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A Selection Problem of Shared Fixed Costs and Network Flows

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  • J. M. W. Rhys

    (Barclays Bank Limited, London, England)

Abstract

An apparently combinatorial problem is defined, and a method given for solution by reduction to a network flow problem. The basic problem defined is that of assessing the desirability of incurring a number of fixed costs, when the benefits to be obtained cannot be related to individual cost-incurring items (facilities) but only to combinations.

Suggested Citation

  • J. M. W. Rhys, 1970. "A Selection Problem of Shared Fixed Costs and Network Flows," Management Science, INFORMS, vol. 17(3), pages 200-207, November.
    • Handle: RePEc:inm:ormnsc:v:17:y:1970:i:3:p:200-207
    DOI: 10.1287/mnsc.17.3.200
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    Cited by:

    1. W. David Pisinger & Anders Bo Rasmussen & Rune Sandvik, 2007. "Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 280-290, May.
    2. Rolf H. Möhring & Andreas S. Schulz & Frederik Stork & Marc Uetz, 2003. "Solving Project Scheduling Problems by Minimum Cut Computations," Management Science, INFORMS, vol. 49(3), pages 330-350, March.
    3. Chunli Liu & Jianjun Gao, 2015. "A polynomial case of convex integer quadratic programming problems with box integer constraints," Journal of Global Optimization, Springer, vol. 62(4), pages 661-674, August.
    4. Gabriel Lopez Zenarosa & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2021. "On exact solution approaches for bilevel quadratic 0–1 knapsack problem," Annals of Operations Research, Springer, vol. 298(1), pages 555-572, March.
    5. Jesus Cunha & Luidi Simonetti & Abilio Lucena, 2016. "Lagrangian heuristics for the Quadratic Knapsack Problem," Computational Optimization and Applications, Springer, vol. 63(1), pages 97-120, January.
    6. Warren P. Adams & Julie Bowers Lassiter & Hanif D. Sherali, 1998. "Persistency in 0-1 Polynomial Programming," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 359-389, May.
    7. José R. Correa & Andreas S. Schulz, 2005. "Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1005-1021, November.
    8. Olszewski, Wojciech & Vohra, Rakesh, 2014. "Selecting a discrete portfolio," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 69-73.
    9. Dorit S. Hochbaum, 2004. "50th Anniversary Article: Selection, Provisioning, Shared Fixed Costs, Maximum Closure, and Implications on Algorithmic Methods Today," Management Science, INFORMS, vol. 50(6), pages 709-723, June.
    10. Alberto Caprara & David Pisinger & Paolo Toth, 1999. "Exact Solution of the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 125-137, May.
    11. Dorit S. Hochbaum & Anna Chen, 2000. "Performance Analysis and Best Implementations of Old and New Algorithms for the Open-Pit Mining Problem," Operations Research, INFORMS, vol. 48(6), pages 894-914, December.
    12. Arbib, Claudio & Servilio, Mara & Archetti, Claudia & Speranza, M. Grazia, 2014. "The directed profitable location Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 811-819.
    13. Britta Schulze & Michael Stiglmayr & Luís Paquete & Carlos M. Fonseca & David Willems & Stefan Ruzika, 2020. "On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 107-132, August.
    14. Sourour Elloumi & Amélie Lambert & Arnaud Lazare, 2021. "Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation," Journal of Global Optimization, Springer, vol. 80(2), pages 231-248, June.
    15. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    16. Queyranne, M. & Wolsey, L.A., 2015. "Modeling poset convex subsets," LIDAM Discussion Papers CORE 2015049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Ali Koç & David P. Morton, 2015. "Prioritization via Stochastic Optimization," Management Science, INFORMS, vol. 61(3), pages 586-603, March.
    18. Z. Y. Wu & Y. J. Yang & F. S. Bai & M. Mammadov, 2011. "Global Optimality Conditions and Optimization Methods for Quadratic Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 241-259, November.
    19. Renato de Matta & Vernon Ning Hsu & Timothy J. Lowe, 1999. "Capacitated selection problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(1), pages 19-37, February.
    20. Hans Kellerer & Vitaly A. Strusevich, 2016. "Optimizing the half-product and related quadratic Boolean functions: approximation and scheduling applications," Annals of Operations Research, Springer, vol. 240(1), pages 39-94, May.
    21. Julie Ward & Bin Zhang & Shailendra Jain & Chris Fry & Thomas Olavson & Holger Mishal & Jason Amaral & Dirk Beyer & Ann Brecht & Brian Cargille & Russ Chadinha & Kathy Chou & Gavin DeNyse & Qi Feng & , 2010. "HP Transforms Product Portfolio Management with Operations Research," Interfaces, INFORMS, vol. 40(1), pages 17-32, February.
    22. Hezhi Luo & Xiaodi Bai & Jiming Peng, 2019. "Enhancing Semidefinite Relaxation for Quadratically Constrained Quadratic Programming via Penalty Methods," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 964-992, March.

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