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Large complex equipment PSSC
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Optimization of the product service supply chain under the influence of presale services
| 1. | Institute of Logistics Science and Engineering, Shanghai Maritime University, Shanghai 201306, China |
| 2. | School of Business, Shanghai Dianji University, Shanghai 201306, China |
For some high-value and technology-intensive products, customers first ask service integrators to provide presales consulting services for products with potential demand. Improving the service level of presales service will increase service costs and reduce profits, but it can also increase the demand for products. The change in market demand under the influence of services will result in a series of chain reactions, such as changes in supply chain inventory costs and distribution costs. Thus, this paper considers the changes in the product service supply chain (PSSC) network caused by changes in presale service levels and service prices from the overall perspective of the supply chain and chooses a reasonable service level and price so that service integrators and product suppliers in PSSCs can achieve a win-win situation while meeting customer needs. First, a PSSC network optimization model is established considering the presale service level and price. Then, a double-layer nested genetic algorithm with constraint reasoning is proposed to solve this problem. Finally, by calculating the PSSC case of a building material company that produces a water mist spray system for ships, the feasibility and practicability of the algorithm was verified.
Keywords:
Product service supply chain,
presales service,
service level,
service price,
service integrator.
Mathematics Subject Classification:
90B06.
Citation:
Xiaohui Ren, Daofang Chang, Jin Shen.
Optimization of the product service supply chain under the influence of presale services. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021130
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References:
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S. Axsäter,
Using the deterministic eoq formula in stochastic inventory control, Management Science, 42 (1996), 830-834.
|
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T. Baines, H. Lightfoot and P. Smart,
Servitization within manufacturing, Journal of Manufacturing Technology Management, 22 (2011), 947-954.
doi: 10.1108/17410381111160988. |
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J. F. Bard and J. E. Falk,
An explicit solution to the multi-level programming problem, Comput. Oper. Res., 9 (1982), 77-100.
doi: 10.1016/0305-0548(82)90007-7. |
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W. Candler and R. Townsley,
A linear two - level programming problem, Comput. Oper. Res., 9 (1982), 59-76.
doi: 10.1016/0305-0548(82)90006-5. |
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M. S. Chen and C. T. Lin, Effects of centralization on expected costs in a multi-location newsboy problem, J Oper Res Soc, 755–761. |
| [6] |
P. J. Colen and M. R. Lambrecht,
Product service systems: Exploring operational practices, The Service Industries Journal, 33 (2013), 501-515.
doi: 10.1080/02642069.2011.614344. |
| [7] |
B. Dan, H. Gao, Y. Zhang, R. Liu and S. Ma,
Integrated order acceptance and scheduling decision making in product service supply chain with hard time windows constraints, J. Ind. Manag. Optim., 14 (2018), 165-182.
doi: 10.3934/jimo.2017041. |
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C. C. Fang, Optimal price and warranty decision for durable products in a competitive duopoly market - sciencedirect, Reliability Engineering & System Safety, 203. |
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H. Gebauer, A. Gustafsson and L. Witell,
Competitive advantage through service differentiation by manufacturing companies, Journal of Business Research, 64 (2011), 1270-1280.
doi: 10.1016/j.jbusres.2011.01.015. |
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J. A. Guajardo,
Pay-as-you-go business models in developing economies: Consumer behavior and repayment performance, Social Science Electronic Publishing, 62 (2016), 1860-1877.
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J. A. Guajardo, M. A. Cohen and S. Netessine,
Service competition and product quality in the us automobile industry, Management Science, 66 (2012), 1-32.
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Gu pta and Di wakar,
Flexible carrier-forwarder contracts for air cargo business, Journal of Revenue & Pricing Management, 7 (2008), 341-356.
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J. R. Jiao, Q. Xu, Z. Wu and N. K. Ng,
Coordinating product, process, and supply chain decisions: A constraint satisfaction approach, Engineering Applications of Artificial Intelligence, 22 (2009), 992-1004.
doi: 10.1016/j.engappai.2009.02.002. |
| [14] |
M. Johnson and C. Mena,
Supply chain management for servitised products: A multi-industry case study, International Journal of Production Economics, 114 (2008), 27-39.
doi: 10.1016/j.ijpe.2007.09.011. |
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U. Karmarkar,
Will you survive the services revolution?, Harvard Business Review, 82 (2004), 100-107.
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V. B. Kreng and T. P. Lee,
Modular product design with grouping genetic algorithm-a case study, Computers & Industrial Engineering, 46 (2004), 443-460.
