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

Optimal pricing and ordering policy for defective items under temporary price reduction with inspection errors and price sensitive demand

  • * Corresponding author: Guiyang Zhu

    * Corresponding author: Guiyang Zhu
Abstract Full Text(HTML) Figure(6) / Table(8) Related Papers Cited by
  • This paper studies the retailer's optimal promotional pricing, special order quantity and screening rate for defective items when a temporary price reduction (i.e., TPR) is offered. Although previous studies have examined the similar issue, they assume a constant demand and an error-free screening process. A subversion of these two assumptions differentiates our paper. First, using a price-sensitive demand, we analyze that the original screening rate may be insufficient, and propose the CPD (i.e., control the promotional demand) and the ISR (i.e., increase the screening rate through investment) strategy to handle it. Second, we incorporate both Type I and Type II inspection errors into our model. Then we establish an inventory model aiming to maximize the retailer's profit under CPD and ISR, respectively. Finally, numerical examples are conducted and several results are obtained: (1) a higher portion of defects makes ISR more profitable; (2) both a higher probability of a Type I error and a Type II error decrease the profit under CPD and ISR, but a Type I error has a more pronounced negative impact; and (3) comparing with the existing studies with a constant demand, our model generates a higher profit especially in markets with a higher price sensitivity.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  Retailer's regular order policy

    Figure 2.  Retailer's special order policy with TPR at time 0

    Figure 3.  Retailer's special order policy with TPR at time 0 (corresponding to ISR)

    Figure 4.  Comparison of the solutions and profits under the CPD and ISR strategy as $ p $ increases

    Figure 5.  Comparison between the changing trends of the results as $ m_1 $ increases and those as $ m_2 $ increases

    Figure 6.  Effects of an increase in $ b $ on the profits of our model and the EOQ model in Hsu and Yu [22]

    Table 1.  Brief literature on inventory models under limited-time price incentives and/or with defective items

     | Show Table
    DownLoad: CSV

    Table 2.  Model parameters

    Parameters Value
    $ A $ $ $500/order $
    $ r $ $ 0.1$/$/day $
    $ c $ $ $25/unit $
    $ x_0 $ $ 242 units/day $
    $ d $ $ $0.5/unit $
    $ v $ $ $20/unit $
    $ s_0 $ $ $50/unit $
    $ p $ $ p $ varies between 0.001 and 0.025; for example, $ p=0.001 $
    $ m_1 $ $ m_1 $ varies between 0.01 to 0.05; for example, $ m_1=0.01 $
    $ m_2 $ $ m_2 $ varies between 0.01 to 0.05; for example, $ m_2=0.01 $
    $ p_e $ $ p_e=(1-p)m_1+p(1-m_2) $; for example, when $ p=0.001 $, $ m_1=0.01 $, and $ m_2=0.01 $, we have $ p_e=0.01098 $
    $ c_a $ $ $500/unit $
    $ c_r $ $ $100/unit $
    $ N $ 365
    $ k $ $ $7.5/unit $
     | Show Table
    DownLoad: CSV

    Table 3.  Effects of an increase in defect proportion $ p $ on the solutions and profits under the CPD and ISR strategy ($ m_1 = 0.02 $, and $ m_2 = 0.02 $. $ G^{(1)\star} $ represents $ G^{(1)}(s^\star_1, Q^\star_1) $, and $ G^{(2)\star} $ represents $ G^{(2)}(s^\star_1, Q^\star_1, z^\star) $. Tables 4-8 follow this marking method)

