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May
2022, 18(3): 1949-1977.
doi: 10.3934/jimo.2021051
Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences
| 1. | School of Business Administration, Northeastern University, Shenyang 110167, China |
| 2. | School of Economics and Management, Shenyang Aerospace University, Shenyang 110136, China |
| 3. | Department of Management Science and Statistics, University of Texas at San Antonio, San Antonio, TX 78249-0632, USA |
A combined location-routing-inventory system (CLRIS) in a three-echelon supply chain network is studied with environmental considerations. Specifically, a bi-objective mixed integer programming model is formulated for the CLRIS to deal with the trade-offs between the total cost and the carbon-capped difference (CCD). A multi-objective particle swarm optimization (MOPSO) heuristic solution procedure is developed and implemented to solve the bi-objective mixed integer programming problem. The bi-objective mixed integer programming model and the MOPSO heuristic procedure are applied to a real-life problem as an illustrative example. The approximate nondominated frontier formed by solutions not dominated by others can be used for the decision makers to make trade-offs between the total cost and the CCD. Sensitivity analyses are conducted, and the relationship among the carbon cap, CCD, the total cost and the carbon prices are examined, and relevant managerial insights are provided. Comparisons with other existing algorithms show that the MSPSO heuristic procedure has very good performance.
Keywords:
Location-routing-inventory,
Carbon emissions,
Carbon-capped difference,
MOPSO heuristic procedure,
Nondominated frontier.
Mathematics Subject Classification:
Primary: 65K05; Secondary: 90C08.
Citation:
Shoufeng Ji, Jinhuan Tang, Minghe Sun, Rongjuan Luo. Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences. Journal of Industrial and Management Optimization,
2022, 18
(3)
: 1949-1977.
doi: 10.3934/jimo.2021051
![]()
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show all references
References:
| [1] |
M. A. Alhaj, D. Svetinovic and A. Diabat,
A carbon-sensitive two-echelon-inventory supply chain model with stochastic demand, Resources Conservation & Recycling, 108 (2016), 82-87.
doi: 10.1016/j.resconrec.2015.11.011. |
| [2] |
M. J. Amoshahy, M. Shamsi and M. H. Sedaaghi, A novel flexible inertia weight particle swarm optimization algorithm, PLoS One, 11 (2016), e0161558.
doi: 10.1371/journal.pone.0161558. |
| [3] |
Z. N. Ansari and R. Kant,
A state-of-art literature review reflecting 15 years of focus on sustainable supply chain management, Journal of Cleaner Production, 142 (2017), 2524-2543.
doi: 10.1016/j.jclepro.2016.11.023. |
| [4] |
V. Artale, C. L. Milazzo, C. Orlando and A. Ricciardello, Comparison of GA and PSO approaches for the direct and LQR tuning of a multirotor PD controller, Journal of Industrial & Management Optimization, 13 (2017), 2067-2091.
doi: 10.3934/jimo.2017032. |
| [5] |
Q. Bai, J. Xu, F. Meng and N. Yu, Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning, Journal of Industrial & Management Optimization, 2020.
doi: 10.3934/jimo.2020126. |
| [6] |
J. C. Bansal, P. Singh, M. Saraswat, A. Verma, S. S. Jadon and A. Abraham, Inertia weight strategies in particle swarm optimization, in Third World Congress on Nature and Biologically Inspired Computing, Salamanca, 2011,633-640.
doi: 10.1109/NaBIC.2011.6089659. |
| [7] |
E. Bazan, M. Y. Jaber and S. Zanoni,
Carbon emissions and energy effects on a two-level manufacturer-retailer closed-loop supply chain model with remanufacturing subject to different coordination mechanisms, International Journal of Production Economics, 183 (2017), 394-408.
doi: 10.1016/j.ijpe.2016.07.009. |
| [8] |
S. Benjaafar, Y. Li and M. Daskin, Carbon footprint and the management of supply chains: Insights from simple models, IEEE Transactions on Automation Science and Engineering, 10 (2012), 99-116.
doi: 10.1109/TASE.2012.2203304. |
| [9] |
J. Cong, T. Pang and H. Peng, Optimal strategies for capital constrained low-carbon supply chains under yield uncertainty, Journal of Cleaner Production, 256 (2020), 120339.
doi: 10.1016/j.jclepro.2020.120339. |
| [10] |
Y. Daryanto, H. M. Wee and R. D. Astanti,
Three-echelon supply chain model considering carbon emission and item deterioration, Transportation Research Part E: Logistics and Transportation Review, 122 (2019), 368-383.
doi: 10.1016/j.tre.2018.12.014. |
| [11] |
K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: Nsga-II, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.
doi: 10.1109/4235.996017. |
| [12] |
M. Desrochers and G. Laporte, Improvements and extensions to the miller-tucker-zemlin subtour elimination constraints, Operations Research Letters, 10 (1991), 27-36.
doi: 10.1016/0167-6377(91)90083-2. |
| [13] |
S. Du, J. Zhu, H. Jiao and W. Ye, Game-theoretical analysis for supply chain with consumer preference to low carbon, International Journal of Production Research, 53 (2015), 3753-3768.
doi: 10.1080/00207543.2014.988888. |
| [14] |
R. M. Everson, J. E. Fieldsend and S. Singh, Full elite sets for multi-objective optimisation, in I. C. Parmee (ed.), Adaptive Computing in Design and Manufacture, Springer, 2002,343-354.
doi: 10.1007/978-0-85729-345-9_29. |
| [15] |
R. Z. Farahani, H. Rashidi Bajgan, B. Fahimnia and M. Kaviani, Location-inventory problem in supply chains: A modelling review, International Journal of Production Research, 53 (2015), 3769-3788.
doi: 10.1080/00207543.2014.988889. |
| [16] |
A. Ghorbani and M. R. A. Jokar,
A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem, Computers & Industrial Engineering, 101 (2016), 116-127.
doi: 10.1016/j.cie.2016.08.027. |
| [17] |
K. Hoen, T. Tan, J. Fransoo and G. Van Houtum, Effect of carbon emission regulations on transport mode selection under stochastic demand, Flexible Services and Manufacturing Journal, 26 (2014), 170-195.
doi: 10.1007/s10696-012-9151-6. |
| [18] |
Y.-S. Huang, C. C. Fang and Y. A. Lin, Inventory management in supply chains with consideration of logistics, green investment and different carbon emissions policies, Computers & Industrial Engineering, 139 (2020), 106207.
doi: 10.1016/j.cie.2019.106207. |
| [19] |
M. Y. Jaber, C. H. Glock and A. M. El. Saadany, Supply chain coordination with emissions reduction incentives, International Journal of Production Research, 51 (2013), 69-82.
doi: 10.1080/00207543.2011.651656. |
| [20] |
A. A. Javid and N. Azad, Incorporating location, routing and inventory decisions in supply chain network design, Transportation Research Part E: Logistics and Transportation Review, 46 (2010), 582-597. |
| [21] |
S. F. Ji, R. J. Luo and X. S. Peng, A probability guided evolutionary algorithm for multi-objective green express cabinet assignment in urban last-mile logistics, International Journal of Production Research, 57 (2019), 3382-3404.
doi: 10.1080/00207543.2018.1533653. |
| [22] |
J. Kennedy and R. Eberhart, Particle swarm optimization, in, IEEE International Conference on Neural Networks, Perth, Australia, 1995, 1942-1948.
doi: 10.1109/ICNN.1995.488968. |
| [23] |
J. S. L. Lam and Y. Gu,
A market-oriented approach for intermodal network optimisation meeting cost, time and environmental requirements, International Journal of Production Economics, 171 (2016), 266-274.
doi: 10.1016/j.ijpe.2015.09.024. |
| [24] |
H. F. Ling, X. Z. Zhou, X. L. Jiang and Y. H. Xiao, Improved constrained multi-objective particle swarm optimization algorithm, Journal of Computer Applications, 32 (2012), 1320-1324.
doi: 10.3724/SP.J.1087.2012.01320. |
| [25] |
R. J. Luo, S. F. Ji and B. L. Zhu,
A Pareto evolutionary algorithm based on incremental learning for a kind of multi-objective multidimensional knapsack problem, Computers & Industrial Engineering, 135 (2019), 537-559.
