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Optimal ordering policy and preservation technology for deteriorating items with maximum lifetime under a resilient hybrid payment decision

  • *Corresponding author: Jui-Jung Liao

    *Corresponding author: Jui-Jung Liao
Abstract Full Text(HTML) Figure(1) / Table(8) Related Papers Cited by
  • This study demonstrates an inventory system with items changing value over time under various realistic environments. It is assumed that the time-varying deterioration rate depending on the maximum lifetime of items and the items exceeding the maximum lifetime are regarded as scarp and no longer serviceable. As a result, the retailer will invest in preservation technology to reduce the reckless deterioration. On the other hand, the retailer receives an upstream advance-cash-credit payment plan from the supplier while offering a downstream cash-credit payment plan to customers to stimulate sales. As above description, we incorporate the relevant phenomena into the proposed inventory model, then the primary objective is to determine the replenishment cycle time and the preservation technology which maximizes the retailer's total profit. Consequently, the contributions of this study have three parts as follows: (1) Addressing the economic (total profit) and technology (preservation technology) impacts simultaneously; (2) The propositions and theorems are derived along with a solution procedure; (3) It is proved that the optimal solution not only exists but also is unique under some conditions. Next, an algorithm is developed which simplifies the search for the sustainable optimal ordering strategies. Numerical examples and a sensitivity analysis are elaborated to validate the mathematical formulation. Findings are summarized and managerial implications are also discussed.

    Mathematics Subject Classification: Primary: 90B50; Secondary: 93A30.

    Citation:

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  • Figure 1.  Graphical presentation of the hybrid payment scheme

    Table 1.  A brief comparison of related papers

    References Advance Cash Credit Deterioration Expiration PT
    Chen & Teng (2014) $ \checkmark$ $ \checkmark$ $ \checkmark$
    Chang et al. (2019) $ \checkmark$ $ \checkmark$ $ \checkmark$
    Chaudhari et al. (2020) $ \checkmark$ $ \checkmark$
    Dye & Hsieh (2012) $ \checkmark$
    Iqbal & Sarkar (2020) $ \checkmark$ $ \checkmark$ $ \checkmark$
    Li et al. (2019a) $ \checkmark$ $ \checkmark$ $ \checkmark$ $ \checkmark$
    Mishra et al. (2018) $ \checkmark$ $ \checkmark$
    Mishra et al. (2020) $ \checkmark$ $ \checkmark$
    Mahata et al. (2020) $ \checkmark$ $ \checkmark$
    Mohanty et al. (2018) $ \checkmark$ $ \checkmark$ $ \checkmark$
    Singh et al. (2016) $ \checkmark$ $ \checkmark$
    Shah et al. (2017) $ \checkmark$ $ \checkmark$ $ \checkmark$ $ \checkmark$
    Wu et al. (2016a) $ \checkmark$ $ \checkmark$ $ \checkmark$
    Wu et al. (2018) $ \checkmark$ $ \checkmark$ $ \checkmark$ $ \checkmark$
    Yang et al. (2015) $ \checkmark$ $ \checkmark$
    Teng et al. (2016) $ \checkmark$ $ \checkmark$ $ \checkmark$
    Mahata & De (2017) $ \checkmark$ $ \checkmark$ $ \checkmark$ $ \checkmark$
    Tiwari et al. (2018) $ \checkmark$ $ \checkmark$ $ \checkmark$ $ \checkmark$
    Shi et al. (2020) $ \checkmark$ $ \checkmark$ $ \checkmark$
    Sepehri (2021) $ \checkmark$ $ \checkmark$ $ \checkmark$
    This paper $ \checkmark$ $ \checkmark$ $ \checkmark$ $ \checkmark$ $ \checkmark$
     | Show Table
    DownLoad: CSV

