IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v155y2014icp194-203.html
   My bibliography  Save this article

Optimal lot size for a production–inventory system with partial backlogging and mixture of dispatching policies

Author

Listed:
  • San-José, Luis A.
  • Sicilia, Joaquín
  • García-Laguna, Juan

Abstract

In this paper we study a production–inventory model for a single product where shortages are partially backlogged. Both the backorder cost and the lost sale cost depend on a fixed cost and a cost proportional to the shortage time. We assume a mixture between the dispatching policies known as LIFO (last in, first out) and FIFO (first in, first out) in the discipline of service to fill the backlogged demand. By using a sequential optimization procedure, we determine in a closed-form the optimal production policies and the optimal profit for all the possible cases obtained from the developed model. We show how this new model generalizes several inventory models proposed in the literature. Finally, numerical results are presented to analyze the sensitivity of the optimal policies with respect to changes in some parameters of the system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:proeco:v:155:y:2014:i:c:p:194-203
    DOI: 10.1016/j.ijpe.2013.08.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527313003721
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijpe.2013.08.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Karimi-Nasab, M. & Konstantaras, I., 2013. "An inventory control model with stochastic review interval and special sale offer," European Journal of Operational Research, Elsevier, vol. 227(1), pages 81-87.
    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. 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.
    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. Jason Chang, S.K. & Chuang, Jones P.C. & Chen, Hsiao-Jung, 2005. "Short comments on technical note--The EOQ and EPQ models with shortages derived without derivatives," International Journal of Production Economics, Elsevier, vol. 97(2), pages 241-243, August.
    6. 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.
    7. 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.
    8. Ouyang, Liang-Yuh & Chang, Chun-Tao, 2013. "Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging," International Journal of Production Economics, Elsevier, vol. 144(2), pages 610-617.
    9. 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.
    10. Niu, Bo & Xie, Jinxing, 2008. "A note on "Two-warehouse inventory model with deterioration under FIFO dispatch policy"," European Journal of Operational Research, Elsevier, vol. 190(2), pages 571-577, October.
    11. Mahmut Parlar & David Perry & Wolfgang Stadje, 2011. "FIFO Versus LIFO Issuing Policies for Stochastic Perishable Inventory Systems," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 405-417, June.
    12. Cárdenas-Barrón, Leopoldo Eduardo, 2009. "Optimal ordering policies in response to a discount offer: Extensions," International Journal of Production Economics, Elsevier, vol. 122(2), pages 774-782, December.
    13. Ronald, Robert & Yang, Gino K. & Chu, Peter, 2004. "Technical note: The EOQ and EPQ models with shortages derived without derivatives," International Journal of Production Economics, Elsevier, vol. 92(2), pages 197-200, November.
    14. 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.
    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. Chang, Hung-Chi & Ho, Chia-Huei, 2010. "Exact closed-form solutions for "optimal inventory model for items with imperfect quality and shortage backordering"," Omega, Elsevier, vol. 38(3-4), pages 233-237, June.
    17. Minner, Stefan, 2007. "A note on how to compute economic order quantities without derivatives by cost comparisons," International Journal of Production Economics, Elsevier, vol. 105(1), pages 293-296, January.
    18. 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.
    19. 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.
    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.
    21. 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.
    22. Lee, Chun Chen, 2006. "Two-warehouse inventory model with deterioration under FIFO dispatching policy," European Journal of Operational Research, Elsevier, vol. 174(2), pages 861-873, October.
    23. 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.
    24. Hsieh, Tsu-Pang & Dye, Chung-Yuan, 2012. "A note on "The EPQ with partial backordering and phase-dependent backordering rate"," Omega, Elsevier, vol. 40(1), pages 131-133, January.
    25. Stojkovska, Irena, 2013. "On the optimality of the optimal policies for the deterministic EPQ with partial backordering," Omega, Elsevier, vol. 41(5), pages 919-923.
    26. 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.
    27. 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.
    28. 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.
    29. Wee, Hui-Ming & Wang, Wan-Tsu, 2012. "A supplement to the EPQ with partial backordering and phase-dependent backordering rate," Omega, Elsevier, vol. 40(3), pages 264-266.
    30. Cárdenas-Barrón, Leopoldo Eduardo, 2009. "Optimal ordering policies in response to a discount offer: Corrections," International Journal of Production Economics, Elsevier, vol. 122(2), pages 783-789, December.
    31. 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.
    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. Hadi Mokhtari & Mohammad Taghi Rezvan, 2020. "A single-supplier, multi-buyer, multi-product VMI production-inventory system under partial backordering," Operational Research, Springer, vol. 20(1), pages 37-57, March.
    2. 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.
    3. 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.

    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. 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.
    3. 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.
    4. Stojkovska, Irena, 2013. "On the optimality of the optimal policies for the deterministic EPQ with partial backordering," Omega, Elsevier, vol. 41(5), pages 919-923.
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Sphicas, Georghios P., 2014. "Generalized EOQ formula using a new parameter: Coefficient of backorder attractiveness," International Journal of Production Economics, Elsevier, vol. 155(C), pages 143-147.
    15. Teng, Jinn-Tsair & Min, Jie & Pan, Qinhua, 2012. "Economic order quantity model with trade credit financing for non-decreasing demand," Omega, Elsevier, vol. 40(3), pages 328-335.
    16. Hsieh, Tsu-Pang & Dye, Chung-Yuan, 2012. "A note on "The EPQ with partial backordering and phase-dependent backordering rate"," Omega, Elsevier, vol. 40(1), pages 131-133, January.
    17. Ata Allah Taleizadeh & Shayan Tavakoli & Luis Augusto San-José, 2018. "A lot sizing model with advance payment and planned backordering," Annals of Operations Research, Springer, vol. 271(2), pages 1001-1022, December.
    18. 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.
    19. Taleizadeh, Ata Allah & Khanbaglo, Mahboobeh Perak Sari & Cárdenas-Barrón, Leopoldo Eduardo, 2016. "An EOQ inventory model with partial backordering and reparation of imperfect products," International Journal of Production Economics, Elsevier, vol. 182(C), pages 418-434.
    20. Mohsen Lashgari & Ata Allah Taleizadeh & Abbas Ahmadi, 2016. "Partial up-stream advanced payment and partial down-stream delayed payment in a three-level supply chain," Annals of Operations Research, Springer, vol. 238(1), pages 329-354, March.

    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:155:y:2014:i:c:p:194-203. 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/ijpe .

    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.