IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v214y2011i2p179-198.html
   My bibliography  Save this article

A survey of deterministic models for the EOQ and EPQ with partial backordering

Author

Listed:
  • Pentico, David W.
  • Drake, Matthew J.

Abstract

Models for the basic deterministic EOQ or EPQ problem with partial backordering or backlogging make all the assumptions of the classic EOQ or EPQ model with full backordering except that only a fraction of the demand during the stockout period is backordered. In this survey we review deterministic models that have been developed over the past 40Â years that address the basic models and extensions that add other considerations, such as pricing, perishable or deteriorating inventory, time-varying or stock-dependent demand, quantity discounts, or multiple-warehouses.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:214:y:2011:i:2:p:179-198
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711001020
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Z T Balkhi, 2000. "On the optimal production stopping and restarting times for an EOQ model with deteriorating items," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(8), pages 999-1001, August.
    3. Hung, Kuo-Chen, 2011. "An inventory model with generalized type demand, deterioration and backorder rates," European Journal of Operational Research, Elsevier, vol. 208(3), pages 239-242, February.
    4. Pentico, David W. & Drake, Matthew J. & Toews, Carl, 2009. "The deterministic EPQ with partial backordering: A new approach," Omega, Elsevier, vol. 37(3), pages 624-636, June.
    5. Chang, Horng-Jinh & Teng, Jinn-Tsair & Ouyang, Liang-Yuh & Dye, Chung-Yuan, 2006. "Retailer's optimal pricing and lot-sizing policies for deteriorating items with partial backlogging," European Journal of Operational Research, Elsevier, vol. 168(1), pages 51-64, January.
    6. Arvind Rajan & Richard Rakesh, 1992. "Dynamic Pricing and Ordering Decisions by a Monopolist," Management Science, INFORMS, vol. 38(2), pages 240-262, February.
    7. Yang, Hui-Ling & Teng, Jinn-Tsair & Chern, Maw-Sheng, 2010. "An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages," International Journal of Production Economics, Elsevier, vol. 123(1), pages 8-19, January.
    8. Chang, Chun-Tao & Teng, Jinn-Tsair & Goyal, Suresh Kumar, 2010. "Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand," International Journal of Production Economics, Elsevier, vol. 123(1), pages 62-68, January.
    9. Sharma, Sanjay, 2008. "On the flexibility of demand and production rate," European Journal of Operational Research, Elsevier, vol. 190(2), pages 557-561, October.
    10. Chern, Maw-Sheng & Yang, Hui-Ling & Teng, Jinn-Tsair & Papachristos, Sotiris, 2008. "Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation," European Journal of Operational Research, Elsevier, vol. 191(1), pages 127-141, November.
    11. Dye, Chung-Yuan & Chang, Horng-Jinh & Teng, Jinn-Tsair, 2006. "A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging," European Journal of Operational Research, Elsevier, vol. 172(2), pages 417-429, July.
    12. Abad, P. L., 2003. "Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale," European Journal of Operational Research, Elsevier, vol. 144(3), pages 677-685, February.
    13. Sanjay Sharma, 2009. "Extending Sanjay Sharma's theory of exchange," International Journal of Applied Management Science, Inderscience Enterprises Ltd, vol. 1(4), pages 325-339.
    14. Goyal, S. K. & Giri, B. C., 2003. "The production-inventory problem of a product with time varying demand, production and deterioration rates," European Journal of Operational Research, Elsevier, vol. 147(3), pages 549-557, June.
    15. J-T Teng & H-L Yang, 2004. "Deterministic economic order quantity models with partial backlogging when demand and cost are fluctuating with time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(5), pages 495-503, May.
    16. Abad, Prakash L., 2008. "Optimal price and order size under partial backordering incorporating shortage, backorder and lost sale costs," International Journal of Production Economics, Elsevier, vol. 114(1), pages 179-186, July.
    17. Yang, Gino K., 2007. "Note on sensitivity analysis of inventory model with partial backorders," European Journal of Operational Research, Elsevier, vol. 177(2), pages 865-871, March.
    18. Yang, Hui-Ling, 2006. "Two-warehouse partial backlogging inventory models for deteriorating items under inflation," International Journal of Production Economics, Elsevier, vol. 103(1), pages 362-370, September.
    19. Skouri, K. & Papachristos, S., 2003. "Optimal stopping and restarting production times for an EOQ model with deteriorating items and time-dependent partial backlogging," International Journal of Production Economics, Elsevier, vol. 81(1), pages 525-531, January.
