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1

Davis, Samuel G. "Scheduling Economic Lot Size Production Runs." Management Science 36, no. 8 (August 1990): 985–98. http://dx.doi.org/10.1287/mnsc.36.8.985.

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2

Aggarwal, Alok, and James K. Park. "Improved Algorithms for Economic Lot Size Problems." Operations Research 41, no. 3 (June 1993): 549–71. http://dx.doi.org/10.1287/opre.41.3.549.

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3

Corbey, Michael, and Rutger Jansen. "The economic lot size and relevant costs." International Journal of Production Economics 30-31 (July 1993): 519–30. http://dx.doi.org/10.1016/0925-5273(93)90117-4.

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4

Hsu, Vernon Ning. "Dynamic Economic Lot Size Model with Perishable Inventory." Management Science 46, no. 8 (August 2000): 1159–69. http://dx.doi.org/10.1287/mnsc.46.8.1159.12021.

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5

Wagner, Harvey M., and Thomson M. Whitin. "Dynamic Version of the Economic Lot Size Model." Management Science 50, no. 12_supplement (December 2004): 1770–74. http://dx.doi.org/10.1287/mnsc.1040.0262.

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6

Glock, Christoph H. "The joint economic lot size problem: A review." International Journal of Production Economics 135, no. 2 (February 2012): 671–86. http://dx.doi.org/10.1016/j.ijpe.2011.10.026.

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7

Shree, A. Senthil, and C. Elango. "Economic Lot Size Inventory Problem–Discounted Cost Dynamic System." Annals of Pure and Applied Mathematics 15, no. 2 (December 11, 2017): 289–93. http://dx.doi.org/10.22457/apam.v15n2a15.

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8

Khouja, Moutaz. "The economic production lot size model under volume flexibility." Computers & Operations Research 22, no. 5 (May 1995): 515–23. http://dx.doi.org/10.1016/0305-0548(94)00032-4.

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9

Pishchulov, Grigory, Imre Dobos, Barbara Gobsch, Nadezhda Pakhomova, and Knut Richter. "A vendor–purchaser economic lot size problem with remanufacturing." Journal of Business Economics 84, no. 5 (May 22, 2014): 749–91. http://dx.doi.org/10.1007/s11573-014-0731-7.

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10

Zhou, Yong-Wu, and Hon-Shiang Lau. "An economic lot-size model for deteriorating items with lot-size dependent replenishment cost and time-varying demand." Applied Mathematical Modelling 24, no. 10 (August 2000): 761–70. http://dx.doi.org/10.1016/s0307-904x(00)00015-9.

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11

Sousa Junior, W. T. de, J. A. B. Montevechi, R. de C. Miranda, F. Rocha, and F. F. Vilela. "Economic Lot-Size Using Machine Learning, Parallelism, Metaheuristic and Simulation." International Journal of Simulation Modelling 18, no. 2 (June 15, 2019): 205–16. http://dx.doi.org/10.2507/ijsimm18(2)461.

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12

Banerjee, Avijit. "A JOINT ECONOMIC-LOT-SIZE MODEL FOR PURCHASER AND VENDOR." Decision Sciences 17, no. 3 (July 1986): 292–311. http://dx.doi.org/10.1111/j.1540-5915.1986.tb00228.x.

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13

Sarker, Ruhul, and Charles Newton. "A genetic algorithm for solving economic lot size scheduling problem." Computers & Industrial Engineering 42, no. 2-4 (April 2002): 189–98. http://dx.doi.org/10.1016/s0360-8352(02)00027-x.

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14

Moarefdoost, M. Mohsen, Shiva Zokaee, and Rasoul Haji. "Economic Lot Size Formula Under VMI Program with Poisson Demand." Arabian Journal for Science and Engineering 39, no. 10 (August 26, 2014): 7459–65. http://dx.doi.org/10.1007/s13369-014-1330-1.

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15

Ferretti, Ivan, Laura Mazzoldi, Simone Zanoni, and Lucio Enrico Zavanella. "A joint economic lot size model with third-party processing." Computers & Industrial Engineering 106 (April 2017): 222–35. http://dx.doi.org/10.1016/j.cie.2017.01.014.