doi: 10.1016/j.cie.2019.06.027. |
| [26] |
J. M. C. Martí, J. S. Tancrez and R. W. Seifert,
Carbon footprint and responsiveness trade-offs in supply chain network design, International Journal of Production Economics, 166 (2015), 129-142.
|
| [27] |
H. Min, V. Jayaraman and R. Srivastava,
Combined location-routing problems: A synthesis and future research directions, European Journal of Operational Research, 108 (1998), 1-15.
doi: 10.1016/S0377-2217(97)00172-0. |
| [28] |
S. M. Mousavi, A. Bahreininejad, S. N. Musa and F. Yusof, A modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network, Journal of Intelligent Manufacturing, 28 (2017), 191-206.
doi: 10.1007/s10845-014-0970-z. |
| [29] |
M. Musavi and A. Bozorgi-Amiri,
A multi-objective sustainable hub location-scheduling problem for perishable food supply chain, Computers & Industrial Engineering, 113 (2017), 766-778.
doi: 10.1016/j.cie.2017.07.039. |
| [30] |
T. Paksoy, E. }Ozceylan and G. W. Weber, A multi objective model for optimization of a green supply chain network, AIP Conference Proceedings, 311 (2010), 1239.
doi: 10.1063/1.3459765. |
| [31] |
A. Palmer, The Development of an Integrated Routing and Carbon Dioxide Emissions Model for Goods Vehicles, Ph.D thesis, Cranfield University, London, 2007. |
| [32] |
B. Qian, L. Wang, D.-X. Huang and X. Wang, Scheduling multi-objective job shops using a memetic algorithm based on differential evolution, The International Journal of Advanced Manufacturing Technology, 35 (2008), 1014-1027.
doi: 10.1007/s00170-006-0787-9. |
| [33] |
C. N. Samuel, U. Venkatadri, C. Diallo and A. Khatab, Robust closed-loop supply chain design with presorting, return quality and carbon emission considerations, Journal of Cleaner Production, 247 (2020), 119086.
doi: 10.1016/j.jclepro.2019.119086. |
| [34] |
L. K. Saxena, P. K. Jain and A. K. Sharma, Tactical supply chain planning for tyre remanufacturing considering carbon tax policy, The International Journal of Advanced Manufacturing Technology, 97 (2018), 1505-1528.
doi: 10.1007/s00170-018-1972-3. |
| [35] |
B. L. Shankar, S. Basavarajappa, J. C. Chen and R. S. Kadadevaramath, Location and allocation decisions for multi-echelon supply chain network-a multi-objective evolutionary approach, Expert Systems with Applications, 40 (2013), 551-562.
doi: 10.1016/j.eswa.2012.07.065. |
| [36] |
Y. Shi and R. C. Eberhart, Empirical study of particle swarm optimization, in Proceedings of Twelfth IEEE International Conference on Artificial Intelligence (IJCA), Washington, D. C., USA, 1999, 1945-1950.
doi: 10.1109/CEC.1999.785511. |
| [37] |
M. R. Sierra and C. A. C. Coello, Improving Pso-Based Multi-Objective Optimization Using Crowding, Mutation and $\varepsilon$-dominance, in, Third International Conference on Evolutionary Multi-Criterion Optimization, Evolutionary Multi-Criterion Optimization, Guanajuato, Mexico, 2005. |
| [38] |
R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Applications, John Wiley and Sons, New York, 1986. |
| [39] |
M. Sun, Interactive Multiple Objective Programming Procedures Via Adaptive Random Search and Feed-Forward Artificial Neural Networks, Ph.D. dissertation, the University of Georgia, Athens, GA, 1992. |
| [40] |
M. Sun,
Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures, European Journal of Operational Research, 162 (2005), 468-483.
doi: 10.1016/j.ejor.2003.08.058. |
| [41] |
M. Sun, Multiple objective programming, in J. Wang (ed.), Encyclopedia of Business Analytics and Optimization, IGI Global, Hershey, PA, 3 (2014), 1585-1604. |
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Figure 2.
Locations of the Plants, the potential DCs and the Retailers
Figure 3.
The nondominated frontier of the CLRIS considering CCD
Figure 4.
The nondominated frontier of the CLRIS considering carbon emissions
Figure 5.
Nondominated frontiers of the model minimizing CCD by varying the carbon cap
Figure 6.
Box plots for the three evaluation indicators
Figure 7.
The obtained nondominated frontiers of the all three procedures
Table 1.
Summary of relevant literature for low carbon supply chains
| Literature category | Issues considered | Related publications |
| Translating carbon emissions into cost | Carbon cost; carbon price; pollution cost; cap-and-trade; emissions trading scheme | Tseng and Hung [44]; Treitl et al. [43]; Alhaj et al. [1]; Bai et al. [5]; Wang, Tao and Shi [50]. |
| Treating carbon emissions as a constraint in supply chain models | Carbon footprints; carbon-constrained | Benjaafar et al. [8]; Xu et al. [53]; Lam and Gu [23]; Martí et al. [26]. |
| Policies for carbon emission reduction | Carbon trading; carbon tax | Bazan et al. [7]; Wang et al. [47]; Wang, Zhao and Herty [49]; Saxena et al. [34]; Xin et al. [51]; Huang et al. [18]; Samuel et al. [33]. |
| Multiple objectives with carbon emissions | Trade-offs between cost and environment | Paksoy et al. [30]; Musavi and Bozorgi-Amiri [29]; Daryanto et al. [10]. |
| Carbon emission reduction with coordination mechanisms | Green production; green purchasing; coordination mechanism; life cycle assessment | Palmer [31]; Jaber et al. [19]; Du et al. [13]; Xu et al. [52]; Zhang et al. [56]. |
| Supply chain network design | Location; routing; inventory | Min et al. [27]; Wang, Tao and Shi [50]; Javid and Azad [20]; Farahani et al. [15]; Tang et al. [42]; Zhalechian et al. [55]. |
| Literature category | Issues considered | Related publications |
| Translating carbon emissions into cost | Carbon cost; carbon price; pollution cost; cap-and-trade; emissions trading scheme | Tseng and Hung [44]; Treitl et al. [43]; Alhaj et al. [1]; Bai et al. [5]; Wang, Tao and Shi [50]. |
| Treating carbon emissions as a constraint in supply chain models | Carbon footprints; carbon-constrained | Benjaafar et al. [8]; Xu et al. [53]; Lam and Gu [23]; Martí et al. [26]. |
| Policies for carbon emission reduction | Carbon trading; carbon tax | Bazan et al. [7]; Wang et al. [47]; Wang, Zhao and Herty [49]; Saxena et al. [34]; Xin et al. [51]; Huang et al. [18]; Samuel et al. [33]. |
| Multiple objectives with carbon emissions | Trade-offs between cost and environment | Paksoy et al. [30]; Musavi and Bozorgi-Amiri [29]; Daryanto et al. [10]. |
| Carbon emission reduction with coordination mechanisms | Green production; green purchasing; coordination mechanism; life cycle assessment | Palmer [31]; Jaber et al. [19]; Du et al. [13]; Xu et al. [52]; Zhang et al. [56]. |
| Supply chain network design | Location; routing; inventory | Min et al. [27]; Wang, Tao and Shi [50]; Javid and Azad [20]; Farahani et al. [15]; Tang et al. [42]; Zhalechian et al. [55]. |
Table 2.
Distances from the plants to the potential DCs (km)
| Shenbei | Yuhong | Sujiatun | Dongling | |
| Fushun | 77.5 | 71.1 | 64.6 | 36.5 |
| Liaoyang | 112.8 | 65.5 | 44.7 | 35.8 |
| Shenbei | Yuhong | Sujiatun | Dongling | |
| Fushun | 77.5 | 71.1 | 64.6 | 36.5 |
| Liaoyang | 112.8 | 65.5 | 44.7 | 35.8 |
Table 3.
Parameters of the potential DCs
| Shenbei | Yuhong | Sujiatun | Dongling | |
| Lead time (days) | 3 | 2 | 3 | 4 |
| Service level | 95% | 95% | 95% | 95% |
| Shenbei | Yuhong | Sujiatun | Dongling | |
| Lead time (days) | 3 | 2 | 3 | 4 |
| Service level | 95% | 95% | 95% | 95% |
Table 4.