    20. Skouri, K. & Konstantaras, I. & Papachristos, S. & Ganas, I., 2009. "Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate," European Journal of Operational Research, Elsevier, vol. 192(1), pages 79-92, January.
    21. Wee, Hui-Ming, 1995. "Joint pricing and replenishment policy for deteriorating inventory with declining market," International Journal of Production Economics, Elsevier, vol. 40(2-3), pages 163-171, August.
    22. Maw-Sheng Chern & Ya-Lan Chan & Jinn-Tsair Teng, 2005. "A Comparison Among Various Inventory Shortage Models For Deteriorating Items On The Basis Of Maximizing Profit," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 121-134.
    23. Wu, Kun-Shan & Ouyang, Liang-Yuh & Yang, Chih-Te, 2006. "An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging," International Journal of Production Economics, Elsevier, vol. 101(2), pages 369-384, June.
    24. Dye, Chung-Yuan & Hsieh, Tsu-Pang & Ouyang, Liang-Yuh, 2007. "Determining optimal selling price and lot size with a varying rate of deterioration and exponential partial backlogging," European Journal of Operational Research, Elsevier, vol. 181(2), pages 668-678, September.
    25. Chang, Chun-Tao & Goyal, Suresh Kumar & Teng, Jinn-Tsair, 2006. "On "An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging" by Dye and Ouyang," European Journal of Operational Research, Elsevier, vol. 174(2), pages 923-929, October.
    26. Yu-Chung Tsao, 2010. "Two-phase pricing and inventory management for deteriorating and fashion goods under trade credit," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 107-127, August.
    27. Padmanabhan, G. & Vrat, Prem, 1995. "EOQ models for perishable items under stock dependent selling rate," European Journal of Operational Research, Elsevier, vol. 86(2), pages 281-292, October.
    28. Lo, Sh-Tyan & Wee, Hui-Ming & Huang, Wen-Chang, 2007. "An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation," International Journal of Production Economics, Elsevier, vol. 106(1), pages 248-260, March.
    29. Zhou, Yong-Wu & Lau, Hon-Shiang & Yang, Shan-Lin, 2004. "A finite horizon lot-sizing problem with time-varying deterministic demand and waiting-time-dependent partial backlogging," International Journal of Production Economics, Elsevier, vol. 91(2), pages 109-119, September.
    30. Sanjay Sharma, 2009. "On price increases and temporary price reductions with partial backordering," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 3(1), pages 70-89.
    31. J-T Teng & H-L Yang & L-Y Ouyang, 2003. "On an EOQ model for deteriorating items with time-varying demand and partial backlogging," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 432-436, April.
    32. Lo, Sh-Tyan & Wee, Hui-Ming & Huang, Wen-Chang, 2007. "An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation," International Journal of Production Economics, Elsevier, vol. 106(2), pages 493-505, April.
    33. Sharma, Sanjay, 2008. "Theory of exchange," European Journal of Operational Research, Elsevier, vol. 186(1), pages 128-136, April.
    34. San José, L.A. & Sicilia, J. & Garcia-Laguna, J., 2006. "Analysis of an inventory system with exponential partial backordering," International Journal of Production Economics, Elsevier, vol. 100(1), pages 76-86, March.
    35. L. San-José & J. García-Laguna & J. Sicilia, 2009. "An economic order quantity model with partial backlogging under general backorder cost function," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 366-384, December.
    36. Dye, Chung-Yuan & Ouyang, Liang-Yuh, 2005. "An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging," European Journal of Operational Research, Elsevier, vol. 163(3), pages 776-783, June.
    37. Chung, Kun-Jen & Chu, Peter & Lan, Shaw-Ping, 2000. "A note on EOQ models for deteriorating items under stock dependent selling rate," European Journal of Operational Research, Elsevier, vol. 124(3), pages 550-559, August.
    38. Zhang, Ren-qian, 2009. "A note on the deterministic EPQ with partial backordering," Omega, Elsevier, vol. 37(5), pages 1036-1038, October.
    39. Pentico, David W. & Drake, Matthew J. & Toews, Carl, 2011. "The EPQ with partial backordering and phase-dependent backordering rate," Omega, Elsevier, vol. 39(5), pages 574-577, October.
    40. Chih-Te Yang & Liang-Yuh Ouyang & Kun-Shan Wu & Hsiu-Feng Yen, 2011. "An optimal replenishment policy for deteriorating items with stock-dependent demand and relaxed terminal conditions under limited storage space," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(1), pages 139-153, March.
    41. Teng, Jinn-Tsair & Ouyang, Liang-Yuh & Chen, Liang-Ho, 2007. "A comparison between two pricing and lot-sizing models with partial backlogging and deteriorated items," International Journal of Production Economics, Elsevier, vol. 105(1), pages 190-203, January.
    42. 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.
    43. Sharma, Sanjay, 2009. "Revisiting the shelf life constrained multi-product manufacturing problem," European Journal of Operational Research, Elsevier, vol. 193(1), pages 129-139, February.
    44. H Yan & T C E Cheng, 2000. "A Reply to Balkhi," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(8), pages 1001-1002, August.
    45. 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.
    46. Francis Leung, Kit-Nam, 2008. "Technical note: A use of the complete squares method to solve and analyze a quadratic objective function with two decision variables exemplified via a deterministic inventory model with a mixture of b," International Journal of Production Economics, Elsevier, vol. 113(1), pages 275-281, May.
    47. Bhunia, A.K. & Kundu, S. & Sannigrahi, T. & Goyal, S.K., 2009. "An application of tournament genetic algorithm in a marketing oriented economic production lot-size model for deteriorating items," International Journal of Production Economics, Elsevier, vol. 119(1), pages 112-121, May.
    48. Urban, Timothy L., 1995. "Inventory models with the demand rate dependent on stock and shortage levels," International Journal of Production Economics, Elsevier, vol. 40(1), pages 21-28, June.
    49. Zhang, Ren-qian & Kaku, Ikou & Xiao, Yi-yong, 2011. "Deterministic EOQ with partial backordering and correlated demand caused by cross-selling," European Journal of Operational Research, Elsevier, vol. 210(3), pages 537-551, May.
    50. Pal, A.K. & Bhunia, A.K. & Mukherjee, R.N., 2006. "Optimal lot size model for deteriorating items with demand rate dependent on displayed stock level (DSL) and partial backordering," European Journal of Operational Research, Elsevier, vol. 175(2), pages 977-991, December.
    51. P. L. Abad, 1996. "Optimal Pricing and Lot-Sizing Under Conditions of Perishability and Partial Backordering," Management Science, INFORMS, vol. 42(8), pages 1093-1104, August.
    52. Z T Balkhi & S K Goyal & B C Giri, 2001. "Some notes on the optimal production stopping and restarting times for an EOQ model with deteriorating items," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(11), pages 1300-1301, November.
    53. Z T Balkhi, 2000. "Response to Yan and Cheng," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(8), pages 1002-1003, August.
    54. Chu, Peter & Chung, Kun-Jen, 2004. "The sensitivity of the inventory model with partial backorders," European Journal of Operational Research, Elsevier, vol. 152(1), pages 289-295, January.
    55. S K Goyal & B C Giri, 2001. "A comment on Chang and Dye (1999): EOQ model for deteriorating items with time-varying demand and partial backlogging," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(2), pages 238-239, February.
    56. Leung, Kit-Nam Francis, 2009. "A generalization of sensitivity of the inventory model with partial backorders," European Journal of Operational Research, Elsevier, vol. 196(2), pages 554-562, July.
    57. Dye, Chung-Yuan & Ouyang, Liang-Yuh & Hsieh, Tsu-Pang, 2007. "Deterministic inventory model for deteriorating items with capacity constraint and time-proportional backlogging rate," European Journal of Operational Research, Elsevier, vol. 178(3), pages 789-807, May.
    58. Dye, Chung-Yuan, 2007. "Joint pricing and ordering policy for a deteriorating inventory with partial backlogging," Omega, Elsevier, vol. 35(2), pages 184-189, April.
    59. Hu, Wan-ting & Kim, Seung-Lae & Banerjee, Avijit, 2009. "An inventory model with partial backordering and unit backorder cost linearly increasing with the waiting time," European Journal of Operational Research, Elsevier, vol. 197(2), pages 581-587, September.
    60. Chu, Peter & Yang, Kuo-Lung & Liang, Shing-Ko & Niu, Thomas, 2004. "Note on inventory model with a mixture of back orders and lost sales," European Journal of Operational Research, Elsevier, vol. 159(2), pages 470-475, December.
