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

Yong Zhang; Huifen Zhong; Yue Liu; Menghu Huang

doi:10.3934/jimo.2018114

Article Contents

2019, Volume 15, Issue 4: 1617-1630. Doi: 10.3934/jimo.2018114

This issue Previous Article Equilibrium and optimal balking strategies for low-priority customers in the M/G/1 queue with two classes of customers and preemptive priority Next Article Coordinating a multi-echelon supply chain under production disruption and price-sensitive stochastic demand

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

* Corresponding author: Huifen Zhong
* Corresponding author: Huifen Zhong

Received: November 30, 2016

Revised: April 30, 2018

Early access: August 2018

Published: July 2019

This research was supported by the National Natural Science Foundation of China (71501049, 71301029) and GDUPS(2016).

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Abstract

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.

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

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

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

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

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

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

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

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

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

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

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

Trials	Days
Trials	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

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

Trials	Days
Trials	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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