    $ p $ $ Q^\star_0 $ the CPD strategy the ISR strategy
    $ s^\star_1 $ $ Q^\star_1 $ $ G^{(1)\star} $ $ s^\star_1 $ $ Q^\star_1 $ $ z^\star $ $ x^\star $ $ G^{(2)\star} $
    0.001 283.81 46.92 1472.15 5221.87 46.02 1499.90 0.76 324.92 5089.82
    0.003 283.89 46.96 1469.48 5207.56 46.03 1500.85 0.73 339.41 5084.93
    0.005 283.97 47.00 1466.81 5193.30 46.04 1501.93 0.70 353.31 5080.96
    0.007 284.04 47.04 1464.16 5179.07 46.05 1503.12 0.67 366.69 5077.82
    0.009 284.12 47.08 1461.51 5164.89 46.06 1504.42 0.65 379.60 5075.43
    0.011 284.19 47.12 1458.87 5150.74 46.07 1505.81 0.63 392.09 5073.71
    0.013 284.26 47.16 1456.24 5136.64 46.08 1507.29 0.61 404.20 5072.60
    0.015 284.33 47.19 1453.62 5122.58 46.09 1508.85 0.59 415.97 5072.06
    0.017 284.41 47.23 1451.00 5108.56 46.10 1510.48 0.58 427.42 5072.05
    0.019 284.48 47.27 1448.40 5094.59 46.11 1512.18 0.56 438.58 5072.51
    0.021 284.54 47.31 1445.80 5080.66 46.13 1513.94 0.55 449.46 5073.43
    0.023 284.61 47.35 1443.21 5066.78 46.14 1515.76 0.54 460.11 5074.77
    0.025 284.68 47.39 1440.63 5052.96 46.15 1517.64 0.52 470.51 5076.52
     | Show Table
    DownLoad: CSV

    Table 4.  Effects of an increase in the proportion of a Type I error $ m_1 $ on the solutions and profits under the CPD and ISR strategy ($ p = 0.02 $, and $ m_2 = 0.02 $)

    $ m_1 $ $ Q^\star_0 $ the CPD strategy the ISR strategy
    $ s^\star_1 $ $ Q^\star_1 $ $ G^{(1)\star} $ $ s^\star_1 $ $ Q^\star_1 $ $ z^\star $ $ x^\star $ $ G^{(2)\star} $
    0.010 284.12 47.09 1478.09 5353.91 45.62 1547.53 0.6340 398.43 5346.96
    0.015 284.32 47.19 1462.26 5217.06 45.87 1529.80 0.5903 422.82 5203.96
    0.020 284.51 47.30 1447.10 5087.62 46.12 1513.05 0.5552 444.05 5072.92
    0.025 284.70 47.39 1432.59 4965.51 46.38 1497.22 0.5263 462.63 4953.37
    0.030 284.88 47.49 1418.73 4850.64 46.64 1482.26 0.5018 478.93 4845.05
    0.035 285.05 47.59 1405.54 4742.93 46.91 1468.16 0.4807 493.23 4747.85
    0.040 285.22 47.69 1393.00 4642.31 47.18 1454.91 0.4623 505.74 4661.78
    0.045 285.38 47.91 1377.04 4549.81 47.46 1442.51 0.4461 516.66 4586.92
    0.050 285.53 48.23 1359.58 4469.73 47.74 1430.96 0.4316 526.13 4523.48
     | Show Table
    DownLoad: CSV

    Table 5.  Effects of an increase in the proportion of a Type II error $ m_2 $ on the solutions and profits under the CPD and ISR strategy ($ p = 0.02 $, and $ m_1 = 0.02 $)