    61. Joaquín Sicilia & Luis San-José & Juan García-Laguna, 2009. "An optimal replenishment policy for an EOQ model with partial backlogging," Annals of Operations Research, Springer, vol. 169(1), pages 93-115, July.
    62. Yang, Hui-Ling, 2005. "A comparison among various partial backlogging inventory lot-size models for deteriorating items on the basis of maximum profit," International Journal of Production Economics, Elsevier, vol. 96(1), pages 119-128, April.
    63. Hemant K. Bhargava & Daewon Sun & Susan H. Xu, 2006. "Stockout Compensation: Joint Inventory and Price Optimization in Electronic Retailing," INFORMS Journal on Computing, INFORMS, vol. 18(2), pages 255-266, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joaquín Sicilia & Luis San-José & Juan García-Laguna, 2012. "An inventory model where backordered demand ratio is exponentially decreasing with the waiting time," Annals of Operations Research, Springer, vol. 199(1), pages 137-155, October.
    2. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.
    3. Pahl, Julia & Voß, Stefan, 2014. "Integrating deterioration and lifetime constraints in production and supply chain planning: A survey," European Journal of Operational Research, Elsevier, vol. 238(3), pages 654-674.
    4. R. Sundara rajan & R. Uthayakumar, 2017. "Comprehensive solution procedure for optimizing replenishment policies of instantaneous deteriorating items with stock-dependent demand under partial trade credit linked to order quantity," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1343-1373, November.
    5. 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.
    6. Toews, Carl & Pentico, David W. & Drake, Matthew J., 2011. "The deterministic EOQ and EPQ with partial backordering at a rate that is linearly dependent on the time to delivery," International Journal of Production Economics, Elsevier, vol. 131(2), pages 643-649, June.
    7. San-José, Luis A. & Sicilia, Joaquín & García-Laguna, Juan, 2014. "Optimal lot size for a production–inventory system with partial backlogging and mixture of dispatching policies," International Journal of Production Economics, Elsevier, vol. 155(C), pages 194-203.
    8. 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.
    9. Wee, Hui-Ming & Huang, Yen-Deng & Wang, Wan-Tsu & Cheng, Yung-Lung, 2014. "An EPQ model with partial backorders considering two backordering costs," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 898-907.
    10. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    11. Lodree, Emmett Jr., 2007. "Advanced supply chain planning with mixtures of backorders, lost sales, and lost contract," European Journal of Operational Research, Elsevier, vol. 181(1), pages 168-183, August.
    12. L. San-José & J. García-Laguna & J. Sicilia, 2009. "An economic order quantity model with partial backlogging under general backorder cost function," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 366-384, December.
    13. 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.
    14. Pando, Valentín & San-José, Luis A. & García-Laguna, Juan & Sicilia, Joaquín, 2013. "A newsboy problem with an emergency order under a general backorder rate function," Omega, Elsevier, vol. 41(6), pages 1020-1028.
    15. Manish Shukla & Sanjay Jharkharia, 2014. "An inventory model for continuously deteriorating agri-fresh produce: an artificial immune system-based solution approach," International Journal of Integrated Supply Management, Inderscience Enterprises Ltd, vol. 9(1/2), pages 110-135.
    16. Abad, Prakash L., 2008. "Optimal price and order size under partial backordering incorporating shortage, backorder and lost sale costs," International Journal of Production Economics, Elsevier, vol. 114(1), pages 179-186, July.
    17. Chih-Te Yang & Liang-Yuh Ouyang & Kun-Shan Wu & Hsiu-Feng Yen, 2011. "An optimal replenishment policy for deteriorating items with stock-dependent demand and relaxed terminal conditions under limited storage space," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(1), pages 139-153, March.
    18. Ali Salmasnia & Ali Talesh-Kazemi & Mohammad Reza Maleki, 2022. "Joint optimization of inventory planning, maintenance policy and pricing for perishable complementary products by considering the product freshness and technology level," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 49(4), pages 713-746, December.
    19. Sarkar, Biswajit & Sarkar, Sumon, 2013. "An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand," Economic Modelling, Elsevier, vol. 30(C), pages 924-932.
    20. Pentico, David W. & Drake, Matthew J. & Toews, Carl, 2011. "The EPQ with partial backordering and phase-dependent backordering rate," Omega, Elsevier, vol. 39(5), pages 574-577, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:214:y:2011:i:2:p:179-198. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.