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16

Glock, Christoph H., and Taebok Kim. "A joint economic lot size model with returnable transport items." International Journal of Integrated Supply Management 9, no. 3 (2015): 202. http://dx.doi.org/10.1504/ijism.2015.068105.

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17

Ma, Huimin, Zigang Zhang, shaofu Zhou, and Weilai Huang. "A relative benefit algorithm for basic economic lot size problem." Acta Mathematica Scientia 21, no. 2 (April 2001): 159–65. http://dx.doi.org/10.1016/s0252-9602(17)30393-4.

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18

Wagner, Harvey M. "Comments on “Dynamic Version of the Economic Lot Size Model”." Management Science 50, no. 12_supplement (December 2004): 1775–77. http://dx.doi.org/10.1287/mnsc.1040.0306.

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19

Golany, B., R. Maman, and M. Yadin. "An efficient algorithm for the dynamic economic lot size problem." Computers & Operations Research 19, no. 6 (August 1992): 495–504. http://dx.doi.org/10.1016/0305-0548(92)90004-o.

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20

Bhandari, R. M., and P. K. Sharma. "The Economic Production Lot-Size Model with Variable Cost Function." OPSEARCH 36, no. 2 (June 1999): 137–50. http://dx.doi.org/10.1007/bf03398569.

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21

Liu, Jiyin, Lina Wu, and Zhili Zhou. "A time-varying lot size method for the economic lot scheduling problem with shelf life considerations." European J. of Industrial Engineering 2, no. 3 (2008): 337. http://dx.doi.org/10.1504/ejie.2008.017689.

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22

DAVIS, S. G. "An improved algorithm for solving the economic lot size problem (ELSP)." International Journal of Production Research 33, no. 4 (April 1995): 1007–26. http://dx.doi.org/10.1080/00207549508930191.

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23

Huang, Shih-Tao. "Research on changes of total cost of dynamic economic lot-size." Production Planning & Control 11, no. 1 (January 2000): 54–61. http://dx.doi.org/10.1080/095372800232487.

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24

Bertazzi, Luca. "Rounding off the optimal solution of the economic lot size problem." International Journal of Production Economics 81-82 (January 2003): 385–92. http://dx.doi.org/10.1016/s0925-5273(02)00272-4.

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25

Sana, Shib Sankar. "An economic production lot size model in an imperfect production system." European Journal of Operational Research 201, no. 1 (February 2010): 158–70. http://dx.doi.org/10.1016/j.ejor.2009.02.027.

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26

Siajadi, Hans, Raafat N. Ibrahim, and Paul B. Lochert. "Joint economic lot size in distribution system with multiple shipment policy." International Journal of Production Economics 102, no. 2 (August 2006): 302–16. http://dx.doi.org/10.1016/j.ijpe.2005.04.003.

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27

Sargut, F. Zeynep, and Gül Işık. "Dynamic economic lot size model with perishable inventory and capacity constraints." Applied Mathematical Modelling 48 (August 2017): 806–20. http://dx.doi.org/10.1016/j.apm.2017.02.024.

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28

Hayat, Mubashir, Bashir Salah, Misbah Ullah, Iftikhar Hussain, and Razaullah Khan. "Shipment Policy for an Economic Production Quantity Model Considering Imperfection and Transportation Cost." Sustainability 12, no. 21 (October 28, 2020): 8964. http://dx.doi.org/10.3390/su12218964.

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Determining replenishment lot size and number of shipments in a traditional production setup has been of great interest among researchers during the last decades. In order to survive modern competition, the manufacturer has to make good decisions about the lot size that is to be shipped to the retailer. Recently, several researchers have developed mathematical models for modelling different real-world situations; however, these models are lacking due to a combination of imperfection in process and shipment lot sizing. Therefore, in the proposed research, shipment policy for an imperfect production setup has been developed with transportation costs taken into consideration. The model analyzed lot sizing for manufacturers and retailers with imperfections in terms of equally sized shipments. Furthermore, an all-unit-discount policy for shipment is considered in the proposed research, and at the end, numerical computation and sensitivity analyses are carried out to gain more insight into the specifications of the model.
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29

Ho, Wen Tsung, Yu Chi Tseng, and Yu Cheng Hsiao. "The economic lot-size scheduling problem with equally sized batch shipment policy and stochastic demands." European J. of Industrial Engineering 9, no. 2 (2015): 195. http://dx.doi.org/10.1504/ejie.2015.068689.

