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An Economic Order Quantity model with partial backordering and all-units discount

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  • Taleizadeh, Ata Allah
  • Pentico, David W.

Abstract

The classic Economic Order Quantity model assumes that the unit purchasing cost is not based on the order quantity. In practice, a supplier may offer purchasers an all-units discount. We develop a model and solution procedure for the EOQ with all-unit discounts and partial backordering at a constant rate. We show, and illustrate with a numerical example, how that model can be used to find the solution for the EOQ with discount and full backordering. A multi-factor experiment is used to gain insights into the improvement in performance of the proposed procedure relative to using the basic EOQ or the EOQ with full backordering and to identify the model parameters that have the greatest impact on the model׳s performance.

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  • Taleizadeh, Ata Allah & Pentico, David W., 2014. "An Economic Order Quantity model with partial backordering and all-units discount," International Journal of Production Economics, Elsevier, vol. 155(C), pages 172-184.
    • Handle: RePEc:eee:proeco:v:155:y:2014:i:c:p:172-184
    DOI: 10.1016/j.ijpe.2014.01.012
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    1. Ford W. Harris, 1990. "How Many Parts to Make at Once," Operations Research, INFORMS, vol. 38(6), pages 947-950, December.
    2. Wee, Hui-Ming, 1999. "Deteriorating inventory model with quantity discount, pricing and partial backordering," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 511-518, March.
    3. Kevin Weng, Z., 1995. "Modeling quantity discounts under general price-sensitive demand functions: Optimal policies and relationships," European Journal of Operational Research, Elsevier, vol. 86(2), pages 300-314, October.
    4. Taleizadeh, Ata Allah & Pentico, David W., 2013. "An economic order quantity model with a known price increase and partial backordering," European Journal of Operational Research, Elsevier, vol. 228(3), pages 516-525.
    5. Lin, Chen-Sin & Kroll, Dennis E., 1997. "The single-item newsboy problem with dual performance measures and quantity discounts," European Journal of Operational Research, Elsevier, vol. 100(3), pages 562-565, August.
    6. San-José, Luis A. & García-Laguna, Juan, 2009. "Optimal policy for an inventory system with backlogging and all-units discounts: Application to the composite lot size model," European Journal of Operational Research, Elsevier, vol. 192(3), pages 808-823, February.
    7. Burwell, Timothy H. & Dave, Dinesh S. & Fitzpatrick, Kathy E. & Roy, Melvin R., 1997. "Economic lot size model for price-dependent demand under quantity and freight discounts," International Journal of Production Economics, Elsevier, vol. 48(2), pages 141-155, January.
    8. Munson, C.L. & Hu, J., 2010. "Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision," European Journal of Operational Research, Elsevier, vol. 201(2), pages 581-592, March.
    9. Taleizadeh, Ata Allah & Pentico, David W. & Aryanezhad, Mirbahador & Ghoreyshi, Seyed Mohammad, 2012. "An economic order quantity model with partial backordering and a special sale price," European Journal of Operational Research, Elsevier, vol. 221(3), pages 571-583.
    10. Chang, Hung-Chi, 2013. "A note on an economic lot size model for price-dependent demand under quantity and freight discounts," International Journal of Production Economics, Elsevier, vol. 144(1), pages 175-179.
    11. Zhou, Yong-Wu, 2007. "A comparison of different quantity discount pricing policies in a two-echelon channel with stochastic and asymmetric demand information," European Journal of Operational Research, Elsevier, vol. 181(2), pages 686-703, September.
    12. Pentico, David W. & Drake, Matthew J., 2011. "A survey of deterministic models for the EOQ and EPQ with partial backordering," European Journal of Operational Research, Elsevier, vol. 214(2), pages 179-198, October.
    13. Lap Mui Ann Chan & Ana Muriel & Zuo-Jun Shen & David Simchi-Levi, 2002. "On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures," Operations Research, INFORMS, vol. 50(6), pages 1058-1067, December.
    14. Papachristos, S. & Skouri, K., 2003. "An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging," International Journal of Production Economics, Elsevier, vol. 83(3), pages 247-256, March.
    15. Pentico, David W. & Drake, Matthew J., 2009. "The deterministic EOQ with partial backordering: A new approach," European Journal of Operational Research, Elsevier, vol. 194(1), pages 102-113, April.
    16. Benton, W. C. & Park, Seungwook, 1996. "A classification of literature on determining the lot size under quantity discounts," European Journal of Operational Research, Elsevier, vol. 92(2), pages 219-238, July.
    17. Hong, Ki-sung & Lee, Chulung, 2013. "Optimal time-based consolidation policy with price sensitive demand," International Journal of Production Economics, Elsevier, vol. 143(2), pages 275-284.
    18. Burke, Gerard J. & Carrillo, Janice & Vakharia, Asoo J., 2008. "Heuristics for sourcing from multiple suppliers with alternative quantity discounts," European Journal of Operational Research, Elsevier, vol. 186(1), pages 317-329, April.
    19. Mendoza, Abraham & Ventura, José A., 2008. "Incorporating quantity discounts to the EOQ model with transportation costs," International Journal of Production Economics, Elsevier, vol. 113(2), pages 754-765, June.
    20. Chung, Chia-Shin & Hum, Sin-Hoon & Kirca, Omer, 1996. "The coordinated replenishment dynamic lot-sizing problem with quantity discounts," European Journal of Operational Research, Elsevier, vol. 94(1), pages 122-133, October.
    21. Du, Ruo & Banerjee, Avijit & Kim, Seung-Lae, 2013. "Coordination of two-echelon supply chains using wholesale price discount and credit option," International Journal of Production Economics, Elsevier, vol. 143(2), pages 327-334.
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    Cited by:

    1. Lin Feng & Konstantina Skouri & Wan-Chih Wang & Jinn-Tsair Teng, 2022. "Optimal selling price, replenishment cycle and payment time among advance, cash, and credit payments from the seller’s perspective," Annals of Operations Research, Springer, vol. 315(2), pages 791-812, August.
    2. Janssen, Larissa & Claus, Thorsten & Sauer, Jürgen, 2016. "Literature review of deteriorating inventory models by key topics from 2012 to 2015," International Journal of Production Economics, Elsevier, vol. 182(C), pages 86-112.
    3. Taleizadeh, Ata Allah & Noori-daryan, Mahsa & Cárdenas-Barrón, Leopoldo Eduardo, 2015. "Joint optimization of price, replenishment frequency, replenishment cycle and production rate in vendor managed inventory system with deteriorating items," International Journal of Production Economics, Elsevier, vol. 159(C), pages 285-295.
    4. Khan, Md. Al-Amin & Shaikh, Ali Akbar & Cárdenas-Barrón, Leopoldo Eduardo, 2021. "An inventory model under linked-to-order hybrid partial advance payment, partial credit policy, all-units discount and partial backlogging with capacity constraint," Omega, Elsevier, vol. 103(C).
    5. Hossein Salehi & Ata Allah Taleizadeh & Reza Tavakkoli-Moghaddam, 2016. "An EOQ model with random disruption and partial backordering," International Journal of Production Research, Taylor & Francis Journals, vol. 54(9), pages 2600-2609, May.
    6. Zissis, Dimitris & Ioannou, George & Burnetas, Apostolos, 2015. "Supply chain coordination under discrete information asymmetries and quantity discounts," Omega, Elsevier, vol. 53(C), pages 21-29.
    7. Ata Allah Taleizadeh & Elham Haji-Sami & Mahsa Noori-daryan, 2020. "A robust optimization model for coordinating pharmaceutical reverse supply chains under return strategies," Annals of Operations Research, Springer, vol. 291(1), pages 875-896, August.
    8. Taleizadeh, Ata Allah & Moshtagh, Mohammad Sadegh, 2019. "A consignment stock scheme for closed loop supply chain with imperfect manufacturing processes, lost sales, and quality dependent return: Multi Levels Structure," International Journal of Production Economics, Elsevier, vol. 217(C), pages 298-316.
    9. Noori-Daryan, Mahsa & Taleizadeh, Ata Allah & Jolai, Fariborz, 2019. "Analyzing pricing, promised delivery lead time, supplier-selection, and ordering decisions of a multi-national supply chain under uncertain environment," International Journal of Production Economics, Elsevier, vol. 209(C), pages 236-248.
    10. Ata Allah Taleizadeh & Bita Hazarkhani & Ilkyeong Moon, 2020. "Joint pricing and inventory decisions with carbon emission considerations, partial backordering and planned discounts," Annals of Operations Research, Springer, vol. 290(1), pages 95-113, July.
    11. Ata Allah Taleizadeh & Masoumeh Sadat Babaei & Seyed Taghi Akhavan Niaki & Mahsa Noori-daryan, 2020. "Bundle pricing and inventory decisions on complementary products," Operational Research, Springer, vol. 20(2), pages 517-541, June.
    12. Li, Yanhai & Ou, Jinwen, 2020. "Optimal ordering policy for complementary components with partial backordering and emergency replenishment under spectral risk measure," European Journal of Operational Research, Elsevier, vol. 284(2), pages 538-549.