    $ m_2 $ $ Q^\star_0 $ the CPD strategy the ISR strategy
    $ s^\star_1 $ $ Q^\star_1 $ $ G^{(1)\star} $ $ s^\star_1 $ $ Q^\star_1 $ $ z^\star $ $ x^\star $ $ G^{(2)\star} $
    0.010 284.55 47.30 1449.00 5108.07 46.07 1521.57 0.5347 462.17 5126.40
    0.015 284.53 47.30 1448.05 5097.85 46.10 1518.91 0.5359 460.61 5110.85
    0.020 284.51 47.30 1447.10 5087.62 46.12 1513.05 0.5552 444.05 5072.92
    0.025 284.49 47.29 1446.14 5077.39 46.15 1510.42 0.5564 442.55 5057.65
    0.030 284.47 47.29 1445.19 5067.15 46.17 1507.80 0.5576 441.06 5042.48
    0.035 284.46 47.29 1444.23 5056.90 46.20 1505.19 0.5588 439.56 5027.42
    0.040 284.44 47.29 1443.28 5046.65 46.22 1502.59 0.5600 438.07 5012.46
    0.045 284.42 47.29 1442.32 5036.39 46.25 1500.00 0.5612 436.58 4997.62
    0.050 284.40 47.28 1441.36 5026.12 46.27 1497.42 0.5625 435.10 4982.86
     | Show Table
    DownLoad: CSV

    Table 6.  Effects of an increase in the unit price discount $ k $ on the solutions and profits under the CPD and ISR strategy ($ p = 0.02 $, $ m_1 = 0.02 $, and $ m_2 = 0.02 $)

    $ k $ $ Q^\star_0 $ the CPD strategy the ISR strategy
    $ s^\star_1 $ $ Q^\star_1 $ $ G^{(1)\star} $ $ s^\star_1 $ $ Q^\star_1 $ $ z^\star $ $ x^\star $ $ G^{(2)\star} $
    2.5 284.51 47.68 603.27 531.03 - - - - -
    5 284.51 47.30 975.23 2063.16 46.82 987.63 0.6429 370.45 1966.43
    7.5 284.51 47.30 1447.10 5087.62 46.12 1513.05 0.5552 444.05 5072.92
    10 284.51 47.30 2076.25 10343.92 45.41 2237.55 0.4932 517.20 10619.61
    12.5 284.51 47.30 2957.06 19171.15 44.69 3280.39 0.4462 590.96 20142.16
    15 284.51 47.30 4278.28 34247.53 43.97 4880.25 0.4090 665.97 36711.51
     | Show Table
    DownLoad: CSV

    Table 7.  Effects of an increase in $ M $ on the solutions and profits under the ISR strategy ($ p = 0.02 $, $ m_1 = 0.02 $, and $ m_2 = 0.02 $)

    $ M $ $ Q^\star_0 $ the CPD strategy the ISR strategy
    $ s^\star_1 $ $ Q^\star_1 $ $ G^{(1)\star} $ $ s^\star_1 $ $ Q^\star_1 $ $ z^\star $ $ x^\star $ $ G^{(2)\star} $
    20 284.51 47.30 1447.10 5087.62 46.13 1534.35 0.4359 565.26 5222.67
    25 284.51 47.30 1447.10 5087.62 46.13 1524.82 0.4889 504.16 5155.54
    30 284.51 47.30 1447.10 5087.62 46.12 1516.26 0.5370 459.06 5095.41
    35 284.51 47.30 1447.10 5087.62 46.12 1508.43 0.5816 424.01 5040.58
    40 284.51 47.30 1447.10 5087.62 46.11 1501.18 0.6232 395.76 4989.93
    45 284.51 47.30 1447.10 5087.62 46.11 1494.40 0.6625 372.35 4942.71
     | Show Table
    DownLoad: CSV

    Table 8.  Effects of an increase in $ b $ on the solutions and profits of our model and the EOQ model in Hsu and Yu [22] ($ p = 0.01 $, $ m_1 = 0.02 $, and $ m_2 = 0.02 $)

