IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v42y1995i5p839-859.html
   My bibliography  Save this article

An (s, q) inventory model with stochastic and interrelated lead times

Author

Listed:
  • Ruud Heuts
  • Jan de Klein

Abstract

In this article we introduce a lead time mechanism that allows simultaneous order arrivals. This mechanism ensures that orders never cross each other. For the continuous review (s, q) inventory system with constant demand, we show that the allowance of batch arrivals gives rise to a discontinuous cost function. By exploiting the special structure of this cost function, a search algorithm is derived that yields the optimal order strategy in a reasonable amount of time. The search is restricted to integer order strategies only. We also consider an approximate method of solution that is based on a related model with a continuous cost function. The results obtained by this approximation are, in general, very satisfactory. © 1995 John Wiley & Sons, Inc.

Suggested Citation

  • Ruud Heuts & Jan de Klein, 1995. "An (s, q) inventory model with stochastic and interrelated lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 839-859, August.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:5:p:839-859
    DOI: 10.1002/1520-6750(199508)42:53.0.CO;2-8
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199508)42:53.0.CO;2-8
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199508)42:53.0.CO;2-8?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
    ---><---

    References listed on IDEAS

    as
    1. Awi Federgruen & Yu-Sheng Zheng, 1992. "An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems," Operations Research, INFORMS, vol. 40(4), pages 808-813, August.
    2. Donald Gross & A. Soriano, 1969. "The Effect of Reducing Leadtime on Inventory Levels-Simulation Analysis," Management Science, INFORMS, vol. 16(2), pages 61-76, October.
    3. Yu‐Sheng Zheng & Fangruo Chen, 1992. "Inventory policies with quantized ordering," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 285-305, April.
    4. 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.
    5. Paul Zipkin, 1986. "Stochastic leadtimes in continuous‐time inventory models," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 763-774, November.
    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. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "On the (R,s,Q) Inventory Model when Demand is Modelled as a Compound Process," Discussion Paper 1996-11, Tilburg University, Center for Economic Research.
    2. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "On the (R,s,Q) Inventory Model when Demand is Modelled as a Compound Process," Other publications TiSEM 95c56aed-8108-4122-a689-5, Tilburg University, School of Economics and Management.
    3. Jeon G. Kim & Daewon Sun & Xin James He & Jack C. Hayya, 2004. "The (s, Q) inventory model with Erlang lead time and deterministic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 906-923, September.
    4. Ya Ping Fang & Kaiwen Meng & Xiao Qi Yang, 2012. "Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization," Operations Research, INFORMS, vol. 60(2), pages 398-409, April.

    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. Tamer Boyacı & Guillermo Gallego, 2002. "Managing waiting times of backordered demands in single‐stage (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 557-573, September.
    2. Marcus Ang & Karl Sigman & Jing-Sheng Song & Hanqin Zhang, 2017. "Closed-Form Approximations for Optimal ( r , q ) and ( S , T ) Policies in a Parallel Processing Environment," Operations Research, INFORMS, vol. 65(5), pages 1414-1428, October.
    3. Vipul Agrawal & Sridhar Seshadri, 2000. "Distribution free bounds for service constrained (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 635-656, December.
    4. Achin Srivastav & Sunil Agrawal, 2020. "On a single item single stage mixture inventory models with independent stochastic lead times," Operational Research, Springer, vol. 20(4), pages 2189-2227, December.
    5. 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.
    6. 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.
    7. Tamjidzad, Shahrzad & Mirmohammadi, S. Hamid, 2015. "An optimal (r, Q) policy in a stochastic inventory system with all-units quantity discount and limited sharable resource," European Journal of Operational Research, Elsevier, vol. 247(1), pages 93-100.
    8. Stanislaw Bylka, 1997. "Strong turnpike policies in the single‐item capacitated lot‐sizing problem with periodical dynamic parameter," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(8), pages 775-790, December.
    9. Chaharsooghi, S. Kamal & Heydari, Jafar, 2010. "Supply chain coordination for the joint determination of order quantity and reorder point using credit option," European Journal of Operational Research, Elsevier, vol. 204(1), pages 86-95, July.
    10. Cigdem Gurgur, 2013. "Optimal configuration of a decentralized, market-driven production/inventory system," Annals of Operations Research, Springer, vol. 209(1), pages 139-157, October.
    11. Johansen, Søren Glud & Thorstenson, Anders, 2014. "Emergency orders in the periodic-review inventory system with fixed ordering costs and compound Poisson demand," International Journal of Production Economics, Elsevier, vol. 157(C), pages 147-157.
    12. Chen, Youhua Frank, 2005. "Fractional programming approach to two stochastic inventory problems," European Journal of Operational Research, Elsevier, vol. 160(1), pages 63-71, January.
    13. Daniela Favaretto & Alessandro Marin & Marco Tolotti, 2023. "A theoretical validation of the DDMRP reorder policy," Computational Management Science, Springer, vol. 20(1), pages 1-28, December.
    14. Riezebos, Jan & Zhu, Stuart X., 2020. "Inventory control with seasonality of lead times," Omega, Elsevier, vol. 92(C).
    15. Johansen, Soren Glud & Thorstenson, Anders, 1998. "An inventory model with Poisson demands and emergency orders," International Journal of Production Economics, Elsevier, vol. 56(1), pages 275-289, September.
    16. Johansen, Soren Glud & Thorstenson, Anders, 1996. "Optimal (r, Q) inventory policies with Poisson demands and lost sales: discounted and undiscounted cases," International Journal of Production Economics, Elsevier, vol. 46(1), pages 359-371, December.
    17. Frank Chen & Tong Wang & Tommy Xu, 2005. "Integrated Inventory Replenishment and Temporal Shipment Consolidation: A Comparison of Quantity-Based and Time-Based Models," Annals of Operations Research, Springer, vol. 135(1), pages 197-210, March.
    18. Johansen, Søren Glud, 2021. "The Markov model for base-stock control of an inventory system with Poisson demand, non-crossing lead times and lost sales," International Journal of Production Economics, Elsevier, vol. 231(C).
    19. Duran, Alfonso & Gutierrez, Gil & Zequeira, Romulo I., 2004. "A continuous review inventory model with order expediting," International Journal of Production Economics, Elsevier, vol. 87(2), pages 157-169, January.
    20. Strijbosch, L.W.G. & Heuts, R.M.J. & van der Schoot, E.H.M., 1998. "Improved Spare Parts Inventory Management : A Case Study," Other publications TiSEM 1594cf21-723c-4899-907b-2, Tilburg University, School of Economics and Management.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:42:y:1995:i:5:p:839-859. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.