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Equilibrium and optimal balking strategies for low-priority customers in the M/G/1 queue with two classes of customers and preemptive priority
Online ordering strategy for the discrete newsvendor problem with order value-based free-shipping
School of Management, Guangdong University of Technology, Guangzhou, Guangdong 510520, China |
Suppliers always provide free-shipping for retailers whose total order value exceeds or equals an explicit promotion threshold. This paper incorporates a shipping fee in the discrete multi-period newsvendor problem and applies Weak Aggregating Algorithm (WAA) to offer explicit online ordering strategy. It further considers an extended case with salvage value and shortage cost. In particular, online ordering strategies are derived based on return loss function. Numerical examples serve to illustrate the competitive performance of the proposed ordering strategies. Results show that newsvendors' cumulative return losses are affected by the threshold of the order value-based free-shipping. Moreover, the introduction of salvage value and shortage cost greatly improves the competitive performance of online ordering strategies.
References:
[1] |
H. Alfares and H. Elmorra,
The distribution-free newsboy problem: Extension to the shortage penalty case, International Journal of Production Economics, 93 (2005), 465-477.
doi: 10.1016/j.ijpe.2004.06.043. |
[2] |
K. Arrow, T. Harris and J. Marshak,
Optimal inventory policy, Econometrica, 19 (1951), 250-272.
doi: 10.2307/1906813. |
[3] |
W. H. Huang, Y. C. Cheng and J. Rose,
Threshold free shipping policies for internet shoppers, Transportation Research Part A, 82 (2015), 193-203.
doi: 10.1016/j.tra.2015.09.015. |
[4] |
Y. Kalnishkan and M. V. Vyugin,
The weak aggregating algorithm and weak mixability, Journal of Computer and System Sciences, 74 (2008), 1228-1244.
doi: 10.1016/j.jcss.2007.08.003. |
[5] |
S. Karlin,
Dynamic inventory policy with varying stochastic demands, Management Science, 6 (1960), 231-258.
doi: 10.1287/mnsc.6.3.231. |
[6] |
M. Khouja,
The single-period (news-vendor) problem: literature review and suggestions for future research, Omega: The International Journal of Management Science, 27 (1999), 537-553.
doi: 10.1016/S0305-0483(99)00017-1. |
[7] |
K. Kwon and T. Cheong,
A minimax distribution-free procedure for a newsvendor problem with free shipping, European Journal of Operational Research, 232 (2014), 234-240.
doi: 10.1016/j.ejor.2013.07.004. |
[8] |
T. Levina, Y. Levin and J. McGill,
Weak aggregating algorithm for the distribution-free perishable inventory problem, Operations Research Letters, 38 (2010), 516-521.
doi: 10.1016/j.orl.2010.09.006. |
[9] |
M. Lewis, V. Singh and S. Fay,
An empirical study of the impact of nonlinear shipping and handling fees on purchase incidence and expenditure decision, Marketing Science, 25 (2006), 51-64.
doi: 10.1287/mksc.1050.0150. |
[10] |
W. Liu, S. Song, Y. Qiao and H. Zhao,
The loss-averse newsvendor problem with random supply capacity, Journal of Industrial and Management Optimization, 13 (2017), 1417-1429.
doi: 10.3934/jimo.2016080. |
[11] |
M. Morse and E. Kimball, Methods of operations research, Published jointly by the Teachnology Press of Massachusetts Institute of Technology, 4 (1951), 18-20. Google Scholar |
[12] |
Y. Qin,
The newsvendor problem: review and directions for future research, European Journal of Operational Research, 213 (2011), 361-374.
doi: 10.1016/j.ejor.2010.11.024. |
[13] |
H. Scarf,
Bayes solution to the statistical inventory problem, Annals of Mathematical Statistics, 30 (1959), 490-508.
doi: 10.1214/aoms/1177706264. |
[14] |
H. Yu, J. Zhai and G. Y. Chen,
Robust optimization for the loss-averse newsvendor problem, European Journal of Operational Research, 171 (2016), 1008-1032.
doi: 10.1007/s10957-016-0870-9. |
[15] |
Y. Zhang, X. Yang and B. Li,
Distribution-free solutions to the extended multi-period newsboy problem, Journal of Industrial and Management Optimization, 13 (2017), 633-647.
doi: 10.3934/jimo.2016037. |
[16] |
Y. Zhang and X. Yang,
Online ordering policies for a two-product, multi-period stationary newsvendor problem, Computers and Operations Research, 74 (2016), 143-151.
