Multi Objective and Multi-Product Perishable Supply Chain with Vendor-Managed Inventory and IoT-Related Technologies
Abstract
:1. Introduction
- Introducing a novel nonlinear integer mathematical model for supply chain design, taking into account IoT-related technologies (RFID and WSN);
- Selecting the suitable technology between RFID and WSN for each level of the supply chain;
- Modeling the inventory management process in the supply chain using these technologies and implementing a vendor-managed inventory management policy;
- Considering simultaneous time and cost optimization in a real case of intelligent supply chain.
Motivation and Contribution
2. Literature Review
3. Model Assumptions and Notations
- IoT involves two technologies, RFID and WSN, but only one of these technologies is used at each node.
- There are multiple types of products and materials.
- The supply time of raw materials is influenced by the use of RFID or WSN technologies.
- The total cost includes the cost of establishing each node in the supply chain, blockchain implementation, RFID implementation, WSN implementation, and transportation among nodes.
- Delivery time is considered as the model’s secondary objective.
- The products are perishable.
- The conversion factor of raw materials to final products is assumed to equal 1.
- The model parameters are deterministic.
Indices | |||||
n | m | l | k | j | i |
Raw materials | Product | Customer | Retailer | Manufacturer | Supplier |
4. Mathematical Model and Analysis
Objective Functions
5. Approach to Model Solution
5.1. Model Validation
Types of raw materials | Types of products | No. of customers | No. of retailers | No. of manufacturers | No. of suppliers |
2 | 3 | 12 | 7 | 3 | 4 |
5.2. Sensitivity Analysis in Small Size
5.3. Parameter Tuning
- Evidently, MOGWO generated the highest number of Pareto points, with NSGA-III closely following. The higher the number of Pareto points, the more efficient the algorithm is considered.
- In terms of distance to the ideal point, NSGA-III yielded the smallest distance to the ideal point, while the other two algorithms show relatively similar performance in this criterion.
- As for crowding distance, where smaller values indicate better efficiency, MOGWO achieved the smallest crowding distance. However, MOWOA yielded the shortest smalling distance in the third example.
- Computation time is another important criterion where lower values suggest that the algorithm is more suitable. MOGWO achieved the shortest computation time, followed closely by NSGA-III. MOWOA produced the highest computation time.
5.4. Results of Solving One of the Problems
5.5. Analysis of the Impact of WSN and RFID
5.6. Analysis of the Impact of Blockchain
5.7. Analysis of the Impact of Online Sales
5.8. Comparison of the Results
- The use of RFID at the customer and supplier levels resulted in a greater reduction in costs compared to WSN.
- For retailers, WSN was more effective in reducing the cost.
- The use of RFID at the retail and supplier levels led to a significant reduction in time.
- Overall, WSN had a more significant impact overall compared to RFID for customers; however, RFID had a more positive impact on time.
- Blockchain contributed to a significant reduction in costs for suppliers, manufacturers, and retailers.
- Blockchain significantly reduced the delivery times of retailers, manufacturers, and suppliers.
- Overall, blockchain had the greatest impact on manufacturers.
