American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Coordinating a multi-echelon supply chain under production disruption and price-sensitive stochastic demand
  • JIMO Home
  • This Issue
  • Next Article
    Equilibrium and optimal balking strategies for low-priority customers in the M/G/1 queue with two classes of customers and preemptive priority
October  2019, 15(4): 1617-1630. doi: 10.3934/jimo.2018114

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

Yong Zhang , Huifen Zhong , , Yue Liu and  Menghu Huang

School of Management, Guangdong University of Technology, Guangzhou, Guangdong 510520, China

* Corresponding author: Huifen Zhong

Received  December 2016 Revised  May 2018 Published  October 2019 Early access  August 2018

Fund Project: 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.

Keywords: Multi-period newsvendor problem, discrete, order value-based free-shipping, WAA, online ordering strategy.
Mathematics Subject Classification: Primary: 90B05, 68W27; Secondary: 68W40.
Citation: Yong Zhang, Huifen Zhong, Yue Liu, Menghu Huang. Online ordering strategy for the discrete newsvendor problem with order value-based free-shipping. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1617-1630. doi: 10.3934/jimo.2018114
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. 

[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. 

[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.

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

Download full-size image

Download as PowerPoint slide

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

Download full-size image

Download as PowerPoint slide

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

Download full-size image

Download as PowerPoint slide

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

Download full-size image

Download as PowerPoint slide

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

Download full-size image

Download as PowerPoint slide

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$
11298.81107.41.17281406.81216.41.1565
21089.8964.601.12981119.8999.301.1206
31161.91049.21.10741209.91019.21.1871
4991.80962.501.03041081.81100.50.9830
51080.6999.701.06221182.61040.41.1367
61104.21000.81.10331224.21059.51.1555
71093.51026.31.06551099.51008.31.0904
8953.60924.401.0316983.60900.401.0924
91130.6990.301.14171124.61037.01.0845
10888.60867.301.0246900.60837.301.0756
111114.21005.21.10841126.2975.201.1548
12922.70922.701.00001072.71072.71.0000
13916.90857.201.06961030.91007.21.0235
141064.11005.51.05831118.11064.21.0506
15983.90928.201.06001079.9906.601.1912
161254.01155.31.08541368.01202.01.1381
17764.10742.901.0285860.10844.901.0180
181129.61035.01.09141141.61049.01.0883
191209.51113.31.08641215.51107.31.0977
20890.10879.701.0118890.10843.701.0763
211145.31053.31.08731157.31047.31.1050
221177.91061.91.10921213.91037.91.1696
23832.90801.101.0397898.90927.100.9696
241086.8989.701.09811098.8953.701.1521
251065.81010.21.05501125.81050.91.0713
26960.60861.901.11451092.61017.91.0734
271138.01057.21.07641162.01033.21.1247
28895.80832.801.0756985.80964.801.0218
291023.7981.301.04321131.71101.31.0276
301244.61107.41.12391352.61216.41.1120
Table Options

Download as excel

Trials$V_0=99$$V_0=110$
$swaa$$best1$$ratio1$$swaa$$best1$$ratio1$
11298.81107.41.17281406.81216.41.1565
21089.8964.601.12981119.8999.301.1206
31161.91049.21.10741209.91019.21.1871
4991.80962.501.03041081.81100.50.9830
51080.6999.701.06221182.61040.41.1367
61104.21000.81.10331224.21059.51.1555
71093.51026.31.06551099.51008.31.0904
8953.60924.401.0316983.60900.401.0924
91130.6990.301.14171124.61037.01.0845
10888.60867.301.0246900.60837.301.0756
111114.21005.21.10841126.2975.201.1548
12922.70922.701.00001072.71072.71.0000
13916.90857.201.06961030.91007.21.0235
141064.11005.51.05831118.11064.21.0506
15983.90928.201.06001079.9906.601.1912
161254.01155.31.08541368.01202.01.1381
17764.10742.901.0285860.10844.901.0180
181129.61035.01.09141141.61049.01.0883
191209.51113.31.08641215.51107.31.0977
20890.10879.701.0118890.10843.701.0763
211145.31053.31.08731157.31047.31.1050
221177.91061.91.10921213.91037.91.1696
23832.90801.101.0397898.90927.100.9696
241086.8989.701.09811098.8953.701.1521
251065.81010.21.05501125.81050.91.0713
26960.60861.901.11451092.61017.91.0734
271138.01057.21.07641162.01033.21.1247
28895.80832.801.0756985.80964.801.0218
291023.7981.301.04321131.71101.31.0276
301244.61107.41.12391352.61216.41.1120
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$
11016.4935.601.08641058.4935.601.0827
21430.71360.81.05141454.71384.81.0505
3877.00832.001.0541895.00850.001.0529
4980.00943.601.03861010.0973.601.0374
5888.80814.801.0908924.80850.801.0870
61030.61081.60.95281048.61117.60.9383
7959.30929.601.0319977.30947.601.0313
81017.7969.21.05001041.71005.21.0363
9784.80722.401.0864808.80746.401.0836
101270.01157.61.09711312.01199.61.0937
111131.51127.21.00381143.51163.20.9831
12964.60924.801.04301000.6966.801.0350
131265.91140.81.10971295.91182.81.0956
14722.50663.601.0888746.50687.601.0857
151366.41272.81.07351390.41296.81.0722
161061.21012.01.04861121.21072.01.0459
171212.71146.81.05751230.71170.81.0512
18844.40810.401.0420856.40822.401.0413
191238.41163.61.06431262.41187.61.0630
201260.71230.41.02461278.71272.41.0050
211300.21200.01.08351330.21230.01.0815
221195.01102.81.08361219.01132.81.0761
231008.9947.101.06531044.91001.11.0438
241187.11096.81.08231211.11132.81.0691
251155.41087.91.06201173.41135.91.0330
26832.90792.601.0508844.90804.601.0501
271035.3942.001.09901035.3942.001.0990
28936.20861.701.0865942.20873.701.0784
29974.80907.501.07421016.8949.501.0709
30872.50825.001.0576896.50873.001.0269
Table Options