doi: 10.1016/j.cor.2016.04.031. |
show all references
References:
[1] |
H. Alfares and H. Elmorra,
The distribution-free newsboy problem: Extension to the shortage penalty case, International Journal of Production Economics, 93 (2005), 465-477.
doi: 10.1016/j.ijpe.2004.06.043. |
[2] |
K. Arrow, T. Harris and J. Marshak,
Optimal inventory policy, Econometrica, 19 (1951), 250-272.
doi: 10.2307/1906813. |
[3] |
W. H. Huang, Y. C. Cheng and J. Rose,
Threshold free shipping policies for internet shoppers, Transportation Research Part A, 82 (2015), 193-203.
doi: 10.1016/j.tra.2015.09.015. |
[4] |
Y. Kalnishkan and M. V. Vyugin,
The weak aggregating algorithm and weak mixability, Journal of Computer and System Sciences, 74 (2008), 1228-1244.
doi: 10.1016/j.jcss.2007.08.003. |
[5] |
S. Karlin,
Dynamic inventory policy with varying stochastic demands, Management Science, 6 (1960), 231-258.
doi: 10.1287/mnsc.6.3.231. |
[6] |
M. Khouja,
The single-period (news-vendor) problem: literature review and suggestions for future research, Omega: The International Journal of Management Science, 27 (1999), 537-553.
doi: 10.1016/S0305-0483(99)00017-1. |
[7] |
K. Kwon and T. Cheong,
A minimax distribution-free procedure for a newsvendor problem with free shipping, European Journal of Operational Research, 232 (2014), 234-240.
doi: 10.1016/j.ejor.2013.07.004. |
[8] |
T. Levina, Y. Levin and J. McGill,
Weak aggregating algorithm for the distribution-free perishable inventory problem, Operations Research Letters, 38 (2010), 516-521.
doi: 10.1016/j.orl.2010.09.006. |
[9] |
M. Lewis, V. Singh and S. Fay,
An empirical study of the impact of nonlinear shipping and handling fees on purchase incidence and expenditure decision, Marketing Science, 25 (2006), 51-64.
doi: 10.1287/mksc.1050.0150. |
[10] |
W. Liu, S. Song, Y. Qiao and H. Zhao,
The loss-averse newsvendor problem with random supply capacity, Journal of Industrial and Management Optimization, 13 (2017), 1417-1429.
doi: 10.3934/jimo.2016080. |
[11] |
M. Morse and E. Kimball, Methods of operations research, Published jointly by the Teachnology Press of Massachusetts Institute of Technology, 4 (1951), 18-20. Google Scholar |
[12] |
Y. Qin,
The newsvendor problem: review and directions for future research, European Journal of Operational Research, 213 (2011), 361-374.
doi: 10.1016/j.ejor.2010.11.024. |
[13] |
H. Scarf,
Bayes solution to the statistical inventory problem, Annals of Mathematical Statistics, 30 (1959), 490-508.
doi: 10.1214/aoms/1177706264. |
[14] |
H. Yu, J. Zhai and G. Y. Chen,
Robust optimization for the loss-averse newsvendor problem, European Journal of Operational Research, 171 (2016), 1008-1032.
doi: 10.1007/s10957-016-0870-9. |
[15] |
Y. Zhang, X. Yang and B. Li,
Distribution-free solutions to the extended multi-period newsboy problem, Journal of Industrial and Management Optimization, 13 (2017), 633-647.
doi: 10.3934/jimo.2016037. |
[16] |
Y. Zhang and X. Yang,
Online ordering policies for a two-product, multi-period stationary newsvendor problem, Computers and Operations Research, 74 (2016), 143-151.
