IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v162y2015icp151-159.html
   My bibliography  Save this article

Approximating the EOQ with partial backordering at an exponential or rational rate by a constant or linearly changing rate

Author

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

Abstract

A significant extension of the classic EOQ model is the assumption that realized demand decreases if customers are forced to backorder. To capture the way this decrease depends on the waiting time, different functional forms have been proposed, ranging from the simple (e.g., constant or linear forms) to the complex (e.g., exponential or rational forms.) This paper explores the question of whether the computationally more tractable simple forms can give high quality approximations to the complex ones. We calculated average and worst case performance on a representative suite of test problems, each characterized by a “backorder resistance” parameter. We show that for low values of this parameter, results from the approximating functions are virtually as good as those from the correct ones, and for high values of the parameter, very good results can be achieved by using an iterative technique.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:proeco:v:162:y:2015:i:c:p:151-159
    DOI: 10.1016/j.ijpe.2015.01.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527315000262
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Yang, Hui-Ling, 2012. "Two-warehouse partial backlogging inventory models with three-parameter Weibull distribution deterioration under inflation," International Journal of Production Economics, Elsevier, vol. 138(1), pages 107-116.
    8. Maihami, Reza & Nakhai Kamalabadi, Isa, 2012. "Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand," International Journal of Production Economics, Elsevier, vol. 136(1), pages 116-122.
    9. 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.
    10. 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.
    11. 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.
    12. Taleizadeh, Ata Allah & Pentico, David W. & Saeed Jabalameli, Mohammad & Aryanezhad, Mirbahador, 2013. "An EOQ model with partial delayed payment and partial backordering," Omega, Elsevier, vol. 41(2), pages 354-368.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. David W. Pentico & Carl Toews & Matthew J. Drake, 2014. "Two Heuristics for the Basic EOQ and EPQ with Partial Backordering," International Journal of Information Systems and Supply Chain Management (IJISSCM), IGI Global, vol. 7(4), pages 31-49, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. K. Skouri, 2018. "An EOQ model with backlog-dependent demand," Operational Research, Springer, vol. 18(2), pages 561-574, July.
    2. 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).
    3. Jianghua Zhang & Felix T. S. Chan & Xinsheng Xu, 0. "The optimal order decisions of a risk-averse newsvendor under backlogging," Annals of Operations Research, Springer, vol. 0, pages 1-23.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Ghiami, Yousef & Beullens, Patrick, 2016. "Planning for shortages? Net Present Value analysis for a deteriorating item with partial backlogging," International Journal of Production Economics, Elsevier, vol. 178(C), pages 1-11.
    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. 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.
    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. M. Palanivel & R. Uthayakumar, 2016. "Two-warehouse inventory model for non-instantaneous deteriorating items with partial backlogging and inflation over a finite time horizon," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 278-302, June.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Ata Allah Taleizadeh & Sara Tavassoli & Arijit Bhattacharya, 2020. "Inventory ordering policies for mixed sale of products under inspection policy, multiple prepayment, partial trade credit, payments linked to order quantity and full backordering," Annals of Operations Research, Springer, vol. 287(1), pages 403-437, April.
    18. A.K. Bhunia & A.A. Shaikh & R.K. Gupta, 2015. "A study on two-warehouse partially backlogged deteriorating inventory models under inflation via particle swarm optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(6), pages 1036-1050, April.
    19. Wang, Kung-Jeng & Lin, Y.S. & Yu, Jonas C.P., 2011. "Optimizing inventory policy for products with time-sensitive deteriorating rates in a multi-echelon supply chain," International Journal of Production Economics, Elsevier, vol. 130(1), pages 66-76, March.
    20. 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.

    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:proeco:v:162:y:2015:i:c:p:151-159. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Nithya Sathishkumar). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.