    Table 2.  For $ N<M $

    Theorem 1
    $ A $ $ N $ $ O_1 $ $ O_2 $ $ \bigtriangleup_1\left( M-N\left| \right.\xi\right) $ $ \bigtriangleup_1\left( M\left| \right.\xi\right) $ $ T^* $ $ TP\left( T^*\left| \right.\xi\right) $
    $ (1\text{-}1) $ 15 0.12 28.9522 29.9728 29.2741 12.7772 $ T^*_1 $=0.1744 407.9934
    $ (1\text{-}2) $ 8.0 0.12 14.9522 15.9728 15.2741 -1.2228 $ T^*_2 $=0.1275 454.3647
    $ (1\text{-}3) $ 1.0 0.10 0.9038 1.9244 -0.0198 -15.1796 $ T^*_3 $=0.0452 539.0858
    $ (2\text{-}1) $ 0.5 0.12 -0.0478 0.9728 0.2741 -16.2228 $ T^*_2 $=0.0320 548.2944
    $ (2\text{-}2) $ 0.1 0.12 -0.8478 0.1728 -0.5259 -17.0228 $ T^*_3 $=0.0143 565.5832
    $ (3\text{-}1) $ 0.01 0.12 -1.0278 -0.0072 -0.7059 -17.2028 $ T^*_3 $=0.0045 575.1418
     | Show Table
    DownLoad: CSV

    Table 3.  For $ N\geq M $

    Theorem 2
    $ A $ $ O_3 $ $ \bigtriangleup^*\left( M\left| \right.\xi\right) $ $ T^* $ $ TP\left( T^*\left| \right.\xi\right) $
    (1) 6.00 11.6734 6.1703 $ T^*_4 $=0.1562 207.9781
    (2) 2.00 3.6734 -1.8297 $ T^*_3 $=0.0901 240.4305
    (3) 0.05 -0.2266 -5.7297 $ T^*_5 $=0.0141 277.6508
     | Show Table
    DownLoad: CSV

    Table 4.  Outcome for the example 3

    $ \xi_0 $ $ O_1 $ $ O_2 $ $ \bigtriangleup_1\left( M-N\right) $ $ \bigtriangleup_1\left( M\right) $ $ T^* $ $ \xi^* $ $ TP\left( T^*,\xi^*\right) $ Iterations
    5 18.952184 19.972784 18.9794 2.373136 0.1553 19.373632 433.76756 3
    15 18.952184 19.972784 19.2502 2.373136 0.1553 19.373632 433.7675608 3
    20 18.952184 19.972784 19.2502 2.37311 0.1553 19.373632 433.7675608 2
     | Show Table
    DownLoad: CSV

    Table 5.  Impact of purchase cost ($ c $)

    $ c $ $ O_1 $ $ O_2 $ $ \bigtriangleup_1\left( M-N\left| \right.\xi\right) $ $ \bigtriangleup_1\left( M\left| \right.\xi\right) $ $ T^* $ $ \xi^* $ $ Q^* $ $ TP\left( \xi^*,T^*\right) $ Iterations
    1 $>0 $ $>0 $ 19.36395 5.682702 $ T^*_1 $=0.1722 14.3749771 51.6611 1670.75725 3
    3 $>0 $ $>0 $ 19.30694 5.682702 $ T^*_1 $=0.1629 18.0695784 48.8702 1050.90845 2
    5 $>0 $ $>0 $ 19.25022 2.37313 $ T^*_1 $=0.1553 19.3736332 46.5901 433.767561 3
     | Show Table
    DownLoad: CSV

    Table 6.  Impact of ordering cost($ A $)

    $ A $ $ O_1 $ $ O_2 $ $ \bigtriangleup_1\left( M-N\left| \right.\xi\right) $ $ \bigtriangleup_1\left( M\left| \right.\xi\right) $ $ T^* $ $ \xi^* $ $ Q^* $ $ TP\left(\xi^*, T^*\right) $ Iterations
    5 $>0 $ $>0 $ 9.250213 -7.626891 $ T^*_2 $=0.1098 20.162955 32.9400 470.716489 2
    10 $>0 $ $>0 $ 19.25022 2.37313 $ T^*_1 $=0.1553 19.373633 46.5901 433.767561 2
    15 $>0 $ $>0 $ 29.25022 12.37316 $ T^*_1 $=0.1903 18.889421 57.0901 405.314944 3
     | Show Table
    DownLoad: CSV

    Table 7.  Impact of holding cost ($ h $)