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Kumar, Mukesh, Harrington, Toms, Seosamh, Srai, Jagjit, Singh, Yuto and Minakata., Industrial system dynamics for environmental sustainability: A case study on the uk medical technology sector., International Journal of Manufacturing Technology & Management, 31 (2017), 100–132. |
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H. Kurata and S.-H. Nam,
After-sales service competition in a supply chain: Optimization of customer satisfaction level or profit or both?, International Journal of Production Economics, 127 (2010), 136-146.
doi: 10.1016/j.ijpe.2010.05.005. |
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Z. L.,
Service-oriented manufacturing: The new tool of enterprise competition, Chinese Mechanics Industry, 12 (2007), 16-17.
|
| [20] |
G. Li, F. F. Huang, T. C. E. Cheng, Q. Zheng and P. Ji,
Make-or-buy service capacity decision in a supply chain providing after-sales service, European Journal of Operational Research, 239 (2014), 377-388.
doi: 10.1016/j.ejor.2014.05.035. |
| [21] |
K. Li, S. Mallik and D. Chhajed,
Design of extended warranties in supply chains under additive demand, Production & Operations Management, 21 (2012), 730-746.
doi: 10.1111/j.1937-5956.2011.01300.x. |
| [22] |
J. Little and E. Tsang, Foundations of constraint satisfaction, Science Direct. |
| [23] |
H. Lockett, M. Johnson, S. Evans and M. Bastl,
Product service systems and supply network relationships: an exploratory case study, Journal of Manufacturing Technology Management, 22 (2011), 293-313.
doi: 10.1108/17410381111112684. |
| [24] |
e. a. Luo,
Equilibrium decisions of product service supply chain netword considering service outsourcing, Computer Integrated Manufacturing Systems, 27 (2020), 260-268.
|
| [25] |
O. K. Mont,
Clarifying the concept of product-service system, Journal of Cleaner Production, 10 (2002), 237-245.
doi: 10.1016/S0959-6526(01)00039-7. |
| [26] |
Y. Peng, D. Xu, Y. Li and K. Wang, A product service supply chain network equilibrium model considering capacity constraints, Math. Probl. Eng., 2020 (2020), Art. ID 1295072, 15 pp.
doi: 10.1155/2020/1295072. |
| [27] |
G. Ryzin, Analyzing inventory cost and service in supply chains., |
| [28] |
J. Shen, J. A. Erkoyuncu, R. Roy and B. Wu,
A framework for cost evaluation in product service system configuration, International Journal of Production Research, 55 (2017), 6120-6144.
doi: 10.1080/00207543.2017.1325528. |
| [29] |
Z. Shuai, X. Song, W. Zhang, D. J. Yu and C. Kai,
A hybrid approach combining an extended bbo algorithm with an intuitionistic fuzzy entropy weight method for qos-aware manufacturing service supply chain optimization, Neurocomputing, 272 (2017), 439-452.
|
| [30] |
J. Sun, T. Qu, D. Nie and P. Li,
Research on "location-inventory" problem of spare parts supply chain based on product service system, Procedia CIRP, 83 (2019), 819-825.
doi: 10.1016/j.procir.2019.05.024. |
| [31] |
Y. Wang, L. Sun, R. Qu and G. Li,
Price and service competition with maintenance service bundling, Journal of Systems Science & Systems Engineering, 24 (2015), 168-189.
doi: 10.1007/s11518-015-5267-z. |
| [32] |
C.-H. Wu,
Price and service competition between new and remanufactured products in a two-echelon supply chain, International Journal of Production Economics, 140 (2012), 496-507.
doi: 10.1016/j.ijpe.2012.06.034. |
| [33] |
W. Xie, Y. Zhao, Z. Jiang and P.-S. Chow,
Optimizing product service system by franchise fee contracts under information asymmetry, Ann. Oper. Res., 240 (2016), 709-729.
doi: 10.1007/s10479-013-1505-2. |
| [34] |
D. Yang, J. Jiao, Y. Ji, G. Du, P. Helo and A. Valente,
Joint optimization for coordinated configuration of product families and supply chains by a leader-follower stackelberg game, European J. Oper. Res., 246 (2015), 263-280.
doi: 10.1016/j.ejor.2015.04.022. |
| [35] |
E. A. Zhang,
Research on cross-chain coordination mechanism of logistics service supply chain considering operational risks, Highway Transportation Science and Technology, 36 (2019), 135-143.
