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On a Basic Class of Multi-Item Inventory Problems

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  • Joseph L. Balintfy

    (Tulane University, New Orleans, Louisiana)

Abstract

The paper evaluates and compares classes of multi-item inventory problems, where joint order of several items may save a part of the setup cost. A cost ratio and simple decision rule are determined for joint versus individual orders in specified cases. The comparisons call for the necessity of a new policy for reorder point-triggered random output multi-item systems. This policy, the "random joint order policy," operates through the determination of a reorder range within which several items can be ordered. The existence of an optimum reorder range is proved, and a computational technique is demonstrated with the help of a machine-interference type queueing model. Under favorable conditions the results exhibited on the diagram of optimum reorder ranges are generally applicable. The random joint order policy model is especially suitable for computer controlled inventory systems.

Suggested Citation

  • Joseph L. Balintfy, 1964. "On a Basic Class of Multi-Item Inventory Problems," Management Science, INFORMS, vol. 10(2), pages 287-297, January.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:2:p:287-297
    DOI: 10.1287/mnsc.10.2.287
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    Citations

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    Cited by:

    1. Dellaert, Nico & van de Poel, Erik, 1996. "Global inventory control in an academic hospital," International Journal of Production Economics, Elsevier, vol. 46(1), pages 277-284, December.
    2. Shi, Ye & Yu, Yugang & Dong, Yuxuan, 2021. "Warehousing platform’s revenue management: A dynamic model of coordinating space allocation for self-use and rent," European Journal of Operational Research, Elsevier, vol. 293(1), pages 167-176.
    3. Eynan, Amit & Kropp, Dean H., 2007. "Effective and simple EOQ-like solutions for stochastic demand periodic review systems," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1135-1143, August.
    4. Kiesmüller, G.P., 2009. "A multi-item periodic replenishment policy with full truckloads," International Journal of Production Economics, Elsevier, vol. 118(1), pages 275-281, March.
    5. Park, Hyungjun & Choi, Dong Gu & Min, Daiki, 2023. "Adaptive inventory replenishment using structured reinforcement learning by exploiting a policy structure," International Journal of Production Economics, Elsevier, vol. 266(C).
    6. Padilla Tinoco, Silvia Valeria & Creemers, Stefan & Boute, Robert N., 2017. "Collaborative shipping under different cost-sharing agreements," European Journal of Operational Research, Elsevier, vol. 263(3), pages 827-837.
    7. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2016. "A coordinated multi-item inventory system for perishables with random lifetime," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 226-237.
    8. Tsai, Chieh-Yuan & Tsai, Chi-Yang & Huang, Po-Wen, 2009. "An association clustering algorithm for can-order policies in the joint replenishment problem," International Journal of Production Economics, Elsevier, vol. 117(1), pages 30-41, January.
    9. Lee, Loo Hay & Chew, Ek Peng, 2005. "A dynamic joint replenishment policy with auto-correlated demand," European Journal of Operational Research, Elsevier, vol. 165(3), pages 729-747, September.
    10. De Moor, Bram J. & Creemers, Stefan & Boute, Robert N., 2023. "Breaking truck dominance in supply chains: Proactive freight consolidation and modal split transport," International Journal of Production Economics, Elsevier, vol. 257(C).
    11. Kiesmüller, G.P., 2010. "Multi-item inventory control with full truckloads: A comparison of aggregate and individual order triggering," European Journal of Operational Research, Elsevier, vol. 200(1), pages 54-62, January.
    12. Rosales, Claudia R. & Magazine, Michael & Rao, Uday, 2015. "The 2Bin system for controlling medical supplies at point-of-use," European Journal of Operational Research, Elsevier, vol. 243(1), pages 271-280.
    13. Creemers, Stefan & Boute, Robert, 2022. "The joint replenishment problem: Optimal policy and exact evaluation method," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1175-1188.
    14. Larsen, Christian, 2019. "A heuristic joint replinishment policy for the case of heterogeneity among items," International Journal of Production Economics, Elsevier, vol. 209(C), pages 164-171.
    15. Larsen, Christian, 2009. "The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands," International Journal of Production Economics, Elsevier, vol. 118(1), pages 292-297, March.
    16. Nielsen, Christina & Larsen, Christian, 2005. "An analytical study of the Q(s,S) policy applied to the joint replenishment problem," European Journal of Operational Research, Elsevier, vol. 163(3), pages 721-732, June.

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