doi: 10.1016/j.cor.2016.04.031. |


Trials | ||||||
1 | 1298.8 | 1107.4 | 1.1728 | 1406.8 | 1216.4 | 1.1565 |
2 | 1089.8 | 964.60 | 1.1298 | 1119.8 | 999.30 | 1.1206 |
3 | 1161.9 | 1049.2 | 1.1074 | 1209.9 | 1019.2 | 1.1871 |
4 | 991.80 | 962.50 | 1.0304 | 1081.8 | 1100.5 | 0.9830 |
5 | 1080.6 | 999.70 | 1.0622 | 1182.6 | 1040.4 | 1.1367 |
6 | 1104.2 | 1000.8 | 1.1033 | 1224.2 | 1059.5 | 1.1555 |
7 | 1093.5 | 1026.3 | 1.0655 | 1099.5 | 1008.3 | 1.0904 |
8 | 953.60 | 924.40 | 1.0316 | 983.60 | 900.40 | 1.0924 |
9 | 1130.6 | 990.30 | 1.1417 | 1124.6 | 1037.0 | 1.0845 |
10 | 888.60 | 867.30 | 1.0246 | 900.60 | 837.30 | 1.0756 |
11 | 1114.2 | 1005.2 | 1.1084 | 1126.2 | 975.20 | 1.1548 |
12 | 922.70 | 922.70 | 1.0000 | 1072.7 | 1072.7 | 1.0000 |
13 | 916.90 | 857.20 | 1.0696 | 1030.9 | 1007.2 | 1.0235 |
14 | 1064.1 | 1005.5 | 1.0583 | 1118.1 | 1064.2 | 1.0506 |
15 | 983.90 | 928.20 | 1.0600 | 1079.9 | 906.60 | 1.1912 |
16 | 1254.0 | 1155.3 | 1.0854 | 1368.0 | 1202.0 | 1.1381 |
17 | 764.10 | 742.90 | 1.0285 | 860.10 | 844.90 | 1.0180 |
18 | 1129.6 | 1035.0 | 1.0914 | 1141.6 | 1049.0 | 1.0883 |
19 | 1209.5 | 1113.3 | 1.0864 | 1215.5 | 1107.3 | 1.0977 |
20 | 890.10 | 879.70 | 1.0118 | 890.10 | 843.70 | 1.0763 |
21 | 1145.3 | 1053.3 | 1.0873 | 1157.3 | 1047.3 | 1.1050 |
22 | 1177.9 | 1061.9 | 1.1092 | 1213.9 | 1037.9 | 1.1696 |
23 | 832.90 | 801.10 | 1.0397 | 898.90 | 927.10 | 0.9696 |
24 | 1086.8 | 989.70 | 1.0981 | 1098.8 | 953.70 | 1.1521 |
25 | 1065.8 | 1010.2 | 1.0550 | 1125.8 | 1050.9 | 1.0713 |
26 | 960.60 | 861.90 | 1.1145 | 1092.6 | 1017.9 | 1.0734 |
27 | 1138.0 | 1057.2 | 1.0764 | 1162.0 | 1033.2 | 1.1247 |
28 | 895.80 | 832.80 | 1.0756 | 985.80 | 964.80 | 1.0218 |
29 | 1023.7 | 981.30 | 1.0432 | 1131.7 | 1101.3 | 1.0276 |
30 | 1244.6 | 1107.4 | 1.1239 | 1352.6 | 1216.4 | 1.1120 |
Trials | ||||||
1 | 1298.8 | 1107.4 | 1.1728 | 1406.8 | 1216.4 | 1.1565 |
2 | 1089.8 | 964.60 | 1.1298 | 1119.8 | 999.30 | 1.1206 |
3 | 1161.9 | 1049.2 | 1.1074 | 1209.9 | 1019.2 | 1.1871 |
4 | 991.80 | 962.50 | 1.0304 | 1081.8 | 1100.5 | 0.9830 |
5 | 1080.6 | 999.70 | 1.0622 | 1182.6 | 1040.4 | 1.1367 |
6 | 1104.2 | 1000.8 | 1.1033 | 1224.2 | 1059.5 | 1.1555 |
7 | 1093.5 | 1026.3 | 1.0655 | 1099.5 | 1008.3 | 1.0904 |
8 | 953.60 | 924.40 | 1.0316 | 983.60 | 900.40 | 1.0924 |
9 | 1130.6 | 990.30 | 1.1417 | 1124.6 | 1037.0 | 1.0845 |
10 | 888.60 | 867.30 | 1.0246 | 900.60 | 837.30 | 1.0756 |
