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Single Cycle Continuous Review Policies for Arborescent Production/Inventory Systems

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  • Stephen C. Graves

    (The University of Rochester)

  • Leroy B. Schwarz

    (The University of Rochester)

Abstract

In this paper we examine optimal and near-optimal continuous review policies for a deterministic arborescent inventory system: Known and constant outside demand must be met without backlogging or lost sales at minimum average system cost per unit time. Costs are of two types: A fixed order cost at each stage and proportional holding costs on each stage's echelon inventory. We describe some characteristics of optimal policies and, under fairly mild conditions (e.g., zero initial inventory), prove that the optimal stationary policy is a "single-cycle" policy. We present an efficient branch-and-bound algorithm for determining optimal single-cycle policies for arborescent systems. We also examine the near-optimality of "system myopic" single-cycle policies.

Suggested Citation

  • Stephen C. Graves & Leroy B. Schwarz, 1977. "Single Cycle Continuous Review Policies for Arborescent Production/Inventory Systems," Management Science, INFORMS, vol. 23(5), pages 529-540, January.
    • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:5:p:529-540
    DOI: 10.1287/mnsc.23.5.529
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    Cited by:

    1. Chu, Chi-Leung & Leon, V. Jorge, 2008. "Power-of-two single-warehouse multi-buyer inventory coordination with private information," International Journal of Production Economics, Elsevier, vol. 111(2), pages 562-574, February.
    2. Karabati, Selcuk & Sayin, Serpil, 2008. "Single-supplier/multiple-buyer supply chain coordination: Incorporating buyers' expectations under vertical information sharing," European Journal of Operational Research, Elsevier, vol. 187(3), pages 746-764, June.
    3. Abdul-Jalbar, Beatriz & Gutierrez, Jose M. & Sicilia, Joaquin, 2007. "An integrated inventory model for the single-vendor two-buyer problem," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 246-258, July.
    4. Qinan Wang, 2001. "Coordinating Independent Buyers in a Distribution System to Increase a Vendor's Profits," Manufacturing & Service Operations Management, INFORMS, vol. 3(4), pages 337-348, May.
    5. Narendra Agrawal & Morris A. Cohen, 2001. "Optimal material control in an assembly system with component commonality," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 409-429, August.
    6. Godichaud, Matthieu & Amodeo, Lionel, 2018. "Economic order quantity for multistage disassembly systems," International Journal of Production Economics, Elsevier, vol. 199(C), pages 16-25.
    7. Abdul-Jalbar, Beatriz & Gutiérrez, Jose M. & Sicilia, Joaquín, 2006. "Single cycle policies for the one-warehouse N-retailer inventory/distribution system," Omega, Elsevier, vol. 34(2), pages 196-208, April.
    8. Yu Xia & Bintong Chen & Panos Kouvelis, 2008. "Market-Based Supply Chain Coordination by Matching Suppliers' Cost Structures with Buyers' Order Profiles," Management Science, INFORMS, vol. 54(11), pages 1861-1875, November.
    9. Hsiao, Yu-Cheng, 2008. "Optimal single-cycle policies for the one-warehouse multi-retailer inventory/distribution system," International Journal of Production Economics, Elsevier, vol. 114(1), pages 219-229, July.
    10. Graves, Stephen C., 1989. "A multi-echelon inventory model with fixed reorder intervals," Working papers 3045-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    11. Qinan Wang & Ruifang Wang, 2005. "Quantity discount pricing policies for heterogeneous retailers with price sensitive demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(7), pages 645-658, October.
    12. Abdul-Jalbar, B. & Gutierrez, J. & Sicilia, J., 2005. "Integer-ratio policies for distribution/inventory systems," International Journal of Production Economics, Elsevier, vol. 93(1), pages 407-415, January.
    13. Lee, Dong Joo & Jeong, In-Jae, 2010. "A distributed coordination for a single warehouse-multiple retailer problem under private information," International Journal of Production Economics, Elsevier, vol. 125(1), pages 190-199, May.
    14. Wang, Qinan & Chay, Yiowmin & Wu, Zhang, 2011. "Streamlining inventory flows with time discounts to improve the profits of a decentralized supply chain," International Journal of Production Economics, Elsevier, vol. 132(2), pages 230-239, August.
    15. Abdul-Jalbar, Beatriz & Gutiérrez, José M. & Sicilia, Joaquín, 2009. "A two-echelon inventory/distribution system with power demand pattern and backorders," International Journal of Production Economics, Elsevier, vol. 122(2), pages 519-524, December.
    16. Qinan Wang, 2004. "Coordinating independent buyers with integer‐ratio time coordination and quantity discounts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 316-331, April.
    17. Ian R. Webb & Bruce R. Buzby & Gerard M. Campbell, 1997. "Cyclical schedules for the joint replenishment problem with dynamic demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(6), pages 577-589, September.
    18. Jeong, In-Jae, 2011. "A dynamic model for the optimization of decoupling point and production planning in a supply chain," International Journal of Production Economics, Elsevier, vol. 131(2), pages 561-567, June.
    19. Abdul-Jalbar, B. & Gutierrez, J. & Puerto, J. & Sicilia, J., 2003. "Policies for inventory/distribution systems: The effect of centralization vs. decentralization," International Journal of Production Economics, Elsevier, vol. 81(1), pages 281-293, January.
    20. Kimms, Alf & Drexl, Andreas, 1996. "Multi-level lot sizing: A literature survey," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 405, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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