IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v10y2019i4d10.1007_s13198-019-00769-x.html
   My bibliography  Save this article

A two-echelon integrated inventory model under generalized lead time distribution with variable backordering rate

Author

Listed:
  • M. Ganesh Kumar

    (The Gandhigram Rural Institute (Deemed to be University))

  • R. Uthayakumar

    (The Gandhigram Rural Institute (Deemed to be University))

Abstract

This paper investigates a generalized lead time distribution with a variable backordering rate in a two-echelon supply chain system. The vendor produces a single product and delivers to the buyer in equal sized batches. The delivery lead time follows a generalized stochastic variable. Shortages are allowed to occur and backordered partially. The backorder rate depends on the demand on stock-out period. Based on this notion, we formulate a mixed integer non-linear cost function which needs to be minimized with respect to reorder point, number of deliveries and lot size from the vendor to the buyer, to operate cooperatively in the integrated model. Analytically we proved the convexity of the generalized lead time distribution cost function with respect to the control parameters. Further, the uniqueness of optimality has been proved. To validate the proposed model, uniform, exponential and normal distributed lead times are presented in numerical example section. Sensitivity analysis also performed to the values of the parameters.

Suggested Citation

  • M. Ganesh Kumar & R. Uthayakumar, 2019. "A two-echelon integrated inventory model under generalized lead time distribution with variable backordering rate," 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. 10(4), pages 552-562, August.
    • Handle: RePEc:spr:ijsaem:v:10:y:2019:i:4:d:10.1007_s13198-019-00769-x
    DOI: 10.1007/s13198-019-00769-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-019-00769-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13198-019-00769-x?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. Lee, W. & Wang, S.-P. & Chen, W.-C., 2017. "Forward and backward stocking policies for a two-level supply chain with consignment stock agreement and stock-dependent demand," European Journal of Operational Research, Elsevier, vol. 256(3), pages 830-840.
    2. Huang, Chao-Kuei, 2004. "An optimal policy for a single-vendor single-buyer integrated production-inventory problem with process unreliability consideration," International Journal of Production Economics, Elsevier, vol. 91(1), pages 91-98, September.
    3. Sajadieh, Mohsen S. & Thorstenson, Anders & Jokar, Mohammad R. Akbari, 2010. "An integrated vendor-buyer model with stock-dependent demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(6), pages 963-974, November.
    4. Ouyang, Liang-Yuh & Wu, Kun-Shan & Ho, Chia-Huei, 2007. "An integrated vendor-buyer inventory model with quality improvement and lead time reduction," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 349-358, July.
    5. Hossain, Md Shahriar J. & Ohaiba, Mohamed M. & Sarker, Bhaba R., 2017. "An optimal vendor-buyer cooperative policy under generalized lead-time distribution with penalty cost for delivery lateness," International Journal of Production Economics, Elsevier, vol. 188(C), pages 50-62.
    6. He, Xin James & Kim, Jeon G. & Hayya, Jack C., 2005. "The cost of lead-time variability: The case of the exponential distribution," International Journal of Production Economics, Elsevier, vol. 97(2), pages 130-142, August.
    7. Hoque, M.A., 2013. "A vendor–buyer integrated production–inventory model with normal distribution of lead time," International Journal of Production Economics, Elsevier, vol. 144(2), pages 409-417.
    8. Fujiwara, Okitsugu & Sedarage, Dayani, 1997. "An optimal (Q,r) policy for a multipart assembly system under stochastic part procurement lead times," European Journal of Operational Research, Elsevier, vol. 100(3), pages 550-556, August.
    9. Georghios P. Sphicas & Farrokh Nasri, 1984. "An inventory model with finite‐range stochastic lead times," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(4), pages 609-616, December.
    10. Ivan Darma Wangsa & Hui Ming Wee, 2017. "Impact of lead time reduction and fuel consumption on a two-echelon supply chain inventory with a subsidised price and pick-up policy," International Journal of Integrated Supply Management, Inderscience Enterprises Ltd, vol. 11(2/3), pages 264-289.
    11. Matthew J. Liberatore, 1977. "Planning Horizons for a Stochastic Lead-Time Inventory Model," Operations Research, INFORMS, vol. 25(6), pages 977-988, December.
    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. Sudip Adak & G. S. Mahapatra, 2021. "Effect of inspection and rework of probabilistic defective production on two-layer supply chain incorporating deterioration and reliability dependent demand," 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. 12(3), pages 565-578, June.
    2. Dipak Barman & Gour Chandra Mahata, 2022. "Two-echelon production inventory model with imperfect quality items with ordering cost reduction depending on controllable lead time," 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. 13(5), pages 2656-2671, October.
    3. Mandeep Mittal & Mahesh Kumar Jayaswal & Vijay Kumar, 2022. "Effect of learning on the optimal ordering policy of inventory model for deteriorating items with shortages and trade-credit financing," 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. 13(2), pages 914-924, June.