    $ b $ Hsu and Yu [22] the CPD strategy the ISR strategy
    $ Q^\star_1 $ $ D^{(1)}(Q^\star_1) $ $ s^\star_1 $ $ Q^\star_1 $ $ G^{(1)\star} $ $ s^\star_1 $ $ Q^\star_1 $ $ z^\star $ $ G^{(2)\star} $
    7 1271.04 4221.78 50 1271.04 4221.78 45.02 1190.03 - 2491.92
    8 1271.04 4221.78 50 1271.04 4221.78 45.65 1271.08 - 3234.62
    9 1271.04 4221.78 49.09 1299.50 4265.23 46.13 1334.12 - 3846.09
    10 1271.04 4221.78 47.95 1354.46 4468.04 46.52 1384.54 - 4356.57
    11 1271.04 4221.78 47.04 1419.59 4790.88 46.81 1424.99 0.66 4633.18
    12 1271.04 4221.78 47.10 1460.19 5157.81 46.06 1505.11 0.64 5074.49
    13 1271.04 4221.78 47.32 1489.28 5477.32 45.44 1591.45 0.62 5585.67
    14 1271.04 4221.78 47.51 1514.22 5756.21 44.92 1682.64 0.61 6153.24
    15 1271.04 4221.78 47.68 1535.83 6001.65 44.48 1777.69 0.59 6767.56
    16 1271.04 4221.78 47.82 1554.74 6219.27 44.09 1875.85 0.57 7421.47
     | Show Table
    DownLoad: CSV
  • [1] P. L. Abad, Optimal policy for a reseller when the supplier offers a temporary reduction in price, Decision Sciences, 28 (1997), 637-653.  doi: 10.1111/j.1540-5915.1997.tb01325.x.
    [2] P. L. Abad, Optimal price and lot size when the supplier offers a temporary price reduction over an interval, Computers & Operations Research, 30 (2003), 63-74.  doi: 10.1016/S0305-0548(01)00081-8.
    [3] A. A. AlamriI. Harris and A. A. Syntetos, Efficient inventory control for imperfect quality items, European J. Oper. Res., 254 (2016), 92-104.  doi: 10.1016/j.ejor.2016.03.058.
    [4] F. J. ArcelusN. H. Shah and G. Srinivasan, Retailer's response to special sales: Price discount vs. trade credit, Omega, 29 (2001), 417-428.  doi: 10.1016/S0305-0483(01)00035-4.
    [5] F. J. Arcelus and G. Srinivasan, Ordering policies under one time only discount and price sensitive demand, Iie Transactions, 30 (1998), 1057-1064.  doi: 10.1080/07408179808966562.
    [6] A. Ardalan, A comparative analysis of approaches for determining optimal price and order quantity when a sale increases demand, European Journal of Operational Research, 84 (1995), 416-430. 
    [7] E. Babaee TirkolaeeA. GoliM. Pahlevan and R. M. Kordestanizadeh, A robust bi-objective multi-trip periodic capacitated arc routing problem for urban waste collection using a multi-objective invasive weed optimization, Waste Management & Research, 37 (2019), 1089-1101.  doi: 10.1177/0734242X19865340.
    [8] K. Ben, Xbox 360 failure rates worse than most consumer electronics, https://arstechnica.com/gaming/2008/02/xbox-360-failure-rates-worse-than-most-consumer-electornics/.
    [9] B. Caroline, Acceptable quality level (aql), https://www.investopedia.com/terms/a/acceptable-quality-level-aql.asp.
    [10] H.-C. Chang, An application of fuzzy sets theory to the EOQ model with imperfect quality items, Comput. Oper. Res., 31 (2004), 2079-2092.  doi: 10.1016/S0305-0548(03)00166-7.
    [11] C.-T. ChangM.-C. Cheng and P.-Y. Soong, Impacts of inspection errors and trade credits on the economic order quantity model for items with imperfect quality, International Journal of Systems Science: Operations & Logistics, 3 (2016), 34-48.  doi: 10.1080/23302674.2015.1036473.
    [12] S. O. Duffuaa and M. Khan, An optimal repeat inspection plan with several classifications, Journal of the Operational Research Society, 53 (2002), 1016-1026.  doi: 10.1057/palgrave.jors.2601392.
    [13] H. GaoD. WangE. D. R. Santibanez Gonzalez and Y. Ju, Optimal stocking strategies for inventory mechanism with a stochastic short-term price discount and partial backordering, International Journal of Production Research, 57 (2019), 7471-7500.  doi: 10.1080/00207543.2019.1567949.
