Article Contents
Article Contents

# Online ordering strategy for the discrete newsvendor problem with order value-based free-shipping

• * Corresponding author: Huifen Zhong
This research was supported by the National Natural Science Foundation of China (71501049, 71301029) and GDUPS(2016).
• 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.

Mathematics Subject Classification: Primary: 90B05, 68W27; Secondary: 68W40.

 Citation:

• Figure 1.  Daily cumulative return losses of $swaa$ and $best1$ when $V_0 = 99$

Figure 2.  Daily cumulative return losses of $swaa$ and $best1$ when $V_0 = 110$

Figure 3.  Cumulative return losses $swaa$ achieved under uniform and norm distribution

Figure 4.  Cumulative return losses $twaa$ achieved under uniform and norm distribution

Figure 5.  Daily cumulative return losses of $twaa$ and $best2$ when $V_0 = 99$

Table 1.  Cumulative return losses of $swaa$ and $best1$ under different $V_0$

 Trials $V_0=99$ $V_0=110$ $swaa$ $best1$ $ratio1$ $swaa$ $best1$ $ratio1$ 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

Table 2.  Cumulative return losses of $twaa$ and $best2$ under different $V_0$

 Trials $V_0=99$ $V_0=110$ $twaa$ $best2$ $ratio2$ $twaa$ $best2$ $ratio2$ 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

Table 3.  $swaa$'s robustness in different computational days

 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 $Avg1$ 1.2055 1.1222 1.1117 1.0585 1.0625 $SD1$ 0.00321 0.00302 0.00087 0.00059 0.00046

Table 4.  $twaa$'s robustness in different computational days

 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 $Avg2$ 1.2053 1.0940 1.0734 1.0642 1.0445 $SD2$ 0.00285 0.00127 0.00052 0.00047 0.00032
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