact of Temperature on Vehicle Emissions and Product Shelf Life" Sustainability 12, no. 16: 6668. https://doi.org/10.3390/su12166668