    $ h $ $ O_1 $ $ O_2 $ $ \bigtriangleup_1\left( M-N\left| \right.\xi\right) $ $ \bigtriangleup_1\left( M\left| \right.\xi\right) $ $ T^* $ $ \xi^* $ $ Q^* $ $ TP\left( \xi^*, T^*\right) $ Iterations
    2 $>0 $ $>0 $ 19.25022 2.37313 $ T^*_1 $=0.1553 19.373633 46.5901 433.767561 3
    4 $>0 $ $>0 $ 18.71024 -11.12623 $ T^*_2 $=0.1183 19.821419 35.4900 393.046297 3
    6 $>0 $ $>0 $ 18.17026 -24.62576 $ T^*_2 $=0.0993 20.089663 29.7900 360.400402 3
     | Show Table
    DownLoad: CSV

    Table 8.  Impact of preservation investment efficiency parameter ($ r $)

    $ r $ $ O_1 $ $ O_2 $ $ \bigtriangleup_1\left( M-N\left| \right.\xi\right) $ $ \bigtriangleup_1\left( M\left| \right.\xi\right) $ $ T^* $ $ \xi^* $ $ Q^* $ $ TP\left( \xi^*, T^*\right) $ Iterations
    0.25 $>0 $ $>0 $ 19.25022 2.3732 $ T^*_1 $=0.1553 35.973433 46.59015 417.16532 3
    0.50 $>0 $ $>0 $ 19.25022 2.3732 $ T^*_1 $ =0.1553 19.373633 46.59007 433.76767 3
    0.75 $>0 $ $>0 $ 19.25022 2.3732 $ T^*_1 $=0.1553 13.456513 46.59005 439.68551 3
     | Show Table
    DownLoad: CSV
  • [1] M. AlinezhadI. MahdaviM. Hematian and E. B. Tirkolaee, A fuzzy multi-objective optimization model for sustainable closed-loop supply chain network design in food industries, Environment Development and Sustainability, 24 (2022), 8779-8806. 
    [2] A. Babaeinesami, H. Tohidi, P. Ghasemi, F. Goodarzian and E. B. Tirkolaee, A closed-loop supply chain configuration considering environmental impacts: A self-adaptive NSGA-II algorithm, Applied Intelligence, 178 (2022).
    [3] M. BakkerJ. Riezebos and R. H. Teunter, Review of inventory systems with deterioration since 2001, European Journal of Operational Research, 221 (2012), 275-284.  doi: 10.1016/j.ejor.2012.03.004.
    [4] S. BardhanH. Pal and B. C. Giri, Optimal replenishment policy and preservation technology investment for a non-instantaneous deteriorating item with stock-dependent demand, Operational Research, 19 (2019), 347-368. 
    [5] C.-T. ChangL.-Y. OuyangJ.-T. TengK.-K. Lai and L. E. Cárdenas-Barrón, Manufacturer's pricing and lot-sizing decisions for perishable goods under various payment terms by a discounted cash flow analysis, International Journal of Production Economics, 218 (2019), 83-95. 
    [6] U. Chaudhari, N. H. Shah and M. Y. Jani, Inventory modelling of deteriorating item and preservation technology with advance payment scheme under quadratic demand, Optimization and Inventory Management, (2020), 69–79.
    [7] S.-C. Chen and J.-T. Teng, Retailer's optimal ordering policy for deteriorating items with maximum lifetime under supplier's trade credit financing, Applied Mathematical Modelling, 38 (2014), 4049-4061.  doi: 10.1016/j.apm.2013.11.056.
    [8] R. B. Covert and G. S. Philip, An EOQ model with Weibull distribution deterioration, AIIE Transactions, 5 (1973), 323-326. 
    [9] A. DiabatA. A. Taleizadeh and M. Lashgari, A lot sizing model with partial downstream delayed payment, partial upstream advance payment, and partial backordering for deteriorating items, Journal of Manufacturing Systems, 45 (2017), 322-342. 
    [10] C.-Y. Dye, The effect of preservation technology investment on a non-instantaneous deteriorating inventory model, Omega, 41 (2013), 872-880. 
    [11] C.-Y. Dye and T.-P. Hsieh, An optimal replenishment policy for deteriorating items with effective investment in preservation technology, European Journal of Operational Research, 218 (2012), 106-112.  doi: 10.1016/j.ejor.2011.10.016.
    [12] P. M. Ghare and G. F. Schrader, A model for an exponential decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243. 
    [13] A. Goli, E. B. Tirkolaee and G. W. Weber, A perishable product sustainable supply chain network design problem with lead time and customer satisfaction using a hybrid whale-genetic algorithm, Logistics Operations and Management for Recycling and Reuse, (2020), 99–124.