Areas and fixed costs of the potential DCs
| Capacity (ton) | Fixed cost per period () | Holding cost (/ton/day) | Areas (m2) | |
| Shenbei | 340 | 20000 | 0.20 | 1100 |
| Yuhong | 500 | 18000 | 0.25 | 1600 |
| Sujiatun | 310 | 11200 | 0.20 | 1000 |
| Dongling | 380 | 15600 | 0.25 | 1200 |
| Capacity (ton) | Fixed cost per period () | Holding cost (/ton/day) | Areas (m2) | |
| Shenbei | 340 | 20000 | 0.20 | 1100 |
| Yuhong | 500 | 18000 | 0.25 | 1600 |
| Sujiatun | 310 | 11200 | 0.20 | 1000 |
| Dongling | 380 | 15600 | 0.25 | 1200 |
Table 5.
Details of some typical solutions on the nondominated frontier
| Solutions | Plants | DC Status | Total cost | CCD | |||
| Shenbei | Yuhong | Sujiatun | Dongling | ||||
| 1 | Fushun | 1 | 0 | 1 | 1 | 80153.5 | 4451.7 |
| Liaoyang | 1 | 0 | 0 | 0 | |||
| 2 | Fushun | 1 | 1 | 0 | 1 | 81875.5 | 3677.2 |
| Liaoyang | 1 | 1 | 0 | 0 | |||
| 3 | Fushun | 0 | 1 | 0 | 1 | 88125.9 | 3025.7 |
| Liaoyang | 1 | 1 | 0 | 0 | |||
| 4 | Fushun | 1 | 1 | 0 | 1 | 93750.3 | 2418.4 |
| Liaoyang | 1 | 1 | 0 | 1 | |||
| 5 | Fushun | 1 | 1 | 0 | 1 | 100104.9 | 1975.1 |
| Liaoyang | 1 | 1 | 1 | 0 | |||
| 6 | Fushun | 1 | 1 | 1 | 0 | 110139.3 | 1575.7 |
| Liaoyang | 1 | 0 | 1 | 0 | |||
| 7 | Fushun | 1 | 1 | 1 | 0 | 117697.4 | 1273.5 |
| Liaoyang | 1 | 1 | 1 | 0 | |||
| 8 | Fushun | 0 | 1 | 1 | 1 | 122385.8 | 968.1 |
| Liaoyang | 0 | 1 | 1 | 1 | |||
| 9 | Fushun | 1 | 1 | 1 | 1 | 134982.2 | 613.9 |
| Liaoyang | 0 | 1 | 1 | 1 | |||
| Solutions | Plants | DC Status | Total cost | CCD | |||
| Shenbei | Yuhong | Sujiatun | Dongling | ||||
| 1 | Fushun | 1 | 0 | 1 | 1 | 80153.5 | 4451.7 |
| Liaoyang | 1 | 0 | 0 | 0 | |||
| 2 | Fushun | 1 | 1 | 0 | 1 | 81875.5 | 3677.2 |
| Liaoyang | 1 | 1 | 0 | 0 | |||
| 3 | Fushun | 0 | 1 | 0 | 1 | 88125.9 | 3025.7 |
| Liaoyang | 1 | 1 | 0 | 0 | |||
| 4 | Fushun | 1 | 1 | 0 | 1 | 93750.3 | 2418.4 |
| Liaoyang | 1 | 1 | 0 | 1 | |||
| 5 | Fushun | 1 | 1 | 0 | 1 | 100104.9 | 1975.1 |
| Liaoyang | 1 | 1 | 1 | 0 | |||
| 6 | Fushun | 1 | 1 | 1 | 0 | 110139.3 | 1575.7 |
| Liaoyang | 1 | 0 | 1 | 0 | |||
| 7 | Fushun | 1 | 1 | 1 | 0 | 117697.4 | 1273.5 |
| Liaoyang | 1 | 1 | 1 | 0 | |||
| 8 | Fushun | 0 | 1 | 1 | 1 | 122385.8 | 968.1 |
| Liaoyang | 0 | 1 | 1 | 1 | |||
| 9 | Fushun | 1 | 1 | 1 | 1 | 134982.2 | 613.9 |
| Liaoyang | 0 | 1 | 1 | 1 | |||
Table 6.
Values of the evaluation indicators for MOPSO, NSGAII and MOEA/D
| Convergence | Diversity | Dominance | |||||||
| MOPSO | NSGAII | MOEA/D | MOPSO | NSGAII | MOEA/D | MOPSO | NSGAII | MOEA/D | |
| 1 | 0.258 | 0.179 | 2.320 | 0.507 | 0.518 | 0.691 | 0.909 | 0.476 | 0.000 |
| 2 | 0.126 | 0.251 | 2.261 | 0.520 | 0.494 | 0.775 | 0.878 | 0.466 | 0.000 |
| 3 | 0.193 | 0.142 | 1.208 | 0.508 | 0.540 | 0.694 | 0.814 | 0.485 | 0.000 |
| 4 | 0.170 | 0.254 | 1.273 | 0.516 | 0.482 | 0.841 | 0.828 | 0.441 | 0.000 |
| 5 | 0.160 | 0.244 | 1.679 | 0.468 | 0.471 | 0.738 | 0.913 | 0.428 | 0.000 |
| 6 | 0.158 | 0.260 | 1.741 | 0.559 | 0.479 | 0.808 | 0.820 | 0.463 | 0.000 |
| 7 | 0.137 | 0.241 | 1.375 | 0.493 | 0.497 | 0.698 | 0.826 | 0.535 | 0.000 |
| 8 | 0.177 | 0.106 | 2.207 | 0.480 | 0.627 | 0.817 | 0.775 | 0.517 | 0.000 |
| 9 | 0.233 | 0.092 | 1.471 | 0.516 | 0.545 | 0.728 | 0.789 | 0.371 | 0.000 |
| 10 | 0.250 | 0.103 | 1.050 | 0.455 | 0.493 | 0.713 | 0.834 | 0.526 | 0.000 |
| 11 | 0.239 | 0.171 | 1.607 | 0.521 | 0.598 | 0.789 | 0.817 | 0.330 | 0.000 |
| 12 | 0.106 | 0.179 | 1.800 | 0.485 | 0.557 | 0.804 | 0.892 | 0.326 | 0.000 |
| 13 | 0.146 | 0.188 | 1.952 | 0.406 | 0.533 | 0.724 | 0.884 | 0.478 | 0.000 |
| 14 | 0.131 | 0.181 | 1.667 | 0.490 | 0.493 | 0.704 | 0.871 | 0.448 | 0.000 |
| 15 | 0.115 | 0.158 | 2.385 | 0.433 | 0.449 | 0.779 | 0.905 | 0.476 | 0.000 |
| 16 | 0.158 | 0.195 | 2.158 | 0.530 | 0.482 | 0.662 | 0.868 | 0.557 | 0.000 |
| 17 | 0.122 | 0.268 | 1.276 | 0.480 | 0.485 | 0.710 | 0.841 | 0.486 | 0.000 |
| 18 | 0.193 | 0.169 | 1.727 | 0.489 | 0.517 | 0.663 | 0.892 | 0.546 | 0.000 |
| 19 | 0.168 | 0.220 | 1.700 | 0.550 | 0.576 | 0.637 | 0.926 | 0.403 | 0.000 |