    [14] A. GoliE. Babaee Tirkolaee and M. Soltani, A robust just-in-time flow shop scheduling problem with outsourcing option on subcontractors, Production & Manufacturing Research, 7 (2019), 294-315.  doi: 10.1080/21693277.2019.1620651.
    [15] A. Goli and S. M. R. Davoodi, Coordination policy for production and delivery scheduling in the closed loop supply chain, Production Engineering, 12 (2018), 621-631.  doi: 10.1007/s11740-018-0841-0.
    [16] A. Goli, H. K. Zare, R. Tavakkoli-Moghaddam and A. Sadeghieh, Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem case study: The dairy products industry, Computers & Industrial Engineering, 137 (2019), 106090. doi: 10.1016/j.cie.2019.106090.
    [17] R. W. Grubbström and B. G. Kingsman, Ordering and inventory policies for step changes in the unit item cost: A discounted cash flow approach, Management Science, 50 (2004), 253-267. 
    [18] Z. Hauck and J. Vörös, Lot sizing in case of defective items with investments to increase the speed of quality control, Omega, 52 (2015), 180-189.  doi: 10.1016/j.omega.2014.04.004.
    [19] L.-F. Hsu, A note on "an economic order quantity (EOQ) for items with imperfect quality and inspection errors", International Journal of Industrial Engineering Computations, 3 (2012), 695-702.  doi: 10.5267/j.ijiec.2012.03.008.
    [20] J.-T. Hsu and L.-F. Hsu, An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns, International Journal of Production Economics, 143 (2013), 162-170. 
    [21] J.-T. Hsu and L.-F. Hsu, Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns, Computers & Industrial Engineering, 64 (2013), 389-402.  doi: 10.1016/j.cie.2012.10.005.
    [22] W.-K. K. Hsu and H.-F. Yu, Eoq model for imperfective items under a one-time-only discount, Omega, 37 (2009), 1018-1026. 
    [23] M. Y. JaberS. K. Goyal and M. Imran, Economic production quantity model for items with imperfect quality subject to learning effects, International Journal of Production Economics, 115 (2008), 143-150.  doi: 10.1016/j.ijpe.2008.05.007.
    [24] Jueves, Powerlocus history - the idea behind our company, https://powerlocus.com/es/blog1/powerlocus-history-the-idea-behind-our-company.
    [25] S. KhalilpourazariS. TeimooriA. MirzazadehS. H. R. Pasandideh and N. Ghanbar Tehrani, Robust fuzzy chance constraint programming for multi-item EOQ model with random disruption and partial backordering under uncertainty, Journal of Industrial and Production Engineering, 36 (2019), 276-285.  doi: 10.1080/21681015.2019.1646328.
    [26] M. KhanM. Y. Jaber and A.-R. Ahmad, An integrated supply chain model with errors in quality inspection and learning in production, Omega, 42 (2014), 16-24.  doi: 10.1016/j.omega.2013.02.002.
    [27] M. KhanM. Y. Jaber and M. Bonney, An economic order quantity (EOQ) for items with imperfect quality and inspection errors, International Journal of Production Economics, 133 (2011), 113-118. 
    [28] M. KhanM. JaberA. Guiffrida and S. Zolfaghari, A review of the extensions of a modified EOQ model for imperfect quality items, International Journal of Production Economics, 132 (2011), 1-12.  doi: 10.1016/j.ijpe.2011.03.009.
    [29] C. KumarN. Naidu and K. Ravindranath, Performance improvement of manufacturing industry by reducing the defectives using six sigma methodologies, IOSR J. Eng, 1 (2012), 1-9. 
    [30] M. LengZ. Li and L. Liang, Implications for the role of retailers in quality assurance, Production and Operations Management, 25 (2016), 779-790.  doi: 10.1111/poms.12501.