    [14] A. GoliH. K. ZareR. Tavakkoli-MoghaddamA. SadeghiehM. Sasanian and R. M. Kordestanizadeh, An integrated approach based on artificial intelligence and novel meta-heuristic algorithms to predict demand for dairy products: A case study, Network: Computation in Neural Systems, 32 (2021), 1-35. 
    [15] S. K. Goyal, Economic order quantity under conditions of permissible delay in payments, Journal of the Operational Research Society, 36 (1985), 335-338. 
    [16] S. K. Goyal and B. C. Giri, Recent trends in modeling of deteriorating inventory, European Journal of Operational Research, 134 (2001), 1-16.  doi: 10.1016/S0377-2217(00)00248-4.
    [17] M. GuptaS. Tiwari and C. K. Jaggi, Retailer's ordering policies for time varying deteriorating items with partial backlogging and permissible delay in payments in a two warehouse environment, Annals of Operations Research, 295 (2020), 139-161.  doi: 10.1007/s10479-020-03673-x.
    [18] P.-H. HsuH.-M. Wee and H.-M. Teng, Optimal lot sizing for deteriorating items with expiration date, Journal of Information and Optimization Sciences, 27 (2006), 271-286.  doi: 10.1080/02522667.2006.10699692.
    [19] P.-H. HsuH.-M. Wee and H.-M. Teng, Preservation technology investment for deteriorating inventory, International Journal of Production Economics, 124 (2010), 388-394. 
    [20] M. W. Iqbal and B. Sarkar, Application of preservation technology for lifetime dependent products in an integrated production system, Journal of Industrial and Management Optimization, 16 (2020), 141-167.  doi: 10.3934/jimo.2018144.
    [21] L. JanssenT. Claus and J. Sauer, Literature review of deteriorating inventory models by key topics from 2012 to 2015, International Journal of Production Economics, 182 (2016), 86-112. 
    [22] D. Jyoti Mohanty, R. S. Kumar and A. Goswami, Trade-credit modelling for deteriorating item inventory system with preservation technology under random planning horizon, Sadhana, 43 (2018), Paper No. 45, 17 pp. doi: 10.1007/s12046-018-0807-0.
    [23] A. Khakbaz and E. B Tirkolaee, A sustainable hybrid manufacturing/remanufacturing system with two-way substitution and WEEE directive under different market conditions, (2021).
    [24] M. A. A. KhanA. A. ShaikhG. C. PandaI. Konstantaras and A. A. Taleizadeh, Inventory system with expiration date: Pricing and replenishment decisions, Computers & Industrial Engineering, 132 (2019), 232-247. 
    [25] M. LashgariA. A. Taleizadeh and S. J. Sadjadi, Ordering policies for non-instantaneous deteriorating items under hybrid partial prepayment, partial trade credit, and partial backordering, Journal of the Operational Research Society, 69 (2018), 1167-1196. 
    [26] M. LashgariA. A. Taleizadeh and S. S. Sana, An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity, Journal of Industrial & Management Optimization, 12 (2016), 1091-1119.  doi: 10.3934/jimo.2016.12.1091.
    [27] G. LiX. HeJ. Zhou and H. Wu, Pricing, replenishment, and preservation technology investment decisions for non-instantaneous deteriorating items, Omega, 84 (2019b), 114-126. 
    [28] R. LiY.-L. ChanC.-T. Chang and L. E. Cárdenas-Barrón, Pricing and lot-sizing policies for perishable products with advance-cash-credit payments by a discounted cash-flow analysis, International Journal of Production Economics, 193 (2017), 578-589. 
    [29] R. LiY.-P. LiuJ.-T. Teng and Y.-C. Tsao, Optimal pricing, lot-sizing and backordering decisions when a seller demands an advance-cash-credit payment scheme, European Journal of Operational Research, 278 (2019), 283-295.  doi: 10.1016/j.ejor.2019.04.033.