| 20 | 0.172 | 1.295 | 1.333 | 0.478 | 0.567 | 0.787 | 0.833 | 0.353 | 0.000 |
| 21 | 0.143 | 1.724 | 1.696 | 0.502 | 0.517 | 0.708 | 0.866 | 0.303 | 0.000 |
| Convergence | Diversity | Dominance | |||||||
| MOPSO | NSGAII | MOEA/D | MOPSO | NSGAII | MOEA/D | MOPSO | NSGAII | MOEA/D | |
| 1 | 0.258 | 0.179 | 2.320 | 0.507 | 0.518 | 0.691 | 0.909 | 0.476 | 0.000 |
| 2 | 0.126 | 0.251 | 2.261 | 0.520 | 0.494 | 0.775 | 0.878 | 0.466 | 0.000 |
| 3 | 0.193 | 0.142 | 1.208 | 0.508 | 0.540 | 0.694 | 0.814 | 0.485 | 0.000 |
| 4 | 0.170 | 0.254 | 1.273 | 0.516 | 0.482 | 0.841 | 0.828 | 0.441 | 0.000 |
| 5 | 0.160 | 0.244 | 1.679 | 0.468 | 0.471 | 0.738 | 0.913 | 0.428 | 0.000 |
| 6 | 0.158 | 0.260 | 1.741 | 0.559 | 0.479 | 0.808 | 0.820 | 0.463 | 0.000 |
| 7 | 0.137 | 0.241 | 1.375 | 0.493 | 0.497 | 0.698 | 0.826 | 0.535 | 0.000 |
| 8 | 0.177 | 0.106 | 2.207 | 0.480 | 0.627 | 0.817 | 0.775 | 0.517 | 0.000 |
| 9 | 0.233 | 0.092 | 1.471 | 0.516 | 0.545 | 0.728 | 0.789 | 0.371 | 0.000 |
| 10 | 0.250 | 0.103 | 1.050 | 0.455 | 0.493 | 0.713 | 0.834 | 0.526 | 0.000 |
| 11 | 0.239 | 0.171 | 1.607 | 0.521 | 0.598 | 0.789 | 0.817 | 0.330 | 0.000 |
| 12 | 0.106 | 0.179 | 1.800 | 0.485 | 0.557 | 0.804 | 0.892 | 0.326 | 0.000 |
| 13 | 0.146 | 0.188 | 1.952 | 0.406 | 0.533 | 0.724 | 0.884 | 0.478 | 0.000 |
| 14 | 0.131 | 0.181 | 1.667 | 0.490 | 0.493 | 0.704 | 0.871 | 0.448 | 0.000 |
| 15 | 0.115 | 0.158 | 2.385 | 0.433 | 0.449 | 0.779 | 0.905 | 0.476 | 0.000 |
| 16 | 0.158 | 0.195 | 2.158 | 0.530 | 0.482 | 0.662 | 0.868 | 0.557 | 0.000 |
| 17 | 0.122 | 0.268 | 1.276 | 0.480 | 0.485 | 0.710 | 0.841 | 0.486 | 0.000 |
| 18 | 0.193 | 0.169 | 1.727 | 0.489 | 0.517 | 0.663 | 0.892 | 0.546 | 0.000 |
| 19 | 0.168 | 0.220 | 1.700 | 0.550 | 0.576 | 0.637 | 0.926 | 0.403 | 0.000 |
| 20 | 0.172 | 1.295 | 1.333 | 0.478 | 0.567 | 0.787 | 0.833 | 0.353 | 0.000 |
| 21 | 0.143 | 1.724 | 1.696 | 0.502 | 0.517 | 0.708 | 0.866 | 0.303 | 0.000 |
Table A1.
Distances from the potential DCs to the retailers (km)
| Shenbei | Yuhong | Dongling | |
| 1 | 82.6 | 47.7 | 55.6 |
| 2 | 80.1 | 47.0 | 37.3 |
| 3 | 80.5 | 27.9 | 54.2 |
| 4 | 64.5 | 35.7 | 42.3 |
| 5 | 62.3 | 40.0 | 47.3 |
| 6 | 64.6 | 49.8 | 15.7 |
| 7 | 61.2 | 55.6 | 7.0 |
| 8 | 58.2 | 45.0 | 27.3 |
| 9 | 64.2 | 36.1 | 49.1 |
| 10 | 66.1 | 27.2 | 49.5 |
| 11 | 66.0 | 12.0 | 50.0 |
| 12 | 66.2 | 48.2 | 60.1 |
| 13 | 63.8 | 60.6 | 12.0 |
| 14 | 56.6 | 40.2 | 58.9 |
| 15 | 55.2 | 35.2 | 67.1 |
| 16 | 58.1 | 7.0 | 55.3 |
| 17 | 62.1 | 54.2 | 42.0 |
| 18 | 56.9 | 42.1 | 41.1 |
| 19 | 50.3 | 38.4 | 47.9 |
| 20 | 45.7 | 39.0 | 52.1 |
| 21 | 50.1 | 32.2 | 50.0 |
| 22 | 50.1 | 12.0 | 57.1 |
| 23 | 40.1 | 36.1 | 37.0 |
| 24 | 50.1 | 48.9 | 12.2 |
| 25 | 30.2 | 45.9 | 52.1 |
| 26 | 25.8 | 40.1 | 67.1 |
| 27 | 32.1 | 40.2 | 55.3 |
| 28 | 23.2 | 38.4 | 55.3 |
| 29 | 25.8 | 42.6 | 65.1 |
| 30 | 22.4 | 48.9 | 54.2 |
| 31 | 20.5 | 52.6 | 62.1 |
| 32 | 23.7 | 46.0 | 70.1 |
| 33 | 7.0 | 55.6 | 66.2 |
| 34 | 15.0 | 61.3 | 72.1 |
| Shenbei | Yuhong | Dongling | |
| 1 | 82.6 | 47.7 | 55.6 |
| 2 | 80.1 | 47.0 | 37.3 |
| 3 | 80.5 | 27.9 | 54.2 |
| 4 | 64.5 | 35.7 | 42.3 |
| 5 | 62.3 | 40.0 | 47.3 |
| 6 | 64.6 | 49.8 | 15.7 |
| 7 | 61.2 | 55.6 | 7.0 |
| 8 | 58.2 | 45.0 | 27.3 |
| 9 | 64.2 | 36.1 | 49.1 |
| 10 | 66.1 | 27.2 | 49.5 |
| 11 | 66.0 | 12.0 | 50.0 |
| 12 | 66.2 | 48.2 | 60.1 |
| 13 | 63.8 | 60.6 | 12.0 |
| 14 | 56.6 | 40.2 | 58.9 |
| 15 | 55.2 | 35.2 | 67.1 |
| 16 | 58.1 | 7.0 | 55.3 |
| 17 | 62.1 | 54.2 | 42.0 |
| 18 | 56.9 | 42.1 | 41.1 |
| 19 | 50.3 | 38.4 | 47.9 |
| 20 | 45.7 | 39.0 | 52.1 |
| 21 | 50.1 | 32.2 | 50.0 |
| 22 | 50.1 | 12.0 | 57.1 |
| 23 | 40.1 | 36.1 | 37.0 |
| 24 | 50.1 | 48.9 | 12.2 |
| 25 | 30.2 | 45.9 | 52.1 |
| 26 | 25.8 | 40.1 | 67.1 |
| 27 | 32.1 | 40.2 | 55.3 |
| 28 | 23.2 | 38.4 | 55.3 |
| 29 | 25.8 | 42.6 | 65.1 |
| 30 | 22.4 | 48.9 | 54.2 |
| 31 | 20.5 | 52.6 | 62.1 |
| 32 | 23.7 | 46.0 | 70.1 |
| 33 | 7.0 | 55.6 | 66.2 |
| 34 | 15.0 | 61.3 | 72.1 |
Table A2.
Distances between the retailers (km)
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | |
| 1 | 0.0 | 17.1 | 15.9 | 18.7 | 50.2 | 52.5 | 55.6 | 52.5 | 48.9 | 50.2 | 49.5 | 48.9 | 58.8 | 52.5 | 47.9 | 51.1 | 60.0 | 50.1 | 52.5 | 49.1 | 50.2 | 50.2 | 55.3 | 55.3 | 56.3 | 52.1 | 56.3 | 62.3 | 67.3 | 69.2 | 70.1 | 75.2 | 77.1 |
| 2 | 17.1 | 0.0 | 18.7 | 7.0 | 10.1 | 18.8 | 50.2 | 20.1 | 15.9 | 15.9 | 24.1 | 52.5 | 55.1 | 18.8 | 19.8 | 45.1 | 53.2 | 47.1 | 20.1 | 50.2 | 50.2 | 51.2 | 53.2 | 54.7 | 55.7 | 53.2 | 54.9 | 66.1 | 66.1 | 67.1 | 67.1 | 69.2 | 70.1 |
| 3 | 15.9 | 18.7 | 0.0 | 17.3 | 47.5 | 49.9 | 52.1 | 48.5 | 45.2 | 17.3 | 16.6 | 16.8 | 60.0 | 45.2 | 47.5 | 45.7 | 60.0 | 49.9 | 45.1 | 46.2 | 44.1 | 50.3 | 60.3 | 60.0 | 57.3 | 49.8 | 55.1 | 57.3 | 57.3 | 60.1 | 61.3 | 67.1 | 68.9 |
| 4 | 18.7 | 7.0 | 17.3 | 0.0 | 7.0 | 55.1 | 40.1 | 30.2 | 25.1 | 7.0 | 15.2 | 32.1 | 41.9 | 30.2 | 27.1 | 25.7 | 41.9 | 56.2 | 30.2 | 29.5 | 35.1 | 26.7 | 36.9 | 36.3 | 41.9 | 39.1 | 36.9 | 50.1 | 53.4 | 57.3 | 59.9 | 64.7 | 66.3 |
| 5 | 50.2 | 10.1 | 47.5 | 7.0 | 0.0 | 7.0 | 49.6 | 7.2 | 5.9 | 28.1 | 50.5 | 25.8 | 32.6 | 27.1 | 13.8 | 45.1 | 32.6 | 44.3 | 40.1 | 46.2 | 49.9 | 43.2 | 32.6 | 36.6 | 39.8 | 39.8 | 37.6 | 55.3 | 55.3 | 59.9 | 62.0 | 65.0 | 66.0 |
| 6 | 52.5 | 18.8 | 49.9 | 55.1 | 7.0 | 0.0 | 18.8 | 8.7 | 20.4 | 24.1 | 29.4 | 48.9 | 55.1 | 55.1 | 57.8 | 35.9 | 54.1 | 55.1 | 54.1 | 32.4 | 48.9 | 58.8 | 57.8 | 48.9 | 53.9 | 54.8 | 55.5 | 58.4 | 58.7 | 62.4 | 67.1 | 68.6 | 68.1 |
| 7 | 55.6 | 50.2 | 52.1 | 40.1 | 49.6 | 18.8 | 0.0 | 18.8 | 49.6 | 50.2 | 47.1 | 52.1 | 5.1 | 49.6 | 50.2 | 54.1 | 10.0 | 49.8 | 47.1 | 50.1 | 52.1 | 48.6 | 19.8 | 19.6 | 23.8 | 50.1 | 50.2 | 49.2 | 46.3 | 54.1 | 59.2 | 59.2 | 60.1 |
| 8 | 52.5 | 20.1 | 48.5 | 30.2 | 7.2 | 8.7 | 18.8 | 0.0 | 6.4 | 15.6 | 20.6 | 28.7 | 19.6 | 14.2 | 20.6 | 35.9 | 19.6 | 24.2 | 22.1 | 20.6 | 28.7 | 19.6 | 20.6 | 28.7 | 30.7 | 32.5 | 34.6 | 50.3 | 45.3 | 50.3 | 54.2 | 55.2 | 66.4 |
| 9 | 48.9 | 15.9 | 45.2 | 25.1 | 5.9 | 20.4 | 49.6 | 6.4 | 0.0 | 15.2 | 18.9 | 25.8 | 26.8 | 6.4 | 15.2 | 35.6 | 26.8 | 27.8 | 10.1 | 35.6 | 38.9 | 30.2 | 38.9 | 39.7 | 40.1 | 37.8 | 41.1 | 45.6 | 45.8 | 47.6 | 50.2 | 50.6 | 50.9 |
| 10 | 50.2 | 15.9 | 17.3 | 7.0 | 28.1 | 24.1 | 50.2 | 15.6 | 15.2 | 0.0 | 5.0 | 17.3 | 55.1 | 15.2 | 5.0 | 15.9 | 45.2 | 36.8 | 15.2 | 36.8 | 38.8 | 39.6 | 45.2 | 43.2 | 43.2 | 40.1 | 43.2 | 45.4 | 47.9 | 47.4 | 45.2 | 52.1 | 52.0 |
| 11 | 50.2 | 24.1 | 16.6 | 15.2 | 50.5 | 29.4 | 47.1 | 20.6 | 18.9 | 5.0 | 0.0 | 10.0 | 45.9 | 27.1 | 9.0 | 7.1 | 27.1 | 20.1 | 16.9 | 16.9 | 17.5 | 18.9 | 27.1 | 26.7 | 27.1 | 25.9 | 32.2 | 36.5 | 45.9 | 47.2 | 46.2 | 53.1 | 53.0 |
| 12 | 48.9 | 52.5 | 16.8 | 32.1 | 25.8 | 48.9 | 52.1 | 28.7 | 25.8 | 17.3 | 10.0 | 0.0 | 60.0 | 25.8 | 9.2 | 10.0 | 50.0 | 40.3 | 25.8 | 11.2 | 12.3 | 40.3 | 49.0 | 45.1 | 44.3 | 40.3 | 44.5 | 40.3 | 50.1 | 53.7 | 56.5 | 58.2 | 59.9 |
| 13 | 58.8 | 55.1 | 60.0 | 41.9 | 32.6 | 55.1 | 5.1 | 19.6 | 26.8 | 55.1 | 45.9 | 60.0 | 0.0 | 35.6 | 41.9 | 45.9 | 12.1 | 20.3 | 32.6 | 50.1 | 45.9 | 35.6 | 17.0 | 43.1 | 45.1 | 55.1 | 58.1 | 59.8 | 45.1 | 62.8 | 69.1 | 59.8 | 60.2 |
| 14 | 52.5 | 18.8 | 45.2 | 30.2 | 27.1 | 55.1 | 49.6 | 14.2 | 6.4 | 15.2 | 27.1 | 25.8 | 35.6 | 0.0 | 6.2 | 15.2 | 45.1 | 16.1 | 5.9 | 23.3 | 29.1 | 20.1 | 40.1 | 38.7 | 38.5 | 29.1 | 32.1 | 37.7 | 39.8 | 42.3 | 45.2 | 46.6 | 47.9 |
| 15 | 47.9 | 19.8 | 47.5 | 27.1 | 13.8 | 57.8 | 50.2 | 20.6 | 15.2 | 5.0 | 9.0 | 9.2 | 41.9 | 6.2 | 0.0 | 15.2 | 45.7 | 48.9 | 10.2 | 15.6 | 20.1 | 21.2 | 40.7 | 41.2 | 40.2 | 38.0 | 40.2 | 43.5 | 45.1 | 47.9 | 47.1 | 48.2 | 48.9 |
| 16 | 51.1 | 45.1 | 45.7 | 25.7 | 45.1 | 35.9 | 54.1 | 35.9 | 35.6 | 15.9 | 7.1 | 10.0 | 45.9 | 15.2 | 15.2 | 0.0 | 37.1 | 29.1 | 25.7 | 10.1 | 11.1 | 23.4 | 37.1 | 32.7 | 33.3 | 23.4 | 30.0 | 31.2 | 36.1 | 46.1 | 45.2 | 47.7 | 49.2 |
| 17 | 60.0 | 53.2 | 60.0 | 41.9 | 32.6 | 54.1 | 10.0 | 19.6 | 26.8 | 45.2 | 27.1 | 50.0 | 12.1 | 45.1 | 45.7 | 37.1 | 0.0 | 18.7 | 21.1 | 45.2 | 44.5 | 25.6 | 8.8 | 18.7 | 25.5 | 45.2 | 46.6 | 55.8 | 45.1 | 50.1 | 68.1 | 63.1 | 60.0 |
| 18 | 52.1 | 50.2 | 45.2 | 39.1 | 49.8 | 18.8 | 10.0 | 22.1 | 25.9 | 40.1 | 23.1 | 48.9 | 15.0 | 25.9 | 57.8 | 31.2 | 11.9 | 7.7 | 18.8 | 40.1 | 44.4 | 21.8 | 7.5 | 44.4 | 24.5 | 43.1 | 46.8 | 48.7 | 40.1 | 45.1 | 55.1 | 58.1 | 58.7 |
| 19 | 50.1 | 47.1 | 49.9 | 56.2 | 44.3 | 55.1 | 49.8 | 24.2 | 27.8 | 36.8 | 20.1 | 40.3 | 20.3 | 16.1 | 48.9 | 29.1 | 18.7 | 0.0 | 7.4 | 35.9 | 40.6 | 10.0 | 22.7 | 20.0 | 24.7 | 27.8 | 35.7 | 40.7 | 49.7 | 50.7 | 52.3 | 57.9 | 58.7 |
| 20 | 52.5 | 20.1 | 45.1 | 30.2 | 40.1 | 54.1 | 47.1 | 22.1 | 10.1 | 15.2 | 16.9 | 25.8 | 32.6 | 5.9 | 10.2 | 25.7 | 21.1 | 7.4 | 0.0 | 20.1 | 25.5 | 5.6 | 27.6 | 28.7 | 32.5 | 30.7 | 35.7 | 45.1 | 45.0 | 43.1 | 48.7 | 49.2 | 50.1 |
| 21 | 49.1 | 50.2 | 46.2 | 29.5 | 46.2 | 32.4 | 50.1 | 20.6 | 35.6 | 36.8 | 16.9 | 11.2 | 50.1 | 23.3 | 15.6 | 10.1 | 45.2 | 35.9 | 20.1 | 0.0 | 8.5 | 22.2 | 40.7 | 34.5 | 32.1 | 18.7 | 24.5 | 38.0 | 42.7 | 43.0 | 43.7 | 45.6 | 46.5 |
| 22 | 50.2 | 50.2 | 44.1 | 35.1 | 49.9 | 48.9 | 52.1 | 28.7 | 38.9 | 38.8 | 17.5 | 12.3 | 45.9 | 29.1 | 20.1 | 11.1 | 44.5 | 40.6 | 25.5 | 8.5 | 0.0 | 27.8 | 45.2 | 40.1 | 38.1 | 18.9 | 26.0 | 30.1 | 44.1 | 44.6 | 45.0 | 46.7 | 48.0 |
| 23 | 50.2 | 51.2 | 50.3 | 26.7 | 43.2 | 58.8 | 48.6 | 19.6 | 30.2 | 39.6 | 18.9 | 40.3 | 35.6 | 20.1 | 21.2 | 23.4 | 25.6 | 10.0 | 5.6 | 22.2 | 27.8 | 0.0 | 27.1 | 14.2 | 15.8 | 20.7 | 24.2 | 33.3 | 38.9 | 40.1 | 43.3 | 45.1 | 45.2 |
| 24 | 55.3 | 53.2 | 60.3 | 36.9 | 32.6 | 57.8 | 19.8 | 20.6 | 38.9 | 45.2 | 27.1 | 49.0 | 17.0 | 40.1 | 40.7 | 37.1 | 8.8 | 22.7 | 27.6 | 40.7 | 45.2 | 27.1 | 0.0 | 13.6 | 19.5 | 33.2 | 34.8 | 45.2 | 33.8 | 38.5 | 46.1 | 55.1 | 50.1 |
| 25 | 55.3 | 54.7 | 60.0 | 36.3 | 36.6 | 48.9 | 19.6 | 28.7 | 39.7 | 43.2 | 26.7 | 45.1 | 43.1 | 38.7 | 41.2 | 32.7 | 18.7 | 20.0 | 28.7 | 34.5 | 40.1 | 14.2 | 13.6 | 0.0 | 6.1 | 18.9 | 17.0 | 41.8 | 20.0 | 25.0 | 40.0 | 45.2 | 46.1 |
| 26 | 56.3 | 55.7 | 57.3 | 41.9 | 39.8 | 53.9 | 23.8 | 30.7 | 40.1 | 43.2 | 27.1 | 44.3 | 45.1 | 38.5 | 40.2 | 33.3 | 25.5 | 24.7 | 32.5 | 32.1 | 38.1 | 15.8 | 19.5 | 6.1 | 0.0 | 20.0 | 17.9 | 36.1 | 30.1 | 36.1 | 36.2 | 37.1 | 38.2 |
| 27 | 52.1 | 53.2 | 49.8 | 39.1 | 39.8 | 54.8 | 50.1 | 32.5 | 37.8 | 40.1 | 25.9 | 40.3 | 55.1 | 29.1 | 38.0 | 23.4 | 45.2 | 27.8 | 30.7 | 18.7 | 18.9 | 20.7 | 33.2 | 18.9 | 20.0 | 0.0 | 7.3 | 18.2 | 36.2 | 38.1 | 38.1 | 40.2 | 44.2 |
| 28 | 56.3 | 54.9 | 55.1 | 36.9 | 37.6 | 55.5 | 50.2 | 34.6 | 41.1 | 43.2 | 32.2 | 44.5 | 58.1 | 32.1 | 40.2 | 30.0 | 46.6 | 35.7 | 35.7 | 24.5 | 26.0 | 24.2 | 34.8 | 17.0 | 17.9 | 7.3 | 0.0 | 13.5 | 30.1 | 36.9 | 40.2 | 42.1 | 43.5 |
| 29 | 62.3 | 66.1 | 57.3 | 50.1 | 55.3 | 58.4 | 49.2 | 50.3 | 45.6 | 45.4 | 36.5 | 40.3 | 59.8 | 37.7 | 43.5 | 31.2 | 55.8 | 40.7 | 45.1 | 38.0 | 30.1 | 33.3 | 45.2 | 41.8 | 36.1 | 18.2 | 13.5 | 0.0 | 35.6 | 37.3 | 20.0 | 45.2 | 46.2 |
| 30 | 67.3 | 66.1 | 57.3 | 53.4 | 55.3 | 58.7 | 46.3 | 45.3 | 45.8 | 47.9 | 45.9 | 50.1 | 45.1 | 39.8 | 45.1 | 36.1 | 45.1 | 49.7 | 45.0 | 42.7 | 44.1 | 38.9 | 33.8 | 20.0 | 30.1 | 36.2 | 30.1 | 35.6 | 0.0 | 7.2 | 37.3 | 30.2 | 32.1 |
| 31 | 69.2 | 67.1 | 60.1 | 57.3 | 59.9 | 62.4 | 54.1 | 50.3 | 47.6 | 47.4 | 47.2 | 53.7 | 62.8 | 42.3 | 47.9 | 46.1 | 50.1 | 50.7 | 43.1 | 43.0 | 44.6 | 40.1 | 38.5 | 25.0 | 36.1 | 38.1 | 36.9 | 37.3 | 7.2 | 0.0 | 25.6 | 20.1 | 26.1 |
| 32 | 70.1 | 67.1 | 61.3 | 59.9 | 62.0 | 67.1 | 59.2 | 54.2 | 50.2 | 45.2 | 46.2 | 56.5 | 69.1 | 45.2 | 47.1 | 45.2 | 68.1 | 52.3 | 48.7 | 43.7 | 45.0 | 43.3 | 46.1 | 40.0 | 36.2 | 38.1 | 40.2 | 20.0 | 37.3 | 25.6 | 0.0 | 38.2 | 45.6 |
| 33 | 75.2 | 69.2 | 67.1 | 64.7 | 65.0 | 68.6 | 59.2 | 55.2 | 50.6 | 52.1 | 53.1 | 58.2 | 59.8 | 46.6 | 48.2 | 47.7 | 63.1 | 57.9 | 49.2 | 45.6 | 46.7 | 45.1 | 55.1 | 45.2 | 37.1 | 40.2 | 42.1 | 45.2 | 30.2 | 20.1 | 38.2 | 0.0 | 8.2 |
| 34 | 77.1 | 70.1 | 68.9 | 66.3 | 66.0 | 68.1 | 60.1 | 66.4 | 50.9 | 52.0 | 53.0 | 59.9 | 60.2 | 47.9 | 48.9 | 49.2 | 60.0 | 58.7 | 50.1 | 46.5 | 48.0 | 45.2 | 50.1 | 46.1 | 38.2 | 44.2 | 43.5 | 46.2 | 32.1 | 26.1 | 45.6 | 8.2 | 0.0 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | |
| 1 | 0.0 | 17.1 | 15.9 | 18.7 | 50.2 | 52.5 | 55.6 | 52.5 | 48.9 | 50.2 | 49.5 | 48.9 | 58.8 | 52.5 | 47.9 | 51.1 | 60.0 | 50.1 | 52.5 | 49.1 | 50.2 | 50.2 | 55.3 | 55.3 | 56.3 | 52.1 | 56.3 | 62.3 | 67.3 | 69.2 | 70.1 | 75.2 | 77.1 |
| 2 | 17.1 | 0.0 | 18.7 | 7.0 | 10.1 | 18.8 | 50.2 | 20.1 | 15.9 | 15.9 | 24.1 | 52.5 | 55.1 | 18.8 | 19.8 | 45.1 | 53.2 | 47.1 | 20.1 | 50.2 | 50.2 | 51.2 | 53.2 | 54.7 | 55.7 | 53.2 | 54.9 | 66.1 | 66.1 | 67.1 | 67.1 | 69.2 | 70.1 |
| 3 | 15.9 | 18.7 | 0.0 | 17.3 | 47.5 | 49.9 | 52.1 | 48.5 | 45.2 | 17.3 | 16.6 | 16.8 | 60.0 | 45.2 | 47.5 | 45.7 | 60.0 | 49.9 | 45.1 | 46.2 | 44.1 | 50.3 | 60.3 | 60.0 | 57.3 | 49.8 | 55.1 | 57.3 | 57.3 | 60.1 | 61.3 | 67.1 | 68.9 |
| 4 | 18.7 | 7.0 | 17.3 | 0.0 | 7.0 | 55.1 | 40.1 | 30.2 | 25.1 | 7.0 | 15.2 | 32.1 | 41.9 | 30.2 | 27.1 | 25.7 | 41.9 | 56.2 | 30.2 | 29.5 | 35.1 | 26.7 | 36.9 | 36.3 | 41.9 | 39.1 | 36.9 | 50.1 | 53.4 | 57.3 | 59.9 | 64.7 | 66.3 |
| 5 | 50.2 | 10.1 | 47.5 | 7.0 | 0.0 | 7.0 | 49.6 | 7.2 | 5.9 | 28.1 | 50.5 | 25.8 | 32.6 | 27.1 | 13.8 | 45.1 | 32.6 | 44.3 | 40.1 | 46.2 | 49.9 | 43.2 | 32.6 | 36.6 | 39.8 | 39.8 | 37.6 | 55.3 | 55.3 | 59.9 | 62.0 | 65.0 | 66.0 |
| 6 | 52.5 | 18.8 | 49.9 | 55.1 | 7.0 | 0.0 | 18.8 | 8.7 | 20.4 | 24.1 | 29.4 | 48.9 | 55.1 | 55.1 | 57.8 | 35.9 | 54.1 | 55.1 | 54.1 | 32.4 | 48.9 | 58.8 | 57.8 | 48.9 | 53.9 | 54.8 | 55.5 | 58.4 | 58.7 | 62.4 | 67.1 | 68.6 | 68.1 |
| 7 | 55.6 | 50.2 | 52.1 | 40.1 | 49.6 | 18.8 | 0.0 | 18.8 | 49.6 | 50.2 | 47.1 | 52.1 | 5.1 | 49.6 | 50.2 | 54.1 | 10.0 | 49.8 | 47.1 | 50.1 | 52.1 | 48.6 | 19.8 | 19.6 | 23.8 | 50.1 | 50.2 | 49.2 | 46.3 | 54.1 | 59.2 | 59.2 | 60.1 |
| 8 | 52.5 | 20.1 | 48.5 | 30.2 | 7.2 | 8.7 | 18.8 | 0.0 | 6.4 | 15.6 | 20.6 | 28.7 | 19.6 | 14.2 | 20.6 | 35.9 | 19.6 | 24.2 | 22.1 | 20.6 | 28.7 | 19.6 | 20.6 | 28.7 | 30.7 | 32.5 | 34.6 | 50.3 | 45.3 | 50.3 | 54.2 | 55.2 | 66.4 |
| 9 | 48.9 | 15.9 | 45.2 | 25.1 | 5.9 | 20.4 | 49.6 | 6.4 | 0.0 | 15.2 | 18.9 | 25.8 | 26.8 | 6.4 | 15.2 | 35.6 | 26.8 | 27.8 | 10.1 | 35.6 | 38.9 | 30.2 | 38.9 | 39.7 | 40.1 | 37.8 | 41.1 | 45.6 | 45.8 | 47.6 | 50.2 | 50.6 | 50.9 |
| 10 | 50.2 | 15.9 | 17.3 | 7.0 | 28.1 | 24.1 | 50.2 | 15.6 | 15.2 | 0.0 | 5.0 | 17.3 | 55.1 | 15.2 | 5.0 | 15.9 | 45.2 | 36.8 | 15.2 | 36.8 | 38.8 | 39.6 | 45.2 | 43.2 | 43.2 | 40.1 | 43.2 | 45.4 | 47.9 | 47.4 | 45.2 | 52.1 | 52.0 |
| 11 | 50.2 | 24.1 | 16.6 | 15.2 | 50.5 | 29.4 | 47.1 | 20.6 | 18.9 | 5.0 | 0.0 | 10.0 | 45.9 | 27.1 | 9.0 | 7.1 | 27.1 | 20.1 | 16.9 | 16.9 | 17.5 | 18.9 | 27.1 | 26.7 | 27.1 | 25.9 | 32.2 | 36.5 | 45.9 | 47.2 | 46.2 | 53.1 | 53.0 |
| 12 | 48.9 | 52.5 | 16.8 | 32.1 | 25.8 | 48.9 | 52.1 | 28.7 | 25.8 | 17.3 | 10.0 | 0.0 | 60.0 | 25.8 | 9.2 | 10.0 | 50.0 | 40.3 | 25.8 | 11.2 | 12.3 | 40.3 | 49.0 | 45.1 | 44.3 | 40.3 | 44.5 | 40.3 | 50.1 | 53.7 | 56.5 | 58.2 | 59.9 |
| 13 | 58.8 | 55.1 | 60.0 | 41.9 | 32.6 | 55.1 | 5.1 | 19.6 | 26.8 | 55.1 | 45.9 | 60.0 | 0.0 | 35.6 | 41.9 | 45.9 | 12.1 | 20.3 | 32.6 | 50.1 | 45.9 | 35.6 | 17.0 | 43.1 | 45.1 | 55.1 | 58.1 | 59.8 | 45.1 | 62.8 | 69.1 | 59.8 | 60.2 |
| 14 | 52.5 | 18.8 | 45.2 | 30.2 | 27.1 | 55.1 | 49.6 | 14.2 | 6.4 | 15.2 | 27.1 | 25.8 | 35.6 | 0.0 | 6.2 | 15.2 | 45.1 | 16.1 | 5.9 | 23.3 | 29.1 | 20.1 | 40.1 | 38.7 | 38.5 | 29.1 | 32.1 | 37.7 | 39.8 | 42.3 | 45.2 | 46.6 | 47.9 |
| 15 | 47.9 | 19.8 | 47.5 | 27.1 | 13.8 | 57.8 | 50.2 | 20.6 | 15.2 | 5.0 | 9.0 | 9.2 | 41.9 | 6.2 | 0.0 | 15.2 | 45.7 | 48.9 | 10.2 | 15.6 | 20.1 | 21.2 | 40.7 | 41.2 | 40.2 | 38.0 | 40.2 | 43.5 | 45.1 | 47.9 | 47.1 | 48.2 | 48.9 |
| 16 | 51.1 | 45.1 | 45.7 | 25.7 | 45.1 | 35.9 | 54.1 | 35.9 | 35.6 | 15.9 | 7.1 | 10.0 | 45.9 | 15.2 | 15.2 | 0.0 | 37.1 | 29.1 | 25.7 | 10.1 | 11.1 | 23.4 | 37.1 | 32.7 | 33.3 | 23.4 | 30.0 | 31.2 | 36.1 | 46.1 | 45.2 | 47.7 | 49.2 |
| 17 | 60.0 | 53.2 | 60.0 | 41.9 | 32.6 | 54.1 | 10.0 | 19.6 | 26.8 | 45.2 | 27.1 | 50.0 | 12.1 | 45.1 | 45.7 | 37.1 | 0.0 | 18.7 | 21.1 | 45.2 | 44.5 | 25.6 | 8.8 | 18.7 | 25.5 | 45.2 | 46.6 | 55.8 | 45.1 | 50.1 | 68.1 | 63.1 | 60.0 |