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Customer demand for product m from retailer k | |
Fixed cost of establishing supplier i | |
Fixed cost of establishing factory j | |
Fixed cost of establishing retailer k | |
Cost of installing RFID technology at customer node l | |
Cost of installing WSN technology at customer node l | |
Cost of installing RFID technology at retailer node k | |
Cost of installing WSN technology at retailer node k | |
Capacity of supplier i for procuring material n | |
Capacity of factory j for manufacturing product m | |
Capacity of retailer k for product m | |
Cost of purchasing factory j’s raw material n from supplier i | |
Cost of purchasing factory j’s product m from retailer k | |
Cost of purchasing product m from retailer k for customer l | |
Delivery time of raw material n from supplier i to factory j | |
Delivery time of product m from factory j to retailer k | |
Delivery time of product m from retailer k to customer l | |
Cost of transporting raw material n from supplier i to factory j | |
Cost of transporting product m from factory j to retailer k | |
Cost of transporting product m from retailer k to customer l | |
Average procurement time of raw material n by supplier i for factory j without RFID | |
Average procurement time of raw material n by supplier i for factory j with RFID | |
Average procurement time of raw material n by supplier i for manufacturer j without WSN | |
Average procurement time of raw material n by supplier i for manufacturer j with WSN | |
Cost of implementing blockchain for supplier i | |
Cost of implementing blockchain for factory j | |
Cost of implementing blockchain for retailer k | |
Cost of implementing online sales for retailer k | |
Maximum inventory level of product m for retailer k | |
Minimum inventory level of product m for retailer k |
Decision Variables
A binary variable that equals 1 if supplier i is active; otherwise, 0 | |
A binary variable that equals 1 if factory j is active; otherwise, 0 | |
A binary variable that equals 1 if retailer k is active; otherwise, 0 | |
A binary variable that equals 1 if supplier i delivers raw material n to factory j; otherwise, 0 | |
A binary variable that equals 1 if factory j delivers product m to retailer k; otherwise, 0 | |
A binary variable that equals 1 if retailer k delivers product m to customer l; otherwise, 0 | |
A binary variable that equals 1 if RFID technology is installed at customer node l; otherwise, 0 | |
A binary variable that equals 1 if WSN technology is used at customer node l; otherwise, 0 | |
A binary variable that equals 1 if RFID technology is installed at retailer node k; otherwise, 0 | |
A binary variable that equals 1 if WSN technology is used at retailer node k; otherwise, 0 | |
A binary variable that equals 1 if RFID technology is installed at supplier node i; otherwise, 0 | |
A binary variable that equals 1 if WSN technology is used at supplier node i; otherwise, 0 | |
Quantity of raw material n transported from supplier i to factory j with blockchain | |
Quantity of raw material n transported from supplier i to factory j without blockchain | |
Quantity of product m transported from factory j to retailer k with blockchain | |
Quantity of product m transported from factory j to retailer k without blockchain | |
Quantity of product m transported from retailer k to customer l with blockchain | |
Quantity of product m transported from retailer k to customer l without blockchain | |
A binary variable that equals 1 if blockchain is used for supplier i; otherwise, 0 | |
A binary variable that equals 1 if blockchain is used for factory j; otherwise, 0 | |