11 | 1114.2 | 1005.2 | 1.1084 | 1126.2 | 975.20 | 1.1548 |
12 | 922.70 | 922.70 | 1.0000 | 1072.7 | 1072.7 | 1.0000 |
13 | 916.90 | 857.20 | 1.0696 | 1030.9 | 1007.2 | 1.0235 |
14 | 1064.1 | 1005.5 | 1.0583 | 1118.1 | 1064.2 | 1.0506 |
15 | 983.90 | 928.20 | 1.0600 | 1079.9 | 906.60 | 1.1912 |
16 | 1254.0 | 1155.3 | 1.0854 | 1368.0 | 1202.0 | 1.1381 |
17 | 764.10 | 742.90 | 1.0285 | 860.10 | 844.90 | 1.0180 |
18 | 1129.6 | 1035.0 | 1.0914 | 1141.6 | 1049.0 | 1.0883 |
19 | 1209.5 | 1113.3 | 1.0864 | 1215.5 | 1107.3 | 1.0977 |
20 | 890.10 | 879.70 | 1.0118 | 890.10 | 843.70 | 1.0763 |
21 | 1145.3 | 1053.3 | 1.0873 | 1157.3 | 1047.3 | 1.1050 |
22 | 1177.9 | 1061.9 | 1.1092 | 1213.9 | 1037.9 | 1.1696 |
23 | 832.90 | 801.10 | 1.0397 | 898.90 | 927.10 | 0.9696 |
24 | 1086.8 | 989.70 | 1.0981 | 1098.8 | 953.70 | 1.1521 |
25 | 1065.8 | 1010.2 | 1.0550 | 1125.8 | 1050.9 | 1.0713 |
26 | 960.60 | 861.90 | 1.1145 | 1092.6 | 1017.9 | 1.0734 |
27 | 1138.0 | 1057.2 | 1.0764 | 1162.0 | 1033.2 | 1.1247 |
28 | 895.80 | 832.80 | 1.0756 | 985.80 | 964.80 | 1.0218 |
29 | 1023.7 | 981.30 | 1.0432 | 1131.7 | 1101.3 | 1.0276 |
30 | 1244.6 | 1107.4 | 1.1239 | 1352.6 | 1216.4 | 1.1120 |
Trials | ||||||
1 | 1016.4 | 935.60 | 1.0864 | 1058.4 | 935.60 | 1.0827 |
2 | 1430.7 | 1360.8 | 1.0514 | 1454.7 | 1384.8 | 1.0505 |
3 | 877.00 | 832.00 | 1.0541 | 895.00 | 850.00 | 1.0529 |
4 | 980.00 | 943.60 | 1.0386 | 1010.0 | 973.60 | 1.0374 |
5 | 888.80 | 814.80 | 1.0908 | 924.80 | 850.80 | 1.0870 |
6 | 1030.6 | 1081.6 | 0.9528 | 1048.6 | 1117.6 | 0.9383 |
7 | 959.30 | 929.60 | 1.0319 | 977.30 | 947.60 | 1.0313 |
8 | 1017.7 | 969.2 | 1.0500 | 1041.7 | 1005.2 | 1.0363 |
9 | 784.80 | 722.40 | 1.0864 | 808.80 | 746.40 | 1.0836 |
10 | 1270.0 | 1157.6 | 1.0971 | 1312.0 | 1199.6 | 1.0937 |
11 | 1131.5 | 1127.2 | 1.0038 | 1143.5 | 1163.2 | 0.9831 |
12 | 964.60 | 924.80 | 1.0430 | 1000.6 | 966.80 | 1.0350 |
13 | 1265.9 | 1140.8 | 1.1097 | 1295.9 | 1182.8 | 1.0956 |
14 | 722.50 | 663.60 | 1.0888 | 746.50 | 687.60 | 1.0857 |
15 | 1366.4 | 1272.8 | 1.0735 | 1390.4 | 1296.8 | 1.0722 |
16 | 1061.2 | 1012.0 | 1.0486 | 1121.2 | 1072.0 | 1.0459 |
17 | 1212.7 | 1146.8 | 1.0575 | 1230.7 | 1170.8 | 1.0512 |
18 | 844.40 | 810.40 | 1.0420 | 856.40 | 822.40 | 1.0413 |
19 | 1238.4 | 1163.6 | 1.0643 | 1262.4 | 1187.6 | 1.0630 |
20 | 1260.7 | 1230.4 | 1.0246 | 1278.7 | 1272.4 | 1.0050 |
21 | 1300.2 | 1200.0 | 1.0835 | 1330.2 | 1230.0 | 1.0815 |
22 | 1195.0 | 1102.8 | 1.0836 | 1219.0 | 1132.8 | 1.0761 |