Download as excel

Trials$V_0=99$$V_0=110$
$twaa$$best2$$ratio2$$twaa$$best2$$ratio2$
11016.4935.601.08641058.4935.601.0827
21430.71360.81.05141454.71384.81.0505
3877.00832.001.0541895.00850.001.0529
4980.00943.601.03861010.0973.601.0374
5888.80814.801.0908924.80850.801.0870
61030.61081.60.95281048.61117.60.9383
7959.30929.601.0319977.30947.601.0313
81017.7969.21.05001041.71005.21.0363
9784.80722.401.0864808.80746.401.0836
101270.01157.61.09711312.01199.61.0937
111131.51127.21.00381143.51163.20.9831
12964.60924.801.04301000.6966.801.0350
131265.91140.81.10971295.91182.81.0956
14722.50663.601.0888746.50687.601.0857
151366.41272.81.07351390.41296.81.0722
161061.21012.01.04861121.21072.01.0459
171212.71146.81.05751230.71170.81.0512
18844.40810.401.0420856.40822.401.0413
191238.41163.61.06431262.41187.61.0630
201260.71230.41.02461278.71272.41.0050
211300.21200.01.08351330.21230.01.0815
221195.01102.81.08361219.01132.81.0761
231008.9947.101.06531044.91001.11.0438
241187.11096.81.08231211.11132.81.0691
251155.41087.91.06201173.41135.91.0330
26832.90792.601.0508844.90804.601.0501
271035.3942.001.09901035.3942.001.0990
28936.20861.701.0865942.20873.701.0784
29974.80907.501.07421016.8949.501.0709
30872.50825.001.0576896.50873.001.0269
Table 3.  $swaa$'s robustness in different computational days
TrialsDays
20406080100
11.21021.17281.10411.03271.0385
21.17381.08521.09331.06801.0718
31.15241.13621.15781.01601.0789
41.28681.16401.11581.06951.0328
51.12681.24411.16101.10561.0996
61.18011.06711.09951.03561.0640
71.32191.09251.13211.07911.0466
81.22621.11511.06611.05591.0424
91.19831.07361.07961.05631.0899
101.17831.06861.10731.06611.0602
$Avg1$1.20551.12221.11171.05851.0625
$SD1$0.003210.003020.000870.000590.00046
Table Options

Download as excel

TrialsDays
20406080100
11.21021.17281.10411.03271.0385
21.17381.08521.09331.06801.0718
31.15241.13621.15781.01601.0789
41.28681.16401.11581.06951.0328
51.12681.24411.16101.10561.0996
61.18011.06711.09951.03561.0640
71.32191.09251.13211.07911.0466
81.22621.11511.06611.05591.0424
91.19831.07361.07961.05631.0899
101.17831.06861.10731.06611.0602
$Avg1$1.20551.12221.11171.05851.0625
$SD1$0.003210.003020.000870.000590.00046
Table 4.  $twaa$'s robustness in different computational days
TrialsDays
20406080100
11.18451.10081.09931.03531.0300
21.24841.14901.04041.09761.0805
31.27521.10331.04571.08051.0503
41.24791.06721.06441.06741.0556
51.15461.10391.09841.06171.0298
61.22511.02571.06841.09381.0303
71.16171.11611.10261.02691.0380
81.10781.13471.09101.05051.0264
91.17721.05031.07761.06301.0696
101.27111.08921.04631.06521.0343
$Avg2$1.20531.09401.07341.06421.0445
$SD2$0.002850.001270.000520.000470.00032
Table Options