|
| [36] |
D. Zhao, X. Zhang, T. Ren and H. Fu, Optimal pricing strategies in a product and service supply chain with extended warranty service competition considering retailer fairness concern, Math. Probl. Eng., 2019 (2019), Art. ID 8657463, 15 pp.
doi: 10.1155/2019/8657463. |
show all references
References:
| [1] |
S. Axsäter,
Using the deterministic eoq formula in stochastic inventory control, Management Science, 42 (1996), 830-834.
|
| [2] |
T. Baines, H. Lightfoot and P. Smart,
Servitization within manufacturing, Journal of Manufacturing Technology Management, 22 (2011), 947-954.
doi: 10.1108/17410381111160988. |
| [3] |
J. F. Bard and J. E. Falk,
An explicit solution to the multi-level programming problem, Comput. Oper. Res., 9 (1982), 77-100.
doi: 10.1016/0305-0548(82)90007-7. |
| [4] |
W. Candler and R. Townsley,
A linear two - level programming problem, Comput. Oper. Res., 9 (1982), 59-76.
doi: 10.1016/0305-0548(82)90006-5. |
| [5] |
M. S. Chen and C. T. Lin, Effects of centralization on expected costs in a multi-location newsboy problem, J Oper Res Soc, 755–761. |
| [6] |
P. J. Colen and M. R. Lambrecht,
Product service systems: Exploring operational practices, The Service Industries Journal, 33 (2013), 501-515.
doi: 10.1080/02642069.2011.614344. |
| [7] |
B. Dan, H. Gao, Y. Zhang, R. Liu and S. Ma,
Integrated order acceptance and scheduling decision making in product service supply chain with hard time windows constraints, J. Ind. Manag. Optim., 14 (2018), 165-182.
doi: 10.3934/jimo.2017041. |
| [8] |
C. C. Fang, Optimal price and warranty decision for durable products in a competitive duopoly market - sciencedirect, Reliability Engineering & System Safety, 203. |
| [9] |
H. Gebauer, A. Gustafsson and L. Witell,
Competitive advantage through service differentiation by manufacturing companies, Journal of Business Research, 64 (2011), 1270-1280.
doi: 10.1016/j.jbusres.2011.01.015. |
| [10] |
J. A. Guajardo,
Pay-as-you-go business models in developing economies: Consumer behavior and repayment performance, Social Science Electronic Publishing, 62 (2016), 1860-1877.
|
| [11] |
J. A. Guajardo, M. A. Cohen and S. Netessine,
Service competition and product quality in the us automobile industry, Management Science, 66 (2012), 1-32.
|
| [12] |
Gu pta and Di wakar,
Flexible carrier-forwarder contracts for air cargo business, Journal of Revenue & Pricing Management, 7 (2008), 341-356.
|
| [13] |
J. R. Jiao, Q. Xu, Z. Wu and N. K. Ng,
Coordinating product, process, and supply chain decisions: A constraint satisfaction approach, Engineering Applications of Artificial Intelligence, 22 (2009), 992-1004.
doi: 10.1016/j.engappai.2009.02.002. |
| [14] |
M. Johnson and C. Mena,
Supply chain management for servitised products: A multi-industry case study, International Journal of Production Economics, 114 (2008), 27-39.
doi: 10.1016/j.ijpe.2007.09.011. |
| [15] |
U. Karmarkar,
Will you survive the services revolution?, Harvard Business Review, 82 (2004), 100-107.
|
| [16] |
V. B. Kreng and T. P. Lee,
Modular product design with grouping genetic algorithm-a case study, Computers & Industrial Engineering, 46 (2004), 443-460.
doi: 10.1016/j.cie.2004.01.007. |
| [17] |
Kumar, Mukesh, Harrington, Toms, Seosamh, Srai, Jagjit, Singh, Yuto and Minakata., Industrial system dynamics for environmental sustainability: A case study on the uk medical technology sector., International Journal of Manufacturing Technology & Management, 31 (2017), 100–132. |
| [18] |
H. Kurata and S.-H. Nam,
After-sales service competition in a supply chain: Optimization of customer satisfaction level or profit or both?, International Journal of Production Economics, 127 (2010), 136-146.
doi: 10.1016/j.ijpe.2010.05.005. |
| [19] |
Z. L.,
Service-oriented manufacturing: The new tool of enterprise competition, Chinese Mechanics Industry, 12 (2007), 16-17.