    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. Rabin Kumar Mallick & Kartik Patra & Shyamal Kumar Mondal, 2020. "Mixture inventory model of lost sale and back-order with stochastic lead time demand on permissible delay in payments," Annals of Operations Research, Springer, vol. 292(1), pages 341-369, September.
    2. Sumon Sarkar & Sunil Tiwari & B. C. Giri, 2022. "Impact of uncertain demand and lead-time reduction on two-echelon supply chain," Annals of Operations Research, Springer, vol. 315(2), pages 2027-2055, August.
    3. Glock, Christoph H., 2012. "The joint economic lot size problem: A review," International Journal of Production Economics, Elsevier, vol. 135(2), pages 671-686.
    4. Oshmita Dey, 2019. "A fuzzy random integrated inventory model with imperfect production under optimal vendor investment," Operational Research, Springer, vol. 19(1), pages 101-115, March.
    5. Hesham K. Alfares & Ahmed M. Attia, 2017. "A supply chain model with vendor-managed inventory, consignment, and quality inspection errors," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5706-5727, October.
    6. Anuraag Gutgutia & J. K. Jha, 2018. "A closed-form solution for the distribution free continuous review integrated inventory model," Operational Research, Springer, vol. 18(1), pages 159-186, April.
    7. Jing-Sheng Song & Candace A. Yano & Panupol Lerssrisuriya, 2000. "Contract Assembly: Dealing with Combined Supply Lead Time and Demand Quantity Uncertainty," Manufacturing & Service Operations Management, INFORMS, vol. 2(3), pages 287-296, July.
    8. S. Sarkar & B. C. Giri, 2020. "A vendor–buyer integrated inventory system with variable lead time and uncertain market demand," Operational Research, Springer, vol. 20(1), pages 491-515, March.
    9. Dey, O. & Giri, B.C., 2014. "Optimal vendor investment for reducing defect rate in a vendor–buyer integrated system with imperfect production process," International Journal of Production Economics, Elsevier, vol. 155(C), pages 222-228.
    10. M. Ganesh Kumar & R. Uthayakumar, 2017. "An integrated single vendor–buyer inventory model for imperfect production process with stochastic demand in controllable lead time," 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 1041-1054, November.
    11. Sajadieh, Mohsen S. & Larsen, Christian, 2015. "A coordinated manufacturer-retailer model under stochastic demand and production rate," International Journal of Production Economics, Elsevier, vol. 168(C), pages 64-70.
    12. Lee, Sunghee & Kim, Daeki, 2014. "An optimal policy for a single-vendor single-buyer integrated production–distribution model with both deteriorating and defective items," International Journal of Production Economics, Elsevier, vol. 147(PA), pages 161-170.
    13. M. A. Hoque, 2021. "An optimal solution policy to an integrated manufacturer-retailers problem with normal distribution of lead times of delivering equal and unequal-sized batches," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 483-512, June.
    14. Thomas Wensing & Heinrich Kuhn, 2015. "Analysis of production and inventory systems when orders may cross over," Annals of Operations Research, Springer, vol. 231(1), pages 265-281, August.
    15. M. Vijayashree & R. Uthayakumar, 2016. "Two-echelon supply chain inventory model with controllable lead time," 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. 7(1), pages 112-125, December.
    16. Babai, M. Zied & Dai, Yong & Li, Qinyun & Syntetos, Aris & Wang, Xun, 2022. "Forecasting of lead-time demand variance: Implications for safety stock calculations," European Journal of Operational Research, Elsevier, vol. 296(3), pages 846-861.
    17. Sana, Shib Sankar, 2012. "A collaborating inventory model in a supply chain," Economic Modelling, Elsevier, vol. 29(5), pages 2016-2023.
    18. Sajadieh, Mohsen S. & Fallahnezhad, Mohammad Saber & Khosravi, Maryam, 2013. "A joint optimal policy for a multiple-suppliers multiple-manufacturers multiple-retailers system," International Journal of Production Economics, Elsevier, vol. 146(2), pages 738-744.
    19. Z X Chen & B R Sarker, 2010. "Multi-vendor integrated procurement-production system under shared transportation and just-in-time delivery system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1654-1666, November.
    20. Ben-Ammar, Oussama & Bettayeb, Belgacem & Dolgui, Alexandre, 2019. "Optimization of multi-period supply planning under stochastic lead times and a dynamic demand," International Journal of Production Economics, Elsevier, vol. 218(C), pages 106-117.

    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:spr:ijsaem:v:10:y:2019:i:4:d:10.1007_s13198-019-00769-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.