    [31] J. LiH. Feng and M. Wang, A replenishment policy with defective products, backlog and delay of payments, J. Ind. Manag. Optim., 5 (2009), 867-880.  doi: 10.3934/jimo.2009.5.867.
    [32] Z. Lin, Price promotion with reference price effects in supply chain, Transportation Research Part E: Logistics and Transportation Review, 85 (2016), 52-68.  doi: 10.1016/j.tre.2015.11.002.
    [33] T.-Y. LinB. R. Sarker and C.-J. Lin, An optimal setup cost reduction and lot size for economic production quantity model with imperfect quality and quantity discounts, J. Ind. Manag. Optim., 17 (2021), 467-484.  doi: 10.3934/jimo.2020043.
    [34] R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, A. Sadeghieh and G.-W. Weber, A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk, Numerical Algebra, Control & Optimization.
    [35] R. LotfiM. A. NayeriS. M. Sajadifar and N. Mardani, Determination of start times and ordering plans for two-period projects with interdependent demand in project-oriented organizations: A case study on molding industry, Journal of Project Management, 2 (2017), 119-142.  doi: 10.5267/j.jpm.2017.9.001.
    [36] R. LotfiG.-W. WeberS. M. Sajadifar and N. Mardani, Interdependent demand in the two-period newsvendor problem, J. Ind. Manag. Optim., 16 (2020), 117-140.  doi: 10.3934/jimo.2018143.
    [37] R. Lotfi, Z. Yadegari, S. H. Hosseini, A. H. Khameneh, E. B. Tirkolaee and G.-W. Weber, A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project, J. Ind. Manag. Optim., 13 (2017).
    [38] G. C. Mahata, Application of fuzzy sets theory in an EOQ model for items with imperfect quality and shortage backordering, International Journal of Services and Operations Management, 14 (2013), 466-490.  doi: 10.1504/IJSOM.2013.052839.
    [39] Y. Meng and Y.Song, Optimal policy for competing retailers when the supplier offers a temporary price discount with uncertain demand, in Proceedings of the 6th International Asia Conference on Industrial Engineering and Management Innovation, Springer, (2016), 703–712. doi: 10.2991/978-94-6239-148-2_69.
    [40] E. Naddor, Inventory Systems, Technical report, 1966.
    [41] H. Öztürk, Economic order quantity models for the shipment containing defective items with inspection errors and a sub-lot inspection policy, European Journal of Industrial Engineering, 14 (2020), 85-126. 
    [42] R. PatroM. M. Nayak and M. Acharya, An EOQ model for fuzzy defective rate with allowable proportionate discount, Opsearch, 56 (2019), 191-215.  doi: 10.1007/s12597-018-00352-1.
    [43] R. V. Ramasesh, Lot-sizing decisions under limited-time price incentives: A review, Omega, 38 (2010), 118-135.  doi: 10.1016/j.omega.2009.07.002.
    [44] M. K. Salameh and M. Y. Jaber, Economic production quantity model for items with imperfect quality, International Journal of Production Economics, 64 (2000), 59-64.  doi: 10.1016/S0925-5273(99)00044-4.
    [45] S. S. Sana, A production-inventory model of imperfect quality products in a three-layer supply chain, Decision Support Systems, 50 (2011), 539-547.  doi: 10.1016/j.dss.2010.11.012.
    [46] A. K. SangaiahE. B. TirkolaeeA. Goli and S. Dehnavi-Arani, Robust optimization and mixed-integer linear programming model for LNG supply chain planning problem, Soft Computing, 24 (2020), 7885-7905.  doi: 10.1007/s00500-019-04010-6.
    [47] B. R. Sarker and M. Al Kindi, Optimal ordering policies in response to a discount offer, International Journal of Production Economics, 100 (2006), 195-211.  doi: 10.1016/j.ijpe.2004.10.015.
