\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

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

  • * Corresponding author: Huifen Zhong

    * Corresponding author: Huifen Zhong 
This research was supported by the National Natural Science Foundation of China (71501049, 71301029) and GDUPS(2016).
Abstract Full Text(HTML) Figure(5) / Table(4) Related Papers Cited by
  • 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:

    \begin{equation} \\ \end{equation}
  • 加载中
  • 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$
    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV
  • [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. ArrowT. Harris and J. Marshak, Optimal inventory policy, Econometrica, 19 (1951), 250-272.  doi: 10.2307/1906813.
    [3] W. H. HuangY. 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. LevinaY. 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. LewisV. 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. LiuS. SongY. 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. YuJ. 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. ZhangX. 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.
  • 加载中

Figures(5)

Tables(4)

SHARE

Article Metrics

HTML views(2511) PDF downloads(361) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return