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Structured Partitioning Problems

Author

Listed:
  • S. Anily

    (University of British Columbia, Vancouver, Canada, and Tel Aviv University, Tel Aviv, Israel)

  • A. Federgruen

    (Columbia University, New York, New York)

Abstract

In many important combinatorial optimization problems, such as bin packing, allocating customer classes to queueing facilities, vehicle routing, multi-item inventory replenishment and combined routing/inventory control, an optimal partition into groups needs to be determined for a finite collection of objects; each is characterized by a single attribute. The cost is often separable in the groups and the group cost often depends on the cardinality and some aggregate measure of the attributes, such as the sum or the maximum element. An upper bound ( capacity ) may be specified for the cardinality of each group and the number of groups in the partition may either be fixed or variable. The objects are indexed in nondecreasing order of their attribute values and within a given partition the groups are indexed in nondecreasing order of their cardinalities. We identify easily verifiable analytical properties of the group cost function under which it is shown that an optimal partition exists of one of three increasingly special structures, thus allowing for increasingly simple solution methods. We give examples of all the above listed types of planning problems, and apply our results for the identification of efficient solution methods (wherever possible).

Suggested Citation

  • S. Anily & A. Federgruen, 1991. "Structured Partitioning Problems," Operations Research, INFORMS, vol. 39(1), pages 130-149, February.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:1:p:130-149
    DOI: 10.1287/opre.39.1.130
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    Citations

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    Cited by:

    1. 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.
    2. Roy Cerqueti & Paolo Falbo & Cristian Pelizzari & Federica Ricca & Andrea Scozzari, 2012. "A Mixed Integer Linear Programming Approach to Markov Chain Bootstrapping," Working Papers 67-2012, Macerata University, Department of Finance and Economic Sciences, revised Nov 2012.
    3. Kumar Satyendra & Venkata Rao, V. & Tirupati Devanath, 2003. "A heuristic procedure for one dimensional bin packing problem with additional constraints," IIMA Working Papers WP2003-11-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    4. N H Moin & S Salhi, 2007. "Inventory routing problems: a logistical overview," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(9), pages 1185-1194, September.
    5. Cerqueti, Roy & Falbo, Paolo & Guastaroba, Gianfranco & Pelizzari, Cristian, 2013. "A Tabu Search heuristic procedure in Markov chain bootstrapping," European Journal of Operational Research, Elsevier, vol. 227(2), pages 367-384.
    6. Baita, Flavio & Ukovich, Walter & Pesenti, Raffaele & Favaretto, Daniela, 1998. "Dynamic routing-and-inventory problems: a review," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(8), pages 585-598, November.
    7. 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.
    8. Inniss, Tasha R., 2006. "Seasonal clustering technique for time series data," European Journal of Operational Research, Elsevier, vol. 175(1), pages 376-384, November.
    9. Gerard J. Chang & Fu-Loong Chen & Lingling Huang & Frank K. Hwang & Su-Tzu Nuan & Uriel G. Rothblum & I-Fan Sun & Jan-Wen Wang & Hong-Gwa Yeh, 1998. "Sortabilities of Partition Properties," Journal of Combinatorial Optimization, Springer, vol. 2(4), pages 413-427, December.

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