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30

Dohi, Tadashi, Yasunori Yamada, Naoto Kaio, and Shunji Osaki. "The Optimal Lot Sizing for Unreliable Economic Manufacturing Model." International Journal of Reliability, Quality and Safety Engineering 04, no. 04 (December 1997): 413–26. http://dx.doi.org/10.1142/s0218539397000308.

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This paper considers the optimal policy for an economic manufacturing model with stochastic machine breakdown and repair. The expected cost function is formulated and the optimal age replacement-like policy which minimizes it is derived analytically. The detailed properties on the resulting optimal lot size are examined for some special cases. Finally, numerical examples are devoted to show that the effect of corrective maintenance operation in the production process is remarkable.
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31

Khouja, Moutaz, and Abraham Mehrez. "Economic Production Lot Size Model with Variable Production Rate and Imperfect Quality." Journal of the Operational Research Society 45, no. 12 (December 1994): 1405. http://dx.doi.org/10.2307/2583934.

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32

Aljazzar, Salem M., and Amulya Gurtu. "Observations on 'a joint economic-lot-size model for purchaser and vendor'." International Journal of Inventory Research 5, no. 3 (2019): 169. http://dx.doi.org/10.1504/ijir.2019.098855.

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33

Gurtu, Amulya, and Salem M. Aljazzar. "Observations on 'a joint economic-lot-size model for purchaser and vendor'." International Journal of Inventory Research 5, no. 3 (2019): 169. http://dx.doi.org/10.1504/ijir.2019.10020327.

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34

Goyal, S. K. ""A JOINT ECONOMIC-LOT-SIZE MODEL FOR PURCHASER AND VENDOR": A COMMENT." Decision Sciences 19, no. 1 (March 1988): 236–41. http://dx.doi.org/10.1111/j.1540-5915.1988.tb00264.x.

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35

OUYANG, B. C., and H. RAU. "AN ECONOMIC PRODUCTION LOT SIZE FOR CONTINUOUS DECREASE IN UNIT PRODUCTION COST." Asia-Pacific Journal of Operational Research 25, no. 05 (October 2008): 673–88. http://dx.doi.org/10.1142/s0217595908001948.

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It is common that prices of raw materials, parts or products decrease significantly after they come onto the market. High technology products are good examples, such as PCs, CPUs, DRAM, and mobile phones. Consequently, the traditional economic production quantity (EPQ) model assuming a constant unit production cost is no longer suitable for today's time-based competition. This study incorporates linearly and exponentially decreasing unit production costs during the mature stage of a product life cycle and presents a mathematical inventory model for production policy. A recursive algorithm is developed to obtain the optimal production schedule and a one-dimension search method is applied to find the optimal number of production cycles. In addition, numerical examples to illustrate the proposed model and its significance with or without considering a continuous reduction in unit production costs for the production policy are discussed as well.
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36

Khouja, Moutaz, and Abraham Mehrez. "Economic Production Lot Size Model with Variable Production Rate and Imperfect Quality." Journal of the Operational Research Society 45, no. 12 (December 1994): 1405–17. http://dx.doi.org/10.1057/jors.1994.217.

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37

Giri, B. "An economic production lot-size model with shortages and time-dependent demand." IMA Journal of Management Mathematics 10, no. 3 (July 1, 1999): 203–11. http://dx.doi.org/10.1093/imaman/10.3.203.

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38

Affisco, John F., M. Javad Paknejad, and Farrokh Nasri. "Quality improvement and setup reduction in the joint economic lot size model." European Journal of Operational Research 142, no. 3 (November 2002): 497–508. http://dx.doi.org/10.1016/s0377-2217(01)00308-3.

