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doi: 10.3934/jimo.2021051
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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

* Corresponding author: Dr Rongjuan Luo

Received  July 2020 Revised  January 2021 Early access March 2021

Fund Project: This research was supported by National Science Foundation of China [grant numbers 71572031, 71971049 and 71702112]

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.

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 & Management Optimization, doi: 10.3934/jimo.2021051
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References:
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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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [8] S. Benjaafar, Y. Li and M. 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Saadany, Supply chain coordination with emissions reduction incentives, International Journal of Production Research, 51 (2013), 69-82. doi: 10.1080/00207543.2011.651656.  Google Scholar [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. Google Scholar [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.  Google Scholar [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.  Google Scholar [23] J. S. L. Lam and Y. 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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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [31] A. Palmer, The Development of an Integrated Routing and Carbon Dioxide Emissions Model for Goods Vehicles, Ph.D thesis, Cranfield University, London, 2007. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [35] B. L. 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A three-echelon supply chain network
Locations of the Plants, the potential DCs and the Retailers
The nondominated frontier of the CLRIS considering CCD
The nondominated frontier of the CLRIS considering carbon emissions
Nondominated frontiers of the model minimizing CCD by varying the carbon cap
Box plots for the three evaluation indicators
The obtained nondominated frontiers of the all three procedures
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].
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
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%
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
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
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
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
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 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 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 18.7 7 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 17.3 47.5 49.9 52.1 48.5 45.2 17.3 16.6 16.8 60 45.2 47.5 45.7 60 49.9 45.1 46.2 44.1 50.3 60.3 60 57.3 49.8 55.1 57.3 57.3 60.1 61.3 67.1 68.9 4 18.7 7 17.3 0 7 55.1 40.1 30.2 25.1 7 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 7 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 65 66 6 52.5 18.8 49.9 55.1 7 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 18.8 49.6 50.2 47.1 52.1 5.1 49.6 50.2 54.1 10 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 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 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 28.1 24.1 50.2 15.6 15.2 0 5 17.3 55.1 15.2 5 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 11 50.2 24.1 16.6 15.2 50.5 29.4 47.1 20.6 18.9 5 0 10 45.9 27.1 9 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 12 48.9 52.5 16.8 32.1 25.8 48.9 52.1 28.7 25.8 17.3 10 0 60 25.8 9.2 10 50 40.3 25.8 11.2 12.3 40.3 49 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 41.9 32.6 55.1 5.1 19.6 26.8 55.1 45.9 60 0 35.6 41.9 45.9 12.1 20.3 32.6 50.1 45.9 35.6 17 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 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 9 9.2 41.9 6.2 0 15.2 45.7 48.9 10.2 15.6 20.1 21.2 40.7 41.2 40.2 38 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 45.9 15.2 15.2 0 37.1 29.1 25.7 10.1 11.1 23.4 37.1 32.7 33.3 23.4 30 31.2 36.1 46.1 45.2 47.7 49.2 17 60 53.2 60 41.9 32.6 54.1 10 19.6 26.8 45.2 27.1 50 12.1 45.1 45.7 37.1 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 18 52.1 50.2 45.2 39.1 49.8 18.8 10 22.1 25.9 40.1 23.1 48.9 15 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 7.4 35.9 40.6 10 22.7 20 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 20.1 25.5 5.6 27.6 28.7 32.5 30.7 35.7 45.1 45 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 8.5 22.2 40.7 34.5 32.1 18.7 24.5 38 42.7 43 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 27.8 45.2 40.1 38.1 18.9 26 30.1 44.1 44.6 45 46.7 48 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 5.6 22.2 27.8 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 17 40.1 40.7 37.1 8.8 22.7 27.6 40.7 45.2 27.1 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 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 28.7 34.5 40.1 14.2 13.6 0 6.1 18.9 17 41.8 20 25 40 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 20 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 23.4 45.2 27.8 30.7 18.7 18.9 20.7 33.2 18.9 20 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 46.6 35.7 35.7 24.5 26 24.2 34.8 17 17.9 7.3 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 30.1 33.3 45.2 41.8 36.1 18.2 13.5 0 35.6 37.3 20 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 42.7 44.1 38.9 33.8 20 30.1 36.2 30.1 35.6 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 44.6 40.1 38.5 25 36.1 38.1 36.9 37.3 7.2 0 25.6 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