    [30] R. LiK. SkouriJ.-T. Teng and W.-G. Yang, Seller's optimal replenishment policy and payment term among advance, cash, and credit payments, International Journal of Production Economics, 197 (2018), 35-42. 
    [31] J.-J. Liao, H. M. Srivastava, K.-J. Chung, S.-F. Lee, K.-N. Huang and S.-D. Lin, Inventory models for non-instantaneous deteriorating items with expiration dates and imperfect quality under hybrid payment policy in the three-level supply chain, Symmetry, 13 (2021), Art. ID 1695, 26 pp.
    [32] F. Lin and Y.-L. Chan, Joint pricing and production decisions for new products with learning curve effects under upstream and downstream trade credits, European Journal of Operational Research, 272 (2019), 905-913.  doi: 10.1016/j.ejor.2018.07.003.
    [33] F. LinY.-L. Chan and L. E. Cárdenas-Barrónc, Pricing and lot-sizing polices for perishable goods when the demand depends on selling price, displayed stocks, and expiration date, International Journal of Production Economics, 185 (2017), 11-20. 
    [34] F. LinT. JiaF. Wu and Z. Yang, Impacts of two-stage deterioration on an integrated inventory model under trade credit and variable capacity utilization, European Journal of Operational Research, 272 (2019), 219-234.  doi: 10.1016/j.ejor.2018.06.022.
    [35] L. LiuL. Zhao and X. Ren, Optimal preservation technology investment and pricing policy for fresh food, Computers & Industrial Engineering, 135 (2019), 746-756. 
    [36] R. Lotfi, B. Kargar, A. Gharehbaghi and G. W. Weber, Viable medical waste chain network design by considering risk and robustness, Environmental Science and Pollution Research, (2021), 1–16.
    [37] R. LotfiB. KargarS. H. HoseiniS. NazariS. Safavi and G. W. Weber, Resilience and sustainable supply chain network design by considering renewable energy, International Journal of Energy Research, 45 (2021), 1-18. 
    [38] R. LotfiN. Mardani and G. W. Weber, Robust bi-level programming for renewable energy location, International Journal of Energy Research, 45 (2021), 7521-7534. 
    [39] R. LotfiY. Z. MehrjerdiM. S. PishvaeeA. 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, 11 (2021), 221-253.  doi: 10.3934/naco.2020023.
    [40] R. Lotfi, S. Safavi, A. Gharehbaghi, S. Ghaboulian Zare, R. Hazrati and G. W. Weber, Viable supply chain network design by considering Blockchain technology and cryptocurrency, Mathematical Problems in Engineering, (2021), 7347389.
    [41] R. Lotfi, Z. Sheikhi, M. Amra, M. AliBakhshi and G. W. Weber, Robust optimization of risk-aware, resilient and sustainable closed-loop supply chain network design with Lagrange relaxation and fix-and-optimize, International Journal of Logistics Research and Applications, (2021).
    [42] R. LotfiZ. YadegariS. H. HosseiniA. H. KhamenehE. 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, Journal of Industrial & Management Optimization, 18 (2022), 375-396.  doi: 10.3934/jimo.2020158.
    [43] G. C. Mahata, Optimal ordering policy with trade credit and variable deterioration for fixed lifetime products, International Journal of Operational Research, 25 (2016), 307-326.  doi: 10.1504/IJOR.2016.074756.
    [44] G. C. Mahata and S. K. De, Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit-risk customers, International Journal of Management Science and Engineering Management, 12 (2017), 21-32. 
    [45] P. MahataG. C. Mahata and S. K. De, An economic order quantity model under two-level partial trade credit for time varying deteriorating items, International Journal of Systems Science: Operations & Logistics, 7 (2020), 1-17. 
    [46] B. Mandal, An EOQ inventory model for Weibull distributed deteriorating items under ramp type demand and shortages, Opsearch, 47 (2010), 158-165.  doi: 10.1007/s12597-010-0018-x.