|
| [20] |
G. Li, F. F. Huang, T. C. E. Cheng, Q. Zheng and P. Ji,
Make-or-buy service capacity decision in a supply chain providing after-sales service, European Journal of Operational Research, 239 (2014), 377-388.
doi: 10.1016/j.ejor.2014.05.035. |
| [21] |
K. Li, S. Mallik and D. Chhajed,
Design of extended warranties in supply chains under additive demand, Production & Operations Management, 21 (2012), 730-746.
doi: 10.1111/j.1937-5956.2011.01300.x. |
| [22] |
J. Little and E. Tsang, Foundations of constraint satisfaction, Science Direct. |
| [23] |
H. Lockett, M. Johnson, S. Evans and M. Bastl,
Product service systems and supply network relationships: an exploratory case study, Journal of Manufacturing Technology Management, 22 (2011), 293-313.
doi: 10.1108/17410381111112684. |
| [24] |
e. a. Luo,
Equilibrium decisions of product service supply chain netword considering service outsourcing, Computer Integrated Manufacturing Systems, 27 (2020), 260-268.
|
| [25] |
O. K. Mont,
Clarifying the concept of product-service system, Journal of Cleaner Production, 10 (2002), 237-245.
doi: 10.1016/S0959-6526(01)00039-7. |
| [26] |
Y. Peng, D. Xu, Y. Li and K. Wang, A product service supply chain network equilibrium model considering capacity constraints, Math. Probl. Eng., 2020 (2020), Art. ID 1295072, 15 pp.
doi: 10.1155/2020/1295072. |
| [27] |
G. Ryzin, Analyzing inventory cost and service in supply chains., |
| [28] |
J. Shen, J. A. Erkoyuncu, R. Roy and B. Wu,
A framework for cost evaluation in product service system configuration, International Journal of Production Research, 55 (2017), 6120-6144.
doi: 10.1080/00207543.2017.1325528. |
| [29] |
Z. Shuai, X. Song, W. Zhang, D. J. Yu and C. Kai,
A hybrid approach combining an extended bbo algorithm with an intuitionistic fuzzy entropy weight method for qos-aware manufacturing service supply chain optimization, Neurocomputing, 272 (2017), 439-452.
|
| [30] |
J. Sun, T. Qu, D. Nie and P. Li,
Research on "location-inventory" problem of spare parts supply chain based on product service system, Procedia CIRP, 83 (2019), 819-825.
doi: 10.1016/j.procir.2019.05.024. |
| [31] |
Y. Wang, L. Sun, R. Qu and G. Li,
Price and service competition with maintenance service bundling, Journal of Systems Science & Systems Engineering, 24 (2015), 168-189.
doi: 10.1007/s11518-015-5267-z. |
| [32] |
C.-H. Wu,
Price and service competition between new and remanufactured products in a two-echelon supply chain, International Journal of Production Economics, 140 (2012), 496-507.
doi: 10.1016/j.ijpe.2012.06.034. |
| [33] |
W. Xie, Y. Zhao, Z. Jiang and P.-S. Chow,
Optimizing product service system by franchise fee contracts under information asymmetry, Ann. Oper. Res., 240 (2016), 709-729.
doi: 10.1007/s10479-013-1505-2. |
| [34] |
D. Yang, J. Jiao, Y. Ji, G. Du, P. Helo and A. Valente,
Joint optimization for coordinated configuration of product families and supply chains by a leader-follower stackelberg game, European J. Oper. Res., 246 (2015), 263-280.
doi: 10.1016/j.ejor.2015.04.022. |
| [35] |
E. A. Zhang,
Research on cross-chain coordination mechanism of logistics service supply chain considering operational risks, Highway Transportation Science and Technology, 36 (2019), 135-143.
|
| [36] |
D. Zhao, X. Zhang, T. Ren and H. Fu, Optimal pricing strategies in a product and service supply chain with extended warranty service competition considering retailer fairness concern, Math. Probl. Eng., 2019 (2019), Art. ID 8657463, 15 pp.
doi: 10.1155/2019/8657463. |
Figure 2.
GA encoding for PSSC
Figure 3.
Algorithm flowchart
Figure 4.
Searching process of optimal solution by genetic algorithm
Figure 5.
Searching process of optimal service price and level of genetic algorithm
Figure 6.
Brief PSSC network diagram
Figure 7.
Search process of the classic double nested genetic algorithm
Figure 8.