A binary variable that equals 1 if blockchain is used for retailer k; otherwise, 0 | |
A binary variable that equals 1 if online sales are used for retailer k; otherwise, 0 | |
The sales quantity of product m through online sales for retailer k | |
Inventory level of product m for retailer k | |
Initial inventory level of product m for retailer k | |
Optimal replenishment level of product m under VMI policy for retailer k |
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Reference Number | Features | ||||||||
---|---|---|---|---|---|---|---|---|---|
Multi-Objective | Perishability | IoT | Blockchain | Online Sales | Mathematical Modeling | ||||
Cost | Time | ||||||||
1 | [36] | * | * | * | * | ||||
2 | [37] | * | * | * | * | ||||
3 | [38] | * | * | * | |||||
4 | [39] | * | * | * | * | * | |||
5 | [40] | * | * | * | |||||
6 | [41] | * | * | * | |||||
7 | [42] | * | * | ||||||
8 | [43] | * | * | * | |||||
9 | [44] | * | * | * | |||||
10 | [33] | * | * | ||||||
11 | [45] | * | * | * | * | ||||
12 | [46] | * | * | ||||||
13 | [47] | * | * | ||||||
14 | [48] | * | * | * | |||||
15 | [49] | * | * | ||||||
16 | [50] | * | * | * | * | * | |||
17 | [51] | * | * | * | |||||
18 | [52] | * | * | ||||||
19 | [53] | * | * | * | |||||
20 | [54] | * | * | * | |||||
21 | [55] | * | * | ||||||
22 | [56] | * | * | * | * | ||||
23 | [57] | * | * | ||||||
24 | [58] | * | * | * | * | ||||
25 | Present article | * | * | * | * | * | * | * | * |
Z1 | Z2 |
---|---|
14,383 | 19,618 |
13,989 | 14,387 |
13,106 | 19,835 |
14,118 | 19,630 |
13,923 | 19,678 |
13,615 | 19,725 |
13,626 | 19,737 |
13,425 | 19,741 |
13,234 | 19,802 |
14,006 | 19,648 |
13,354 | 19,775 |
13,335 | 19,790 |
13,153 | 19,832 |
13,695 | 19,698 |
14,383 | 19,618 |
13,989 | 14,387 |
13,110 | 19,835 |
Problem | Supplier | Manufacturer | Retailer | Customer | Product | Raw Material |
---|---|---|---|---|---|---|
1 | 3 | 2 | 5 | 10 | 2 | 2 |
2 | 3 | 2 | 6 | 11 | 2 | 2 |
3 | 3 | 2 | 6 | 11 | 3 | 2 |
4 | 3 | 2 | 6 | 12 | 3 | 2 |
5 | 4 | 2 | 6 | 12 | 3 | 2 |
6 | 4 | 2 | 7 | 12 | 3 | 2 |
7 | 4 | 3 | 7 | 12 | 3 | 2 |
8 | 4 | 3 | 7 | 13 | 3 | 2 |
9 | 4 | 3 | 7 | 13 | 4 | 2 |
10 | 5 | 3 | 7 | 13 | 4 | 2 |
Problem | Computation Time (s) | Primary Objective Function (Cost) | Secondary Objective Function (Time) |
---|---|---|---|
1 | 37 | 7936 | 11,094 |
2 | 59 | 8780 | 13,907 |
3 | 73 | 8424 | 14,266 |
4 | 96 | 8645 | 15,161 |
5 | 114 | 9397 | 15,923 |
6 | 129 | 10,375 | 18,033 |
7 | 148 | 13,106 | 19,847 |
8 | Low memory | Low memory | Low memory |
9 | Low memory | Low memory | Low memory |
10 | Low memory | Low memory | Low memory |
Demand | Cost | Time | Change in Cost | Change in Time |
---|---|---|---|---|
0% | 11,097 | 7790 | — | — |
10% | 12,942 | 7986 | 0.166261 | 0.02516 |
20% | 16,528 | 8379 | 0.277082 | 0.049211 |
30% | 21,653 | 8950 | 0.31008 | 0.068147 |
40% | 28,515 | 9718 | 0.316908 | 0.08581 |
50% | 37,030 | 10,638 | 0.298615 | 0.09467 |
Installation Cost | Cost | Time | Change in Cost | Change in Time |
---|---|---|---|---|
0% | 11,097 | 7790 | — | — |
10% | 12,682 | 7903 | 0.142831 | 0.014506 |
20% | 15,482 | 8180 | 0.220785 | 0.03505 |
30% | 19,828 | 8585 | 0.280713 | 0.049511 |
40% | 26,038 | 9153 | 0.313193 | 0.066162 |
50% | 33,867 | 9883 | 0.300676 | 0.079755 |
Procurement Cost | Cost | Time | Change in Cost | Change in Time |
---|---|---|---|---|
0% | 11,097 | 7790 | — | — |
10% | 12,211 | 7902 | 0.100387 | 0.014377 |
20% | 14,897 | 8145 | 0.219966 | 0.030752 |
30% | 19,473 | 8507 | 0.307176 | 0.044444 |
40% | 25,247 | 9045 | 0.296513 | 0.063242 |
50% | 32,538 | 9768 | 0.288787 | 0.079934 |
Adjustable Parameters | Values | |||||||
---|---|---|---|---|---|---|---|---|