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39

Zanoni, Simone, Laura Mazzoldi, Lucio Enrico Zavanella, and Mohamad Y. Jaber. "A joint economic lot size model with price and environmentally sensitive demand." Production & Manufacturing Research 2, no. 1 (January 2014): 341–54. http://dx.doi.org/10.1080/21693277.2014.913125.

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40

Chang, Ping-Teng, Ming-Jong Yao, Shih-Fen Huang, and Chia-Tsung Chen. "A genetic algorithm for solving a fuzzy economic lot-size scheduling problem." International Journal of Production Economics 102, no. 2 (August 2006): 265–88. http://dx.doi.org/10.1016/j.ijpe.2005.03.008.

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41

Kabirian, Alireza. "The economic production and pricing model with lot-size-dependent production cost." Journal of Global Optimization 54, no. 1 (June 15, 2011): 1–15. http://dx.doi.org/10.1007/s10898-011-9737-7.

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42

Wee, Hui-Ming. "Economic production lot size model for deteriorating items with partial back-ordering." Computers & Industrial Engineering 24, no. 3 (July 1993): 449–58. http://dx.doi.org/10.1016/0360-8352(93)90040-5.

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43

Suseno, Suseno, and Ari Zaqi Al Faritsy. "APLIKASI MODEL JOINT ECONOMIC LOT SIZE (JELS) DAN QUANTITY DISCOUNT DALAM KERJASAMA PENENTUAN LOT PEMESANAN ANTARA PRODUSEN DAN KONSUMEN." J@ti Undip : Jurnal Teknik Industri 13, no. 3 (November 30, 2018): 151. http://dx.doi.org/10.14710/jati.13.3.151-162.

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PT. Bhakti Karya Mulia (PT BKM) dalam perkembangan bisnis manufaktur pengolahan susu hewan sudah memiliki beberapa pembeli tetap, akan tetapi belum dilakukan ikatan kerjasama, terutama dalam hal penentuan lot rantai pasok antara produsen dan pembeli. Metode JELS (Joint Economic Lot Size) menentukan jumlah lot gabungan yang didasarkan pada semua biaya persediaan menyangkut biaya setup, simpan, pesan yang terdapat pada produsen dan agen pembeli. Selain itu, produsen juga bisa menggunakan model quantity discount untuk mengurangi total biaya pembelian agen akibat kenaikan total biaya persediaan dari aplikasi JELS. Dengan metode tersebut diharapkan menghasilkan lot kerjasama yang dapat mengurangi total biaya persediaan gabungan dalam rantai pasok.Dari hasil pengolahan didapatkan total biaya persediaan dalam sistem rantai pasok untuk: JELS sebesar Rp. 2.357.620,61, independent lot size EOQ sebesar Rp. 3.632.870,41, dan independent perusahaan sebesar Rp. 10.383.836,63, sehingga nilai lot yang dapat membuat total biaya persediaan dalam sistem paling kecil adalah metode joint economic lot size (JELS).Nilai lot masing-masing produk yaitu: agen Hamzah dengan produk lactomax = 633,659 kg, colostrume = 606,099 kg, curah = 932,071 kg; agen Heri dengan produk lactomax = 929,127 kg, colostrume = 888,71 kg, curah = 1366,69 kg; agen Hari dengan produk lactomax = 347,07 kg, colostrume = 331,974 kg, curah = 510,516 kg; agen Heru dengan produk lactomax = 679,526 kg, colostrume = 649,972 kg, curah = 999,538 kg; agen Wiwit dengan produk lactomax = 316,831 kg, colostrume = 303,05 kg, curah = 466,037 kg; agen Danu dengan produk lactomax = 200,381 kg, colostrume = 191,665 kg, curah = 294,748 kg; agen Iwan dengan produk lactomax = 141,691 kg, colostrume = 135,528 kg, curah = 208,417 kg.
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44

Heryanto, Rainisa Maini, Yosi Thedi Setiawan, and Vivi Arisandhy. "Pengendalian Persediaan Produk Obat Herbal pada Permintaan Probabilistik Menggunakan Joint Economic Lot Size." Jurnal Rekayasa Sistem Industri 8, no. 1 (April 30, 2019): 39–46. http://dx.doi.org/10.26593/jrsi.v8i1.3252.39-46.