23 | 1008.9 | 947.10 | 1.0653 | 1044.9 | 1001.1 | 1.0438 |
24 | 1187.1 | 1096.8 | 1.0823 | 1211.1 | 1132.8 | 1.0691 |
25 | 1155.4 | 1087.9 | 1.0620 | 1173.4 | 1135.9 | 1.0330 |
26 | 832.90 | 792.60 | 1.0508 | 844.90 | 804.60 | 1.0501 |
27 | 1035.3 | 942.00 | 1.0990 | 1035.3 | 942.00 | 1.0990 |
28 | 936.20 | 861.70 | 1.0865 | 942.20 | 873.70 | 1.0784 |
29 | 974.80 | 907.50 | 1.0742 | 1016.8 | 949.50 | 1.0709 |
30 | 872.50 | 825.00 | 1.0576 | 896.50 | 873.00 | 1.0269 |
Trials | ||||||
1 | 1016.4 | 935.60 | 1.0864 | 1058.4 | 935.60 | 1.0827 |
2 | 1430.7 | 1360.8 | 1.0514 | 1454.7 | 1384.8 | 1.0505 |
3 | 877.00 | 832.00 | 1.0541 | 895.00 | 850.00 | 1.0529 |
4 | 980.00 | 943.60 | 1.0386 | 1010.0 | 973.60 | 1.0374 |
5 | 888.80 | 814.80 | 1.0908 | 924.80 | 850.80 | 1.0870 |
6 | 1030.6 | 1081.6 | 0.9528 | 1048.6 | 1117.6 | 0.9383 |
7 | 959.30 | 929.60 | 1.0319 | 977.30 | 947.60 | 1.0313 |
8 | 1017.7 | 969.2 | 1.0500 | 1041.7 | 1005.2 | 1.0363 |
9 | 784.80 | 722.40 | 1.0864 | 808.80 | 746.40 | 1.0836 |
10 | 1270.0 | 1157.6 | 1.0971 | 1312.0 | 1199.6 | 1.0937 |
11 | 1131.5 | 1127.2 | 1.0038 | 1143.5 | 1163.2 | 0.9831 |
12 | 964.60 | 924.80 | 1.0430 | 1000.6 | 966.80 | 1.0350 |
13 | 1265.9 | 1140.8 | 1.1097 | 1295.9 | 1182.8 | 1.0956 |
14 | 722.50 | 663.60 | 1.0888 | 746.50 | 687.60 | 1.0857 |
15 | 1366.4 | 1272.8 | 1.0735 | 1390.4 | 1296.8 | 1.0722 |
16 | 1061.2 | 1012.0 | 1.0486 | 1121.2 | 1072.0 | 1.0459 |
17 | 1212.7 | 1146.8 | 1.0575 | 1230.7 | 1170.8 | 1.0512 |
18 | 844.40 | 810.40 | 1.0420 | 856.40 | 822.40 | 1.0413 |
19 | 1238.4 | 1163.6 | 1.0643 | 1262.4 | 1187.6 | 1.0630 |
20 | 1260.7 | 1230.4 | 1.0246 | 1278.7 | 1272.4 | 1.0050 |
21 | 1300.2 | 1200.0 | 1.0835 | 1330.2 | 1230.0 | 1.0815 |
22 | 1195.0 | 1102.8 | 1.0836 | 1219.0 | 1132.8 | 1.0761 |
23 | 1008.9 | 947.10 | 1.0653 | 1044.9 | 1001.1 | 1.0438 |
24 | 1187.1 | 1096.8 | 1.0823 | 1211.1 | 1132.8 | 1.0691 |
25 | 1155.4 | 1087.9 | 1.0620 | 1173.4 | 1135.9 | 1.0330 |
26 | 832.90 | 792.60 | 1.0508 | 844.90 | 804.60 | 1.0501 |
27 | 1035.3 | 942.00 | 1.0990 | 1035.3 | 942.00 | 1.0990 |
28 | 936.20 | 861.70 | 1.0865 | 942.20 | 873.70 | 1.0784 |
29 | 974.80 | 907.50 | 1.0742 | 1016.8 | 949.50 | 1.0709 |
30 | 872.50 | 825.00 | 1.0576 | 896.50 | 873.00 | 1.0269 |
Trials | Days | ||||
20 | 40 | 60 | 80 | 100 | |
1 | 1.2102 | 1.1728 | 1.1041 | 1.0327 | 1.0385 |
2 | 1.1738 | 1.0852 | 1.0933 | 1.0680 | 1.0718 |