    [47] A. H. M. MashudM. R. HasanH.-M. Wee and Y. Daryanto, Non-instantaneous deteriorating inventory model under the joined effect of trade-credit, preservation technology and advertisement policy, Kybernetes, 49 (2020), 1645-1674. 
    [48] U. MishraL. E. Cárdenas-BarrónS. TiwariA. A. Shikh and G. Treviño-Garza, An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment, Annals of Operations Research, 254 (2017), 165-190.  doi: 10.1007/s10479-017-2419-1.
    [49] U. Mishra, J. Tijerina-Aguilera, S. Tiwari and L. E. Cárdenas-Barrón, Retailer's joint ordering, pricing, and preservation technology investment policies for a deteriorating item under permissible delay in payments, Mathematical Problems in Engineering, (2018), Art. ID 6962417, 14 pp. doi: 10.1155/2018/6962417.
    [50] U. MishraJ. Z. WuY. C. Tsao and M. L. Tseng, Sustainable inventory system with controllable non-instantaneous deterioration and environmental emission rates, Journal of Cleaner Production, 244 (2020), 118807. 
    [51] F. Raafat, Survey of literature on continuously deteriorating inventory models, Journal of the Operational Research Society, 42 (1991), 27-37. 
    [52] B. Sarkar, An EOQ model with delay in payments and time-varying deterioration rate, Mathematical and Computer Modelling, 55 (2012), 367-377.  doi: 10.1016/j.mcm.2011.08.009.
    [53] B. SarkarS. Saren and L. E. Cárdenas-Barrónc, An inventory model with trade-credit policy and variable deterioration for fixed lifetime products, Annals of Operation Research, 229 (2015), 677-702.  doi: 10.1007/s10479-014-1745-9.
    [54] B. SarkarS. Sarkar and W. Y. Yun, Retailer's optimal strategy for fixed lifetime products, International Journal of Machine Learning and Cybernetics, 7 (2016), 121-133. 
    [55] A. Sepehri, Optimizing the replenishment cycle and selling price for an inventory model under carbon emission regulation and partially permissible delay in payment, Process Integration and Optimization for Sustainability, (2021), 1–21.
    [56] A. SepehriU. MishraM.-L. Tseng and B. Sarkar, Joint pricing and inventory model for deteriorating items with maximum lifetime and controllable carbon emissions under permissible delay in payments, Mathematics, 9 (2021), 470. 
    [57] N. H. Shah, U. B. Chaudhari and M. Y. Jani, Inventory model with expiration date of items and deterioration under two-level trade credit and preservation technology investment for time and price sensitive demand: DCF approach, International Journal of Logistics Systems and Management, 27 (2017), 420–437.
    [58] N. H. ShahU. B. Chaudhari and M. Y. Jani, Optimal policies for time-varying deteriorating item with preservation technology under selling price and trade credit dependent quadratic demand in a supply chain, International Journal of Applied and Computational Mathematics, 3 (2016), 363-379.  doi: 10.1007/s40819-016-0141-3.
    [59] Y. ShiZ. ZhangS.-C. ChenL. E. Cárdenas-Barrón and K. Skouri, Optimal replenishment decisions for perishable products under cash, advance, and credit payments considering carbon tax regulations, International Journal of Production Economics, 223 (2020), 107514. 
    [60] S. SinghD. Khurana and S. Tayal, An economic order quantity model for deteriorating products having stock dependent demand with trade credit period and preservation technology, Uncertain Supply Chain Management, 4 (2016), 29-42. 
    [61] K. SkouriI. KonstantarasS. Papachristos and I. Ganas, Inventory model for Weibull deteriorating items with ramp-type demand rate and partial backlogging, European Journal of Operation Research, 192 (2009), 79-92.  doi: 10.1016/j.ejor.2007.09.003.
    [62] H. M. SrivastavaJ.-J. LiaoK.-N. HuangK.-J. ChungS.-D. Lin and S.-F. Lee, Supply chain inventory model for deteriorating products with maximum lifetime under trade-credit financing, TWMS Journal of Pure and Applied Mathematics, 13 (2022), 53-71. 