Population size | n | 3n | 3n | 4n | 4n | 4n | 4n | 4n |
Maximum main loop iterations | 2 | 3 | 4 | 25 | 30 | 35 | 40 | 45 |
Number of random start time selections | 1 | 1 | 1 | 4 | 4 | 6 | 6 | 8 |
Crossover rate | 0.1 | 0.1 | 0.2 | 0.2 | 0.6 | 0.6 | 0.6 | 0.6 |
Mutation rate | 0.1 | 0.1 | 0.2 | 0.2 | 0.2 | 0.25 | 0.3 | 0.3 |
Probability of single-point crossover selection | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Probability of arithmetic crossover selection | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Probability of exchange mutation selection | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Probability of direction selection for probability distribution | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Value of α | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.02 | 0.2 |
Value of π | 0.01 | 0.01 | 0.02 | 0.03 | 0.04 | 0.04 | 0.05 | 0.05 |
Average number of non-dominated solutions per 10 algorithm runs | 4 | 4 | 5 | 5 | 7 | 8 | 10 | 11 |
Adjustable Parameters | Values | |||||||
---|---|---|---|---|---|---|---|---|
Population size | n | 3n | 3n | 4n | 4n | 4n | 4n | 4n |
Maximum main loop iterations | 2 | 3 | 4 | 25 | 30 | 30 | 30 | 30 |
Number of random start time selections | 1 | 1 | 1 | 4 | 5 | 5 | 10 | 10 |
Crossover rate | 0.1 | 0.1 | 0.2 | 0.2 | 0.6 | 0.6 | 0.6 | 0.6 |
Mutation rate | 0.1 | 0.1 | 0.2 | 0.2 | 0.2 | 0.25 | 0.3 | 0.3 |
Probability of single-point crossover selection | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Probability of arithmetic crossover selection | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Probability of exchange mutation selection | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Probability of direction selection for probability distribution | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Value of α | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.02 | 0.2 |
Value of π | 0.01 | 0.01 | 0.02 | 0.03 | 0.04 | 0.04 | 0.05 | 0.05 |
Average number of non-dominated solutions per 10 algorithm runs | 4.8 | 5.1 | 6.6 | 6.8 | 7 | 7.5 | 8.5 | 8.8 |
Adjustable Parameters | Values | |||||||
---|---|---|---|---|---|---|---|---|
Population size | n | 3n | 3n | 4n | 4n | 4n | 4n | 4n |
Maximum main loop iterations | 2 | 3 | 3 | 20 | 20 | 30 | 30 | 30 |
Number of random start time selections | 1 | 1 | 1 | 4 | 5 | 5 | 5 | 5 |
Crossover rate | 0.1 | 0.1 | 0.2 | 0.2 | 0.3 | 0.3 | 0.5 | 0.5 |
Mutation rate | 0.1 | 0.1 | 0.2 | 0.2 | 0.2 | 0.2 | 0.2 | 0.2 |
Probability of single-point crossover selection | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Probability of arithmetic crossover selection | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Probability of exchange mutation selection | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Probability of direction selection for probability distribution | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
Value of α | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.02 | 0.2 |
Value of π | 0.01 | 0.01 | 0.02 | 0.03 | 0.04 | 0.04 | 0.05 | 0.05 |
Average number of non-dominated solutions per 10 algorithm runs | 4.2 | 4.6 | 5.5 | 5.7 | 6 | 6.2 | 7.2 | 7.8 |
Problem | Supplier | Manufacturer | Retailer | Customer | Product | Raw Material |
---|---|---|---|---|---|---|
1 | 10 | 3 | 15 | 30 | 5 | 3 |
2 | 11 | 3 | 15 | 32 | 5 | 3 |
3 | 11 | 3 | 16 | 32 | 5 | 3 |
4 | 12 | 3 | 16 | 33 | 5 | 3 |
5 | 12 | 3 | 17 | 35 | 5 | 3 |
6 | 13 | 4 | 17 | 35 | 5 | 3 |
7 | 13 | 4 | 18 | 35 | 5 | 3 |
8 | 14 | 4 | 18 | 36 | 5 | 4 |
9 | 14 | 4 | 18 | 38 | 5 | 4 |
10 | 15 | 5 | 19 | 39 | 5 | 4 |
Problem | NSGA-III | MOGWO | MOWOA | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
