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The Greedy Procedure for Resource Allocation Problems: Necessary and Sufficient Conditions for Optimality

Author

Listed:
  • Awi Federgruen

    (Columbia University, New York, New York)

  • Henri Groenevelt

    (University of Rochester, Rochester, New York)

Abstract

In many resource allocation problems, the objective is to allocate discrete resource units to a set of activities so as to maximize a concave objective function subject to upper bounds on the total amounts allotted to certain groups of activities. If the constraints determine a polymatroid and the objective is linear, it is well known that the greedy procedure results in an optimal solution. In this paper we extend this result to objectives that are “weakly concave,” a property generalizing separable concavity. We exhibit large classes of models for which the set of feasible solutions is a polymatroid and for which efficient implementations of the greedy procedure can be given.

Suggested Citation

  • Awi Federgruen & Henri Groenevelt, 1986. "The Greedy Procedure for Resource Allocation Problems: Necessary and Sufficient Conditions for Optimality," Operations Research, INFORMS, vol. 34(6), pages 909-918, December.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:6:p:909-918
    DOI: 10.1287/opre.34.6.909
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    Cited by:

    1. Pinto, Roberto, 2016. "Stock rationing under a profit satisficing objective," Omega, Elsevier, vol. 65(C), pages 55-68.
    2. Jan A. Van Mieghem & Nils Rudi, 2002. "Newsvendor Networks: Inventory Management and Capacity Investment with Discretionary Activities," Manufacturing & Service Operations Management, INFORMS, vol. 4(4), pages 313-335, August.
    3. Simai He & Jiawei Zhang & Shuzhong Zhang, 2012. "Polymatroid Optimization, Submodularity, and Joint Replenishment Games," Operations Research, INFORMS, vol. 60(1), pages 128-137, February.
    4. Aksin, O. Zeynep & Harker, Patrick T., 2003. "Capacity sizing in the presence of a common shared resource: Dimensioning an inbound call center," European Journal of Operational Research, Elsevier, vol. 147(3), pages 464-483, June.
    5. Rohit Patel & Can Urgun, 2021. "Costly Inspection and Money Burning in Internal Capital Markets," Working Papers 2021-29, Princeton University. Economics Department..
    6. Dorit Hochbaum, 2007. "Complexity and algorithms for nonlinear optimization problems," Annals of Operations Research, Springer, vol. 153(1), pages 257-296, September.
    7. Niederhoff, Julie A., 2007. "Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions," European Journal of Operational Research, Elsevier, vol. 176(2), pages 941-955, January.
    8. Aleksandar Pekeč, 1997. "Optimization under ordinal scales: When is a greedy solution optimal?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 229-239, June.
    9. Harris, Shannon L. & May, Jerrold H. & Vargas, Luis G. & Foster, Krista M., 2020. "The effect of cancelled appointments on outpatient clinic operations," European Journal of Operational Research, Elsevier, vol. 284(3), pages 847-860.
    10. Awi Federgruen & C. Daniel Guetta & Garud Iyengar, 2018. "Two‐echelon distribution systems with random demands and storage constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 594-618, December.
    11. S. Viswanathan, 2007. "An Algorithm for Determining the Best Lower Bound for the Stochastic Joint Replenishment Problem," Operations Research, INFORMS, vol. 55(5), pages 992-996, October.
    12. Hyun-soo Ahn & Mehmet Gümüş & Philip Kaminsky, 2007. "Pricing and Manufacturing Decisions When Demand Is a Function of Prices in Multiple Periods," Operations Research, INFORMS, vol. 55(6), pages 1039-1057, December.
    13. Awi Federgruen & Nan Yang, 2008. "Selecting a Portfolio of Suppliers Under Demand and Supply Risks," Operations Research, INFORMS, vol. 56(4), pages 916-936, August.
    14. Renato de Matta & Vernon Ning Hsu & Timothy J. Lowe, 1999. "The selection allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 707-725, September.

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