    [63] A. A. Taleizadeh, Lot-sizing model with advance payment pricing and disruption in supply under planned partial backordering, International Transactions in Operational Research, 24 (2017), 783-800.  doi: 10.1111/itor.12297.
    [64] J.-T. TengL. E. Cárdenas-BarrónH.-J. ChangJ. Wu and Y. Hu, Inventory lot-size policies for deteriorating items with expiration dates and advance payments, Applied Mathematical Modelling, 40 (2016), 8605-8616.  doi: 10.1016/j.apm.2016.05.022.
    [65] S. TiwariW. Ahmed and B. Sarkar, Sustainable ordering policies for non-instantaneous deteriorating items under carbon emission and multi-trade-credit-policies, Journal of Cleaner Production, 240 (2019), 118183. 
    [66] S. TiwariL. E. Cárdenas-BarrónM. Goh and A. A. Shaikh, Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain, International Journal of Production Economics, 200 (2018), 16-36. 
    [67] S. TiwariL. E. Cárdenas-BarrónA. A. Shaikh and M. Goh, Retailer's optimal ordering policy for deteriorating items under order-size dependent trade credit and complete backlogging, Computers and Industrial Engineering, 139 (2020), 105559. 
    [68] S. TiwariH.-M. Wee and S. Sarkar, Lot-sizing policies for defective and deteriorating items with time dependent demand and trade credit, European Journal of Industrial Engineering, 11 (2017), 683-703. 
    [69] J. WuF. B. Al-KhateebJ.-T. Teng and L. E. Cárdenas-Barrónc, Inventory models for deteriorating items with maximum lifetime under downstream partial trade credits to credit-risk customers by discounted cash-flow analysis, International Journal of Production Economics, 171 (2016), 105-115. 
    [70] J. Wu and Y.-L. Chan, Lot-sizing policies for deteriorating items with expiration dates and partial trade credit to credit-risk customers, International Journal of Production Economics, 155 (2014), 292-301. 
    [71] J. WuC.-T. ChangM.-C. ChengJ.-T. Teng and F. B. Al-Khatee, Inventory management for fresh produce when the time-varying demand depends on product freshness, stock level and expiration date, International Journal of Systems Science: Operations & Logistics, 3 (2016), 138-147. 
    [72] J. WuC.-T. ChangJ.-T. Teng and K.-K. Lai, Optimal order quantity and selling price over a product life cycle with deterioration rate linked to expiration date, International Journal of Production Economics, 193 (2017b), 343-351. 
    [73] J. WuL.-Y. OuyangL. E. Cárdenas-Barrónc and S. K. Goyal, Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing, European Journal of Operational Research, 237 (2014), 898-908.  doi: 10.1016/j.ejor.2014.03.009.
    [74] J. WuJ.-T. Teng and Y.-L. Chan, Inventory policies for perishable products with expiration dates and advance-cash-credit payment schemes, International Journal of Systems Science: Operations & Logistics, 5 (2017), 310-326. 
    [75] J. WuJ.-T. Teng and Y.-L. Chan, Inventory policies for perishable products with expiration dates and advance-cash-credit payment schemes, International Journal of Systems Science: Operations & Logistics, 5 (2018), 310-326. 
    [76] C.-T. YangC.-Y. Dye and J.-F. Ding, Optimal dynamic trade credit and preservation technology allocation for a deteriorating inventory model, Computers & Industrial Engineering, 87 (2015), 356-369. 
    [77] J. ZhangZ. Bai and W. Tang, Optimal pricing policy for deteriorating items with preservation technology investment, Journal of Industrial and Management Optimization, 10 (2014), 1261-1277.  doi: 10.3934/jimo.2014.10.1261.
    [78] N. P. Zia and A. A. Taleizadeh, A lot-sizing model with backordering with hybrid linked-to-order multiple advance payments and delayed payment, Transportation Research Part E: Logistics and Transportation Review, 82 (2015), 19-37. 
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