Search process of the adaptive genetic algorithm
Table 1.
Supply chain nodes and main function
| Node | Main Function |
| product supplier | Providing products, meeting the product demand of the regional warehouse node |
| service integrator | Setting up offices at the service warehouse node to provide services, selling products and giving product demand order to product supplier |
| regional warehouse | Meeting the needs of service warehouse node products |
| service warehouse | Distributing products to customers, provide customers with presale services |
| Node | Main Function |
| product supplier | Providing products, meeting the product demand of the regional warehouse node |
| service integrator | Setting up offices at the service warehouse node to provide services, selling products and giving product demand order to product supplier |
| regional warehouse | Meeting the needs of service warehouse node products |
| service warehouse | Distributing products to customers, provide customers with presale services |
Table 2.
Regional warehouse node parameter table
| Parameters | Regional Warehouse | ||||
| Node | 1.5 | 1 | 1 | 1.3 | 1 |
| Unit inventory cost | 38 | 42 | 40 | 35 | 45 |
| Mean demand | 1 | 1 | 1 | 1 | 1 |
| Lead time | 2 | 2 | 2 | 2 | 2 |
| Counting cycle | 4 | 4.5 | 5.5 | 5 | 5 |
| Distribution cost | 155 | 156 | 200 | 160 | 170 |
| Facility fixed cost | 1.5 | 1 | 1 | 1.3 | 1 |
| 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | |
| Parameters | Regional Warehouse | ||||
| Node | 1.5 | 1 | 1 | 1.3 | 1 |
| Unit inventory cost | 38 | 42 | 40 | 35 | 45 |
| Mean demand | 1 | 1 | 1 | 1 | 1 |
| Lead time | 2 | 2 | 2 | 2 | 2 |
| Counting cycle | 4 | 4.5 | 5.5 | 5 | 5 |
| Distribution cost | 155 | 156 | 200 | 160 | 170 |
| Facility fixed cost | 1.5 | 1 | 1 | 1.3 | 1 |
| 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | |
Table 3.
Service warehouse node S1-S7 parameter table
| Parameters | Service Warehouse | ||||||
| Node | S1 | S2 | S3 | S4 | S5 | S6 | S7 |
| Unit inventory cost | 1.2 | 1.5 | 1.5 | 1 | 1.1 | 1.7 | 1.5 |
| Unit replenishment cost | 2.7 | 2.7 | 2.7 | 2.9 | 2.9 | 2.9 | 3 |
| Mean demand | 15 | 14 | 16 | 20 | 18 | 17 | 15 |
| Lead time | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Counting cycle | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| Facility fixed cost | 150 | 157 | 160 | 155 | 160 | 170 | 190 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | |
| 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | |
| Parameters | Service Warehouse | ||||||
| Node | S1 | S2 | S3 | S4 | S5 | S6 | S7 |
| Unit inventory cost | 1.2 | 1.5 | 1.5 | 1 | 1.1 | 1.7 | 1.5 |
| Unit replenishment cost | 2.7 | 2.7 | 2.7 | 2.9 | 2.9 | 2.9 | 3 |
| Mean demand | 15 | 14 | 16 | 20 | 18 | 17 | 15 |
| Lead time | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Counting cycle | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| Facility fixed cost | 150 | 157 | 160 | 155 | 160 | 170 | 190 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | |
| 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | |
Table 4.
Service warehouse node S8-S14 parameter table
| Parameters | Service Warehouse | ||||||
| Node | S8 | S9 | S10 | S11 | S12 | S13 | S14 |
| Unit inventory cost | 0.9 | 1 | 1 | 1.5 | 1.3 | 1.3 | 1 |
| Unit replenishment cost | 3 | 3 | 2.9 | 2.9 | 3 | 3 | 3 |
| Mean demand | 16 | 14 | 15 | 17 | 15 | 20 | 18 |
| Lead time | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Counting cycle | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| Facility fixed cost | 157 | 160 | 180 | 170 | 165 | 170 | 160 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | |
| 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | |
| Parameters | Service Warehouse | ||||||
| Node | S8 | S9 | S10 | S11 | S12 | S13 | S14 |
| Unit inventory cost | 0.9 | 1 | 1 | 1.5 | 1.3 | 1.3 | 1 |
| Unit replenishment cost | 3 | 3 | 2.9 | 2.9 | 3 | 3 | 3 |
| Mean demand | 16 | 14 | 15 | 17 | 15 | 20 | 18 |
| Lead time | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Counting cycle | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| Facility fixed cost | 157 | 160 | 180 | 170 | 165 | 170 | 160 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | |
| 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | 0.65 | |
Table 5.