3 | 1.1524 | 1.1362 | 1.1578 | 1.0160 | 1.0789 |
4 | 1.2868 | 1.1640 | 1.1158 | 1.0695 | 1.0328 |
5 | 1.1268 | 1.2441 | 1.1610 | 1.1056 | 1.0996 |
6 | 1.1801 | 1.0671 | 1.0995 | 1.0356 | 1.0640 |
7 | 1.3219 | 1.0925 | 1.1321 | 1.0791 | 1.0466 |
8 | 1.2262 | 1.1151 | 1.0661 | 1.0559 | 1.0424 |
9 | 1.1983 | 1.0736 | 1.0796 | 1.0563 | 1.0899 |
10 | 1.1783 | 1.0686 | 1.1073 | 1.0661 | 1.0602 |
1.2055 | 1.1222 | 1.1117 | 1.0585 | 1.0625 | |
0.00321 | 0.00302 | 0.00087 | 0.00059 | 0.00046 |
Trials | Days | ||||
20 | 40 | 60 | 80 | 100 | |
1 | 1.2102 | 1.1728 | 1.1041 | 1.0327 | 1.0385 |
2 | 1.1738 | 1.0852 | 1.0933 | 1.0680 | 1.0718 |
3 | 1.1524 | 1.1362 | 1.1578 | 1.0160 | 1.0789 |
4 | 1.2868 | 1.1640 | 1.1158 | 1.0695 | 1.0328 |
5 | 1.1268 | 1.2441 | 1.1610 | 1.1056 | 1.0996 |
6 | 1.1801 | 1.0671 | 1.0995 | 1.0356 | 1.0640 |
7 | 1.3219 | 1.0925 | 1.1321 | 1.0791 | 1.0466 |
8 | 1.2262 | 1.1151 | 1.0661 | 1.0559 | 1.0424 |
9 | 1.1983 | 1.0736 | 1.0796 | 1.0563 | 1.0899 |
10 | 1.1783 | 1.0686 | 1.1073 | 1.0661 | 1.0602 |
1.2055 | 1.1222 | 1.1117 | 1.0585 | 1.0625 | |
0.00321 | 0.00302 | 0.00087 | 0.00059 | 0.00046 |
Trials | Days | ||||
20 | 40 | 60 | 80 | 100 | |
1 | 1.1845 | 1.1008 | 1.0993 | 1.0353 | 1.0300 |
2 | 1.2484 | 1.1490 | 1.0404 | 1.0976 | 1.0805 |
3 | 1.2752 | 1.1033 | 1.0457 | 1.0805 | 1.0503 |
4 | 1.2479 | 1.0672 | 1.0644 | 1.0674 | 1.0556 |
5 | 1.1546 | 1.1039 | 1.0984 | 1.0617 | 1.0298 |
6 | 1.2251 | 1.0257 | 1.0684 | 1.0938 | 1.0303 |
7 | 1.1617 | 1.1161 | 1.1026 | 1.0269 | 1.0380 |
8 | 1.1078 | 1.1347 | 1.0910 | 1.0505 | 1.0264 |
9 | 1.1772 | 1.0503 | 1.0776 | 1.0630 | 1.0696 |
10 | 1.2711 | 1.0892 | 1.0463 | 1.0652 | 1.0343 |
1.2053 | 1.0940 | 1.0734 | 1.0642 | 1.0445 | |
0.00285 | 0.00127 | 0.00052 | 0.00047 | 0.00032 |
Trials | Days | ||||
20 | 40 | 60 | 80 | 100 | |
1 | 1.1845 | 1.1008 | 1.0993 | 1.0353 | 1.0300 |
2 | 1.2484 | 1.1490 | 1.0404 | 1.0976 | 1.0805 |
3 | 1.2752 | 1.1033 | 1.0457 | 1.0805 | 1.0503 |
4 | 1.2479 | 1.0672 | 1.0644 | 1.0674 | 1.0556 |
5 | 1.1546 | 1.1039 | 1.0984 | 1.0617 | 1.0298 |
6 | 1.2251 | 1.0257 | 1.0684 | 1.0938 | 1.0303 |
7 | 1.1617 | 1.1161 | 1.1026 | 1.0269 | 1.0380 |
8 | 1.1078 | 1.1347 | 1.0910 | 1.0505 | 1.0264 |
9 | 1.1772 | 1.0503 | 1.0776 | 1.0630 | 1.0696 |
10 | 1.2711 | 1.0892 | 1.0463 | 1.0652 | 1.0343 |
1.2053 | 1.0940 | 1.0734 | 1.0642 | 1.0445 | |
0.00285 | 0.00127 | 0.00052 | 0.00047 | 0.00032 |
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