    [48] B. Sarkar and S. Saren, Product inspection policy for an imperfect production system with inspection errors and warranty cost, European Journal of Operational Research, 248 (2016), 263-271. 
    [49] N. H. Shah and M. K. Naik, EOQ model for deteriorating item under full advance payment availing of discount when demand is price-sensitive, International Journal of Supply Chain and Operations Resilience, 3 (2018), 163-197.  doi: 10.1504/IJSCOR.2018.090779.
    [50] Y. Su and J. Geunes, Price promotions, operations cost, and profit in a two-stage supply chain, Omega, 40 (2012), 891-905.  doi: 10.1016/j.omega.2012.01.010.
    [51] Y. Sun, X. Liang, X. Li and C. Zhang, A fuzzy programming method for modeling demand uncertainty in the capacitated road–rail multimodal routing problem with time windows, Symmetry, 11 (2019), 91. doi: 10.3390/sym11010091.
    [52] A. A. TaleizadehB. MohammadiL. E. Cárdenas-Barrón and H. Samimi, An EOQ model for perishable product with special sale and shortage, International Journal of Production Economics, 145 (2013), 318-338.  doi: 10.1016/j.ijpe.2013.05.001.
    [53] E. B. Tirkolaee, A. Goli and G.-W. Weber, Multi-objective aggregate production planning model considering overtime and outsourcing options under fuzzy seasonal demand, in International Scientific-Technical Conference Manufacturing, Springer, (2019), 81–96. doi: 10.1007/978-3-030-18789-7_8.
    [54] G. Treviño-GarzaK. K. Castillo-Villar and L. E. Cárdenas-Barrón, Joint determination of the lot size and number of shipments for a family of integrated vendor–buyer systems considering defective products, International Journal of Systems Science, 46 (2015), 1705-1716. 
    [55] J. Vörös, Economic order and production quantity models without constraint on the percentage of defective items, Central European Journal of Operations Research, 21 (2013), 867-885.  doi: 10.1007/s10100-012-0277-0.
    [56] Y. WangW. Xing and H. Gao, Optimal ordering policy for inventory mechanism with a stochastic short-term price discount, J. Ind. Manag. Optim., 16 (2020), 1187-1202.  doi: 10.3934/jimo.2018199.
    [57] I. D. Wangsa and H. M. Wee, A vendor-buyer inventory model for defective items with errors in inspection, stochastic lead time and freight cost, INFOR Inf. Syst. Oper. Res., 57 (2019), 597-622.  doi: 10.1080/03155986.2019.1607807.
    [58] S. H. YooD. Kim and M.-S. Park, Economic production quantity model with imperfect-quality items, two-way imperfect inspection and sales return, International Journal of Production Economics, 121 (2009), 255-265.  doi: 10.1016/j.ijpe.2009.05.008.
    [59] S. H. YooD. Kim and M.-S. Park, Inventory models for imperfect production and inspection processes with various inspection options under one-time and continuous improvement investment, Comput. Oper. Res., 39 (2012), 2001-2015.  doi: 10.1016/j.cor.2011.09.015.
    [60] H.-F. Yu and W.-K. Hsu, An EOQ model with immediate return for imperfect items under an announced price increase, Journal of the Chinese Institute of Industrial Engineers, 29 (2012), 30-42.  doi: 10.1080/10170669.2012.654828.
    [61] Y. Zare Mehrjerdi and R. Lotfi, Development of a mathematical model for sustainable closed-loop supply chain with efficiency and resilience systematic framework, International Journal of Supply and Operations Management, 6 (2019), 360-388. 
    [62] Y.-W. ZhouJ. ChenY. Wu and W. Zhou, EPQ models for items with imperfect quality and one-time-only discount, Appl. Math. Model., 39 (2015), 1000-1018.  doi: 10.1016/j.apm.2014.07.017.
  • 加载中

Figures(6)

Tables(8)

SHARE

Article Metrics

HTML views(742) PDF downloads(577) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return