No. of Pareto Points | Distance to Ideal Point | Crowding Distance | Solution Time | No. of Pareto Points | Distance to Ideal Point | Crowding Distance | Solution Time | No. of Pareto Points | Distance to Ideal Point | Crowding Distance | Computation Time | |
1 | 11 | 0.77 | 75 | 67 | 8 | 0.79 | 93 | 71 | 14 | 0.81 | 85 | 76 |
2 | 15 | 0.84 | 63 | 78 | 16 | 0.78 | 94 | 84 | 16 | 0.83 | 66 | 90 |
3 | 15 | 0.86 | 97 | 97 | 12 | 0.78 | 86 | 99 | 11 | 0.8 | 50 | 100 |
4 | 11 | 0.71 | 95 | 111 | 13 | 0.79 | 79 | 119 | 13 | 0.81 | 86 | 110 |
5 | 13 | 0.74 | 71 | 126 | 11 | 0.79 | 83 | 136 | 12 | 0.82 | 93 | 121 |
6 | 6 | 0.75 | 82 | 138 | 11 | 0.81 | 97 | 155 | 11 | 0.77 | 97 | 134 |
7 | 7 | 0.79 | 83 | 150 | 9 | 0.8 | 94 | 173 | 16 | 0.83 | 95 | 148 |
8 | 11 | 0.8 | 77 | 170 | 10 | 0.81 | 52 | 186 | 8 | 0.81 | 87 | 160 |
9 | 10 | 0.81 | 100 | 181 | 15 | 0.82 | 74 | 197 | 7 | 0.82 | 64 | 178 |
10 | 6 | 0.8 | 57 | 194 | 6 | 0.82 | 58 | 212 | 16 | 0.81 | 73 | 191 |
Customer | Customer | ||||||
---|---|---|---|---|---|---|---|
RFID | WSN | RFID | WSN | ||||
Cost | Time | Cost | Time | Improvement in cost | Improvement in time | Improvement in cost | Improvement in time |
11,097 | 7790 | 11,111 | 7789 | 0.016921 | 0.001282 | 0.01568 | 0.00141 |
Retailer | Retailer | ||||||
---|---|---|---|---|---|---|---|
RFID | WSN | RFID | WSN | ||||
Cost | Time | Cost | Time | Improvement in cost | Improvement in time | Improvement in cost | Improvement in time |
11,182 | 7780 | 11,130 | 7787 | 0.009391 | 0.002564 | 0.013997 | 0.001667 |
Supplier | Supplier | ||||||
---|---|---|---|---|---|---|---|
RFID | WSN | RFID | WSN | ||||
Cost | Time | Cost | Time | Improvement in cost | Improvement in time | Improvement in cost | Improvement in time |
11,095 | 7780 | 11,096 | 7782 | 0.017098 | 0.002564 | 0.017009 | 0.002308 |
Supplier | Supplier | ||
---|---|---|---|
Cost | Time | Improvement in Cost | Improvement in Time |
11,156 | 7785 | 0.011694 | 0.001923 |
Manufacturer | Manufacturer | ||
---|---|---|---|
Cost | Time | Improvement in Cost | Improvement in Time |
11,116 | 7785 | 0.015237 | 0.001923 |
Retailer | Retailer | ||
---|---|---|---|
Cost | Time | Improvement in Cost | Improvement in Time |
11,156 | 7785 | 0.011694 | 0.001923 |
Retailer | Retailer | ||
---|---|---|---|
Cost | Time | Improvement in Cost | Improvement in Time |
11,170 | 7782 | 0.010454 | 0.002308 |
Cost | RFID | WSN | Time | RFID | WSN |
---|---|---|---|---|---|
Initial | 11,288 | 11,288 | Initial | 7800 | 7800 |
Customer | 11,097 | 11,111 | Customer | 7790 | 7789 |
Retailer | 11,182 | 11,130 | Retailer | 7780 | 7787 |
Supplier | 11,095 | 11,096 | Supplier | 7780 | 7782 |
Cost | Time | |
---|---|---|
Initial | 11,288 | 7800 |
Suppliers | 11,156 | 7785 |
Manufacturers | 11,116 | 7785 |
Retailers | 11,170 | 7785 |
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Mohammadi, T.; Sajadi, S.M.; Najafi, S.E.; Taghizadeh-Yazdi, M. Multi Objective and Multi-Product Perishable Supply Chain with Vendor-Managed Inventory and IoT-Related Technologies. Mathematics 2024, 12, 679. https://doi.org/10.3390/math12050679
Mohammadi T, Sajadi SM, Najafi SE, Taghizadeh-Yazdi M. Multi Objective and Multi-Product Perishable Supply Chain with Vendor-Managed Inventory and IoT-Related Technologies. Mathematics. 2024; 12(5):679. https://doi.org/10.3390/math12050679
Chicago/Turabian StyleMohammadi, Tahereh, Seyed Mojtaba Sajadi, Seyed Esmaeil Najafi, and Mohammadreza Taghizadeh-Yazdi. 2024. "Multi Objective and Multi-Product Perishable Supply Chain with Vendor-Managed Inventory and IoT-Related Technologies" Mathematics 12, no. 5: 679. https://doi.org/10.3390/math12050679