Download as excel

TrialsDays
20406080100
11.18451.10081.09931.03531.0300
21.24841.14901.04041.09761.0805
31.27521.10331.04571.08051.0503
41.24791.06721.06441.06741.0556
51.15461.10391.09841.06171.0298
61.22511.02571.06841.09381.0303
71.16171.11611.10261.02691.0380
81.10781.13471.09101.05051.0264
91.17721.05031.07761.06301.0696
101.27111.08921.04631.06521.0343
$Avg2$1.20531.09401.07341.06421.0445
$SD2$0.002850.001270.000520.000470.00032
[1]

Zongwei Chen. An online-decision algorithm for the multi-period bank clearing problem. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2783-2803. doi: 10.3934/jimo.2021091
[2]

Yong Zhang, Xingyu Yang, Baixun Li. Distribution-free solutions to the extended multi-period newsboy problem. Journal of Industrial and Management Optimization, 2017, 13 (2) : 633-647. doi: 10.3934/jimo.2016037
[3]

Lihua Bian, Zhongfei Li, Haixiang Yao. Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1383-1410. doi: 10.3934/jimo.2020026
[4]

Fatemeh Kangi, Seyed Hamid Reza Pasandideh, Esmaeil Mehdizadeh, Hamed Soleimani. The optimization of a multi-period multi-product closed-loop supply chain network with cross-docking delivery strategy. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021118
[5]

Ning Zhang. A symmetric Gauss-Seidel based method for a class of multi-period mean-variance portfolio selection problems. Journal of Industrial and Management Optimization, 2020, 16 (2) : 991-1008. doi: 10.3934/jimo.2018189
[6]

Zhiping Chen, Jia Liu, Gang Li. Time consistent policy of multi-period mean-variance problem in stochastic markets. Journal of Industrial and Management Optimization, 2016, 12 (1) : 229-249. doi: 10.3934/jimo.2016.12.229
[7]

Reza Lotfi, Gerhard-Wilhelm Weber, S. Mehdi Sajadifar, Nooshin Mardani. Interdependent demand in the two-period newsvendor problem. Journal of Industrial and Management Optimization, 2020, 16 (1) : 117-140. doi: 10.3934/jimo.2018143
[8]

Lin Jiang, Song Wang. Robust multi-period and multi-objective portfolio selection. Journal of Industrial and Management Optimization, 2021, 17 (2) : 695-709. doi: 10.3934/jimo.2019130
[9]

Hongguang Ma, Xiang Li. Multi-period hazardous waste collection planning with consideration of risk stability. Journal of Industrial and Management Optimization, 2021, 17 (1) : 393-408. doi: 10.3934/jimo.2019117
[10]

Lin Jiang, Changzhi Wu, Song Wang. Distributionally robust multi-period portfolio selection subject to bankruptcy constraints. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021218
[11]

Christina Burt, Louis Caccetta, Leon Fouché, Palitha Welgama. An MILP approach to multi-location, multi-period equipment selection for surface mining with case studies. Journal of Industrial and Management Optimization, 2016, 12 (2) : 403-430. doi: 10.3934/jimo.2016.12.403
[12]

Majid Khalilzadeh, Hossein Neghabi, Ramin Ahadi. An application of approximate dynamic programming in multi-period multi-product advertising budgeting. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021202
[13]

John R. Graef, Lingju Kong, Min Wang. Existence of multiple solutions to a discrete fourth order periodic boundary value problem. Conference Publications, 2013, 2013 (special) : 291-299. doi: 10.3934/proc.2013.2013.291
[14]

Lan Yi, Zhongfei Li, Duan Li. Multi-period portfolio selection for asset-liability management with uncertain investment horizon. Journal of Industrial and Management Optimization, 2008, 4 (3) : 535-552. doi: 10.3934/jimo.2008.4.535
[15]

Zhen Wang, Sanyang Liu. Multi-period mean-variance portfolio selection with fixed and proportional transaction costs. Journal of Industrial and Management Optimization, 2013, 9 (3) : 643-657. doi: 10.3934/jimo.2013.9.643
[16]

Hideaki Takagi. Extension of Littlewood's rule to the multi-period static revenue management model with standby customers. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2181-2202. doi: 10.3934/jimo.2020064
[17]

Chuangwei Lin, Li Zeng, Huiling Wu. Multi-period portfolio optimization in a defined contribution pension plan during the decumulation phase. Journal of Industrial and Management Optimization, 2019, 15 (1) : 401-427. doi: 10.3934/jimo.2018059
[18]

Yan Zhou, Chi Kin Chan, Kar Hung Wong. The impacts of retailers' regret aversion on a random multi-period supply chain network. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2651-2675. doi: 10.3934/jimo.2021086
[19]

Yu-Chung Tsao, Hanifa-Astofa Fauziah, Thuy-Linh Vu, Nur Aini Masruroh. Optimal pricing, ordering, and credit period policies for deteriorating products under order-linked trade credit. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021152
[20]

Yu Liu, Chun-xiang Guo, Hong Zhou, Xin-yi Chen. Pre-sale ordering strategy based on the new retail context considering bounded consumer rationality. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021217

2021 Impact Factor: 1.411

Tools

Metrics

  • PDF downloads (339)
  • HTML views (1322)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy