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Deterministic Inventory Lot Size Models--A General Root Law

Author

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  • Lineu C. Barbosa

    (IBM Research Laboratory, San Jose)

  • Moshe Friedman

    (IBM Research Laboratory, San Jose)

Abstract

The article presents a continuous time inventory model with known time varying demand. The relevant costs are the carrying and replenishment costs; backlogs are prohibited, replenishments are instantaneous, and the planning horizon is finite and known, The problem is to find the optimal schedule of replenishments, i.e., their number and the schedule of time intervals between consecutive orders. A complete solution is given for demand functions of the type b(t) = kt r , k > 0, r > -2, where t stands for time, and the asymptotic properties of the solution when the planning horizon tends to infinity are investigated. For r = 0 the solution reduces to the results obtained by Carr and Howe for the constant demand case with finite horizons, and to the classical "square root law" for infinite horizons. For r = 1 it yields the "cubic root law" given by Resh, Friedman, and Barbosa for time proportional demand rate. More generally, for r integer the solution can be expressed in an "(r + 2) root law."

Suggested Citation

  • Lineu C. Barbosa & Moshe Friedman, 1978. "Deterministic Inventory Lot Size Models--A General Root Law," Management Science, INFORMS, vol. 24(8), pages 819-826, April.
    • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:8:p:819-826
    DOI: 10.1287/mnsc.24.8.819
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    Cited by:

    1. Sicilia, Joaquín & González-De-la-Rosa, Manuel & Febles-Acosta, Jaime & Alcaide-López-de-Pablo, David, 2014. "Optimal policy for an inventory system with power demand, backlogged shortages and production rate proportional to demand rate," International Journal of Production Economics, Elsevier, vol. 155(C), pages 163-171.
    2. Hui‐Ling Yang & Jinn‐Tsair Teng & Maw‐Sheng Chern, 2001. "Deterministic inventory lot‐size models under inflation with shortages and deterioration for fluctuating demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(2), pages 144-158, March.
    3. 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.
    4. Hill, Roger M., 1996. "Batching policies for a product life cycle," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 421-427, August.
    5. Laurent Daudet & Frédéric Meunier, 2020. "Minimizing the waiting time for a one-way shuttle service," Journal of Scheduling, Springer, vol. 23(1), pages 95-115, February.
    6. Abbott, Harish & Palekar, Udatta S., 2008. "Retail replenishment models with display-space elastic demand," European Journal of Operational Research, Elsevier, vol. 186(2), pages 586-607, April.
    7. 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.
    8. Massonnet, G. & Gayon, J.-P. & Rapine, C., 2014. "Approximation algorithms for deterministic continuous-review inventory lot-sizing problems with time-varying demand," European Journal of Operational Research, Elsevier, vol. 234(3), pages 641-649.
    9. Urban, Timothy L. & Baker, R. C., 1997. "Optimal ordering and pricing policies in a single-period environment with multivariate demand and markdowns," European Journal of Operational Research, Elsevier, vol. 103(3), pages 573-583, December.
    10. Hong, Jae-Dong & Kim, Seung-Lae & Hayya, Jack C., 1996. "Dynamic setup reduction in production lot sizing with nonconstant deterministic demand," European Journal of Operational Research, Elsevier, vol. 90(1), pages 182-196, April.
    11. 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.
    12. Sarkar, Biswajit & Sarkar, Sumon, 2013. "Variable deterioration and demand—An inventory model," Economic Modelling, Elsevier, vol. 31(C), pages 548-556.
    13. Yang, Hui-Ling & Teng, Jinn-Tsair & Chern, Maw-Sheng, 2002. "A forward recursive algorithm for inventory lot-size models with power-form demand and shortages," European Journal of Operational Research, Elsevier, vol. 137(2), pages 394-400, March.
    14. Hill, Roger M., 1996. "Batching policies for linearly increasing demand with a finite input rate," International Journal of Production Economics, Elsevier, vol. 43(2-3), pages 149-154, June.
    15. David Yao & Morton Klein, 1989. "Lot sizes under continuous demand: The backorder case," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 615-624, October.

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