    13. Chandan Mahato & Gour Chandra Mahata, 2023. "Sustainable partial backordering inventory model under linked-to-order credit policy and all-units discount with capacity constraint and carbon emissions," Flexible Services and Manufacturing Journal, Springer, vol. 35(3), pages 896-944, September.
    14. Ata Allah Taleizadeh, 2018. "A constrained integrated imperfect manufacturing-inventory system with preventive maintenance and partial backordering," Annals of Operations Research, Springer, vol. 261(1), pages 303-337, February.
    15. San-José, L.A. & Sicilia, J. & García-Laguna, J., 2015. "Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost," Omega, Elsevier, vol. 54(C), pages 147-157.
    16. Pourmohammad Zia, Nadia & Taleizadeh, Ata Allah, 2015. "A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 19-37.
    17. Shi, Yan & Zhang, Zhiyong & Chen, Sheng-Chih & Cárdenas-Barrón, Leopoldo Eduardo & Skouri, Konstantina, 2020. "Optimal replenishment decisions for perishable products under cash, advance, and credit payments considering carbon tax regulations," International Journal of Production Economics, Elsevier, vol. 223(C).
    18. Pentico, David W. & Toews, Carl & Drake, Matthew J., 2015. "Approximating the EOQ with partial backordering at an exponential or rational rate by a constant or linearly changing rate," International Journal of Production Economics, Elsevier, vol. 162(C), pages 151-159.
    19. Taleizadeh, Ata Allah & Sadeghi, Razieh, 2019. "Pricing strategies in the competitive reverse supply chains with traditional and e-channels: A game theoretic approach," International Journal of Production Economics, Elsevier, vol. 215(C), pages 48-60.
    20. Alım, Muzaffer & Beullens, Patrick, 2020. "Joint inventory and distribution strategy for online sales with a flexible delivery option," International Journal of Production Economics, Elsevier, vol. 222(C).
    21. Jackson, Jonathan E. & Munson, Charles L., 2019. "Common replenishment cycle order policies for multiple products with capacity expansion opportunities and quantity discounts," International Journal of Production Economics, Elsevier, vol. 218(C), pages 170-184.
    22. Bhaskar Bhaula & Jayanta Kumar Dash & M. Rajendra Kumar, 2019. "An optimal inventory model for perishable items under successive price discounts with permissible delay in payments," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 261-281, March.
    23. Alaa Fouad Momena & Rakibul Haque & Mostafijur Rahaman & Sankar Prasad Mondal, 2023. "A Two-Storage Inventory Model with Trade Credit Policy and Time-Varying Holding Cost under Quantity Discounts," Logistics, MDPI, vol. 7(4), pages 1-25, October.
    24. Taleizadeh, Ata Allah, 2014. "An EOQ model with partial backordering and advance payments for an evaporating item," International Journal of Production Economics, Elsevier, vol. 155(C), pages 185-193.
    25. Zheng, Qi & Zhou, Li & Fan, Tijun & Ieromonachou, Petros, 2019. "Joint procurement and pricing of fresh produce for multiple retailers with a quantity discount contract," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 130(C), pages 16-36.

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