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Integration in supply chain is an important factor to consider. Good integration between entity in supply chain can give some advantages from minimize cost to competitiveness between supply chain. Company X is manufacturer of herbs medicine which has single distributor to sell the product. Currently, manufacturer and distributor have their inventory control policies and there is no coordination among echelon. It causes the difference number of production lot from manufacturer and the number of order from distributor, consequently total inventory cost become expensive.This research will propose Joint Economic Lot Size (JELS) method that can integrate these two echelons and will give the minimum total inventory cost. The proposed JELS method is integration between Cardenas-Barron model about EPQ backorder and Ben-Daya and Hariga model about integration model between single supplier and single consumer. Calculation process begin with forecasting demand, calculation of actual inventory control at echelon manufacturer and distributor, and calculation of proposed method. The result of calculation process show that total actual inventory cost is 5.500.371,476 IDR/month and the proposed method give 4.604.766,665 IDR/month. The proposed method can give saving about 895.604,811 IDR/month or 16,28%. Key words: cost, integration, JELS, inventory
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45

Parsa, Mostafa, Ali Shahandeh Nookabadi, and Zümbül Atan. "A joint economic lot-size model for sustainable industries of recycled content products." International Journal of Production Research 58, no. 24 (August 13, 2020): 7439–70. http://dx.doi.org/10.1080/00207543.2020.1802078.

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46

Hsu, Vernon Ning, and Timothy J. Lowe. "Dynamic Economic Lot Size Models with Period-Pair-Dependent Backorder and Inventory Costs." Operations Research 49, no. 2 (April 2001): 316–21. http://dx.doi.org/10.1287/opre.49.2.316.13534.

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47

Ditt, S., and H. Kuhn. "An improved algorithm for solving the economic lot size problem (ELSP): A note." International Journal of Production Research 35, no. 6 (June 1997): 1785–87. http://dx.doi.org/10.1080/002075497195263.

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48

Nobil, Amir Hossein, Abolfazl Kazemi, and Ata Allah Taleizadeh. "Economic lot-size problem for a cleaner manufacturing system with warm-up period." RAIRO - Operations Research 54, no. 5 (July 23, 2020): 1495–514. http://dx.doi.org/10.1051/ro/2019056.

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There are instances that production machines require a warm-up period to reach their anticipated productivity. This study extends an economic manufacturing quantity (EMQ) problem by considering warm-up issue in the model. Warming up the machine decreases production loss, emission, and machine depreciation. Therefore, this study helps industry to enhance the profitability and also to reduce the environmental impact by decreasing waste generation and improving machine efficiency. In this study, we divide our system into three subsystems based on the relationships between production and consumption. Then we provide a mathematical model for each subsystem (three in total). The first two models are single-item EMQ inventory problems and the third one is a multi-item single-machine EMQ problem. In the third model, a machine/facility manufactures some items under a limited manufacturing volume. The purpose of these proposed models is to find the optimum cycle length to minimize the total system cost that consists of manufacturing, inventory and setup costs. Finally, we propose exact solution procedures after proving the convexity of these mathematical models.
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49

Khouja, Moutaz, Zgibniew Michalewicz, and Michael Wilmot. "The use of genetic algorithms to solve the economic lot size scheduling problem." European Journal of Operational Research 110, no. 3 (November 1998): 509–24. http://dx.doi.org/10.1016/s0377-2217(97)00270-1.

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50

Burwell, Timothy H., Dinesh S. Dave, Kathy E. Fitzpatrick, and Melvin R. Roy. "Economic lot size model for price-dependent demand under quantity and freight discounts." International Journal of Production Economics 48, no. 2 (January 1997): 141–55. http://dx.doi.org/10.1016/s0925-5273(96)00085-0.

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