| 18 | 52.1 | 50.2 | 45.2 | 39.1 | 49.8 | 18.8 | 10.0 | 22.1 | 25.9 | 40.1 | 23.1 | 48.9 | 15.0 | 25.9 | 57.8 | 31.2 | 11.9 | 7.7 | 18.8 | 40.1 | 44.4 | 21.8 | 7.5 | 44.4 | 24.5 | 43.1 | 46.8 | 48.7 | 40.1 | 45.1 | 55.1 | 58.1 | 58.7 |
| 19 | 50.1 | 47.1 | 49.9 | 56.2 | 44.3 | 55.1 | 49.8 | 24.2 | 27.8 | 36.8 | 20.1 | 40.3 | 20.3 | 16.1 | 48.9 | 29.1 | 18.7 | 0.0 | 7.4 | 35.9 | 40.6 | 10.0 | 22.7 | 20.0 | 24.7 | 27.8 | 35.7 | 40.7 | 49.7 | 50.7 | 52.3 | 57.9 | 58.7 |
| 20 | 52.5 | 20.1 | 45.1 | 30.2 | 40.1 | 54.1 | 47.1 | 22.1 | 10.1 | 15.2 | 16.9 | 25.8 | 32.6 | 5.9 | 10.2 | 25.7 | 21.1 | 7.4 | 0.0 | 20.1 | 25.5 | 5.6 | 27.6 | 28.7 | 32.5 | 30.7 | 35.7 | 45.1 | 45.0 | 43.1 | 48.7 | 49.2 | 50.1 |
| 21 | 49.1 | 50.2 | 46.2 | 29.5 | 46.2 | 32.4 | 50.1 | 20.6 | 35.6 | 36.8 | 16.9 | 11.2 | 50.1 | 23.3 | 15.6 | 10.1 | 45.2 | 35.9 | 20.1 | 0.0 | 8.5 | 22.2 | 40.7 | 34.5 | 32.1 | 18.7 | 24.5 | 38.0 | 42.7 | 43.0 | 43.7 | 45.6 | 46.5 |
| 22 | 50.2 | 50.2 | 44.1 | 35.1 | 49.9 | 48.9 | 52.1 | 28.7 | 38.9 | 38.8 | 17.5 | 12.3 | 45.9 | 29.1 | 20.1 | 11.1 | 44.5 | 40.6 | 25.5 | 8.5 | 0.0 | 27.8 | 45.2 | 40.1 | 38.1 | 18.9 | 26.0 | 30.1 | 44.1 | 44.6 | 45.0 | 46.7 | 48.0 |
| 23 | 50.2 | 51.2 | 50.3 | 26.7 | 43.2 | 58.8 | 48.6 | 19.6 | 30.2 | 39.6 | 18.9 | 40.3 | 35.6 | 20.1 | 21.2 | 23.4 | 25.6 | 10.0 | 5.6 | 22.2 | 27.8 | 0.0 | 27.1 | 14.2 | 15.8 | 20.7 | 24.2 | 33.3 | 38.9 | 40.1 | 43.3 | 45.1 | 45.2 |
| 24 | 55.3 | 53.2 | 60.3 | 36.9 | 32.6 | 57.8 | 19.8 | 20.6 | 38.9 | 45.2 | 27.1 | 49.0 | 17.0 | 40.1 | 40.7 | 37.1 | 8.8 | 22.7 | 27.6 | 40.7 | 45.2 | 27.1 | 0.0 | 13.6 | 19.5 | 33.2 | 34.8 | 45.2 | 33.8 | 38.5 | 46.1 | 55.1 | 50.1 |
| 25 | 55.3 | 54.7 | 60.0 | 36.3 | 36.6 | 48.9 | 19.6 | 28.7 | 39.7 | 43.2 | 26.7 | 45.1 | 43.1 | 38.7 | 41.2 | 32.7 | 18.7 | 20.0 | 28.7 | 34.5 | 40.1 | 14.2 | 13.6 | 0.0 | 6.1 | 18.9 | 17.0 | 41.8 | 20.0 | 25.0 | 40.0 | 45.2 | 46.1 |
| 26 | 56.3 | 55.7 | 57.3 | 41.9 | 39.8 | 53.9 | 23.8 | 30.7 | 40.1 | 43.2 | 27.1 | 44.3 | 45.1 | 38.5 | 40.2 | 33.3 | 25.5 | 24.7 | 32.5 | 32.1 | 38.1 | 15.8 | 19.5 | 6.1 | 0.0 | 20.0 | 17.9 | 36.1 | 30.1 | 36.1 | 36.2 | 37.1 | 38.2 |
| 27 | 52.1 | 53.2 | 49.8 | 39.1 | 39.8 | 54.8 | 50.1 | 32.5 | 37.8 | 40.1 | 25.9 | 40.3 | 55.1 | 29.1 | 38.0 | 23.4 | 45.2 | 27.8 | 30.7 | 18.7 | 18.9 | 20.7 | 33.2 | 18.9 | 20.0 | 0.0 | 7.3 | 18.2 | 36.2 | 38.1 | 38.1 | 40.2 | 44.2 |
| 28 | 56.3 | 54.9 | 55.1 | 36.9 | 37.6 | 55.5 | 50.2 | 34.6 | 41.1 | 43.2 | 32.2 | 44.5 | 58.1 | 32.1 | 40.2 | 30.0 | 46.6 | 35.7 | 35.7 | 24.5 | 26.0 | 24.2 | 34.8 | 17.0 | 17.9 | 7.3 | 0.0 | 13.5 | 30.1 | 36.9 | 40.2 | 42.1 | 43.5 |
| 29 | 62.3 | 66.1 | 57.3 | 50.1 | 55.3 | 58.4 | 49.2 | 50.3 | 45.6 | 45.4 | 36.5 | 40.3 | 59.8 | 37.7 | 43.5 | 31.2 | 55.8 | 40.7 | 45.1 | 38.0 | 30.1 | 33.3 | 45.2 | 41.8 | 36.1 | 18.2 | 13.5 | 0.0 | 35.6 | 37.3 | 20.0 | 45.2 | 46.2 |
| 30 | 67.3 | 66.1 | 57.3 | 53.4 | 55.3 | 58.7 | 46.3 | 45.3 | 45.8 | 47.9 | 45.9 | 50.1 | 45.1 | 39.8 | 45.1 | 36.1 | 45.1 | 49.7 | 45.0 | 42.7 | 44.1 | 38.9 | 33.8 | 20.0 | 30.1 | 36.2 | 30.1 | 35.6 | 0.0 | 7.2 | 37.3 | 30.2 | 32.1 |
| 31 | 69.2 | 67.1 | 60.1 | 57.3 | 59.9 | 62.4 | 54.1 | 50.3 | 47.6 | 47.4 | 47.2 | 53.7 | 62.8 | 42.3 | 47.9 | 46.1 | 50.1 | 50.7 | 43.1 | 43.0 | 44.6 | 40.1 | 38.5 | 25.0 | 36.1 | 38.1 | 36.9 | 37.3 | 7.2 | 0.0 | 25.6 | 20.1 | 26.1 |
| 32 | 70.1 | 67.1 | 61.3 | 59.9 | 62.0 | 67.1 | 59.2 | 54.2 | 50.2 | 45.2 | 46.2 | 56.5 | 69.1 | 45.2 | 47.1 | 45.2 | 68.1 | 52.3 | 48.7 | 43.7 | 45.0 | 43.3 | 46.1 | 40.0 | 36.2 | 38.1 | 40.2 | 20.0 | 37.3 | 25.6 | 0.0 | 38.2 | 45.6 |
| 33 | 75.2 | 69.2 | 67.1 | 64.7 | 65.0 | 68.6 | 59.2 | 55.2 | 50.6 | 52.1 | 53.1 | 58.2 | 59.8 | 46.6 | 48.2 | 47.7 | 63.1 | 57.9 | 49.2 | 45.6 | 46.7 | 45.1 | 55.1 | 45.2 | 37.1 | 40.2 | 42.1 | 45.2 | 30.2 | 20.1 | 38.2 | 0.0 | 8.2 |
| 34 | 77.1 | 70.1 | 68.9 | 66.3 | 66.0 | 68.1 | 60.1 | 66.4 | 50.9 | 52.0 | 53.0 | 59.9 | 60.2 | 47.9 | 48.9 | 49.2 | 60.0 | 58.7 | 50.1 | 46.5 | 48.0 | 45.2 | 50.1 | 46.1 | 38.2 | 44.2 | 43.5 | 46.2 | 32.1 | 26.1 | 45.6 | 8.2 | 0.0 |
| [1] |
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