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Technical Note—A Partitioning Problem with Additive Objective with an Application to Optimal Inventory Groupings for Joint Replenishment

Author

Listed:
  • A. K. Chakravarty

    (Washington State University, Pullman, Washington)

  • J. B. Orlin

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • U. G. Rothblum

    (Yale University, New Haven, Connecticut)

Abstract

We consider a problem of optimal grouping and provide conditions under which an optimal partition of an ordered set S = { r 1 , …, r n } consists of subsets of consecutive elements. We transform the problem into the problem of finding a shortest path on a directed acyclic graph with n + 1 vertices (for which efficient algorithms exist). These results may be used to solve the problem of grouping n items in stock into subgroups with a common order cycle per group so as to minimize the resulting economic order quantity costs.

Suggested Citation

  • A. K. Chakravarty & J. B. Orlin & U. G. Rothblum, 1982. "Technical Note—A Partitioning Problem with Additive Objective with an Application to Optimal Inventory Groupings for Joint Replenishment," Operations Research, INFORMS, vol. 30(5), pages 1018-1022, October.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:5:p:1018-1022
    DOI: 10.1287/opre.30.5.1018
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    Citations

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    Cited by:

    1. Ho, Sin C. & Szeto, W.Y. & Kuo, Yong-Hong & Leung, Janny M.Y. & Petering, Matthew & Tou, Terence W.H., 2018. "A survey of dial-a-ride problems: Literature review and recent developments," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 395-421.
    2. Sheikh-Zadeh, Alireza & Rossetti, Manuel D. & Scott, Marc A., 2021. "Performance-based inventory classification methods for large-Scale multi-echelon replenishment systems," Omega, Elsevier, vol. 101(C).
    3. Hrayer Aprahamian & Douglas R. Bish & Ebru K. Bish, 2019. "Optimal Risk-Based Group Testing," Management Science, INFORMS, vol. 65(9), pages 4365-4384, September.
    4. Hussein El Hajj & Douglas R. Bish & Ebru K. Bish & Denise M. Kay, 2022. "Novel Pooling Strategies for Genetic Testing, with Application to Newborn Screening," Management Science, INFORMS, vol. 68(11), pages 7994-8014, November.
    5. Siddhartha Syam & Bala Shetty, 1998. "Coordinated replenishments from multiple suppliers with price discounts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(6), pages 579-598, September.
    6. Huilan Chang & Frank K. Hwang & Uriel G. Rothblum, 2012. "A new approach to solve open-partition problems," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 61-78, January.
    7. Joseph, Anito & Bryson, Noel, 1998. "Parametric linear programming and cluster analysis," European Journal of Operational Research, Elsevier, vol. 111(3), pages 582-588, December.
    8. Hrayer Aprahamian & Hadi El-Amine, 2022. "Optimal Screening of Populations with Heterogeneous Risk Profiles Under the Availability of Multiple Tests," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 150-164, January.
    9. Wildeman, R. E. & Dekker, R. & Smit, A. C. J. M., 1997. "A dynamic policy for grouping maintenance activities," European Journal of Operational Research, Elsevier, vol. 99(3), pages 530-551, June.
    10. Chung‐Lun Li & Zhi‐Long Chen, 2006. "Bin‐packing problem with concave costs of bin utilization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 298-308, June.
    11. Langenberg, Kerstin U. & Seifert, Ralf W. & Tancrez, Jean-Sébastien, 2012. "Aligning supply chain portfolios with product portfolios," International Journal of Production Economics, Elsevier, vol. 135(1), pages 500-513.
    12. Yaakov Malinovsky, 2019. "Sterrett Procedure for the Generalized Group Testing Problem," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 829-840, September.
    13. Ogawa, Sanae & Ohta, Hiroshi, 1995. "Common order cycle system for multi-item inventory model with learning in ordering and transportation," International Journal of Production Economics, Elsevier, vol. 41(1-3), pages 321-325, October.
    14. Frank K. Hwang & Uriel G. Rothblum, 2011. "On the number of separable partitions," Journal of Combinatorial Optimization, Springer, vol. 21(4), pages 423-433, May.

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