Unit delivery cost from regional warehouse node to service warehouse node
| Node | R1 | R2 | R3 | R4 | R5 | Node | R1 | R2 | R3 | R4 | R5 | |
| S1 | 1 | 4 | 2.3 | 3 | 3.5 | S8 | 4.3 | 2.5 | 5 | 4 | 2.5 | |
| S2 | 2 | 3.5 | 3 | 4 | 3 | S9 | 3 | 4 | 2.5 | 3.5 | 2 | |
| S3 | 1 | 2 | 3.5 | 1.3 | 4 | S10 | 1.5 | 3 | 1.5 | 2.6 | 4 | |
| S4 | 1.3 | 3 | 2 | 5 | 4 | S11 | 2.3 | 3 | 1.5 | 4 | 5 | |
| S5 | 3.5 | 2 | 1.3 | 4 | 5 | S12 | 4 | 3 | 1.5 | 1.5 | 1.5 | |
| S6 | 3 | 1.5 | 2 | 2.6 | 1 | S13 | 2 | 4 | 2.6 | 3 | 1.6 | |
| S7 | 2 | 2.6 | 1 | 3.3 | 4 | S14 | 4 | 2.5 | 3 | 5 | 1 |
| Node | R1 | R2 | R3 | R4 | R5 | Node | R1 | R2 | R3 | R4 | R5 | |
| S1 | 1 | 4 | 2.3 | 3 | 3.5 | S8 | 4.3 | 2.5 | 5 | 4 | 2.5 | |
| S2 | 2 | 3.5 | 3 | 4 | 3 | S9 | 3 | 4 | 2.5 | 3.5 | 2 | |
| S3 | 1 | 2 | 3.5 | 1.3 | 4 | S10 | 1.5 | 3 | 1.5 | 2.6 | 4 | |
| S4 | 1.3 | 3 | 2 | 5 | 4 | S11 | 2.3 | 3 | 1.5 | 4 | 5 | |
| S5 | 3.5 | 2 | 1.3 | 4 | 5 | S12 | 4 | 3 | 1.5 | 1.5 | 1.5 | |
| S6 | 3 | 1.5 | 2 | 2.6 | 1 | S13 | 2 | 4 | 2.6 | 3 | 1.6 | |
| S7 | 2 | 2.6 | 1 | 3.3 | 4 | S14 | 4 | 2.5 | 3 | 5 | 1 |
Table 6.
Algorithm result analysis table
| Population size | Genetic algebra | The optimal value | Optimal value first out of modern number | Operation time/s |
| 10 | 400 | 643 | 365 | 1.283 |
| 500 | 643 | 365 | 3.568 | |
| 600 | 643 | 415 | 5.433 | |
| 20 | 400 | 643 | 370 | 0.711 |
| 500 | 643 | 427 | 2.546 | |
| 600 | 643 | 227 | 4.653 | |
| 30 | 400 | 586 | 130 | 1.263 |
| 500 | 643 | 380 | 2.374 | |
| 600 | 643 | 370 | 4.538 | |
| 40 | 400 | 643 | 270 | 0.843 |
| 500 | 597 | 355 | 2.176 | |
| 550 | 643 | 343 | 4.136 | |
| 50 | 400 | 643 | 350 | 0.834 |
| 450 | 643 | 275 | 1.571 | |
| 500 | 643 | 325 | 2.283 |
| Population size | Genetic algebra | The optimal value | Optimal value first out of modern number | Operation time/s |
| 10 | 400 | 643 | 365 | 1.283 |
| 500 | 643 | 365 | 3.568 | |
| 600 | 643 | 415 | 5.433 | |
| 20 | 400 | 643 | 370 | 0.711 |
| 500 | 643 | 427 | 2.546 | |
| 600 | 643 | 227 | 4.653 | |
| 30 | 400 | 586 | 130 | 1.263 |
| 500 | 643 | 380 | 2.374 | |
| 600 | 643 | 370 | 4.538 | |
| 40 | 400 | 643 | 270 | 0.843 |
| 500 | 597 | 355 | 2.176 | |
| 550 | 643 | 343 | 4.136 | |
| 50 | 400 | 643 | 350 | 0.834 |
| 450 | 643 | 275 | 1.571 | |
| 500 | 643 | 325 | 2.283 |
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