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Dynamic programming approaches to the multiple criteria knapsack problem

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  • Kathrin Klamroth
  • Margaret M. Wiecek

Abstract

We study the integer multiple criteria knapsack problem and propose dynamic‐programming‐based approaches to finding all the nondominated solutions. Different and more complex models are discussed, including the binary multiple criteria knapsack problem, problems with more than one constraint, and multiperiod as well as time‐dependent models. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 57–76, 2000

Suggested Citation

  • Kathrin Klamroth & Margaret M. Wiecek, 2000. "Dynamic programming approaches to the multiple criteria knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(1), pages 57-76, February.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:1:p:57-76
    DOI: 10.1002/(SICI)1520-6750(200002)47:13.0.CO;2-4
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    References listed on IDEAS

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    1. Kwak, Wikil & Shi, Yong & Lee, Heeseok & Lee, Cheng F., 1996. "Capital Budgeting with Multiple Criteria and Multiple Decision Makers," Review of Quantitative Finance and Accounting, Springer, vol. 7(1), pages 97-112, July.
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    3. Klein, Dieter & Hannan, Edward, 1982. "An algorithm for the multiple objective integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 9(4), pages 378-385, April.
    4. Meir J. Rosenblatt & Zilla Sinuany-Stern, 1989. "Generating the Discrete Efficient Frontier to the Capital Budgeting Problem," Operations Research, INFORMS, vol. 37(3), pages 384-394, June.
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    Cited by:

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    2. David Bergman & Merve Bodur & Carlos Cardonha & Andre A. Cire, 2022. "Network Models for Multiobjective Discrete Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 990-1005, March.
    3. Sebastian Sitarz, 2009. "Pareto optimal allocations and dynamic programming," Annals of Operations Research, Springer, vol. 172(1), pages 203-219, November.
    4. Djaafar Zouache & Fouad Ben Abdelaziz & Mira Lefkir & Nour El-Houda Chalabi, 2021. "Guided Moth–Flame optimiser for multi-objective optimization problems," Annals of Operations Research, Springer, vol. 296(1), pages 877-899, January.
    5. Li, Yan-Fu & Zhang, Hanxiao, 2022. "The methods for exactly solving redundancy allocation optimization for multi-state series–parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    6. Bashir Bashir & Özlem Karsu, 2022. "Solution approaches for equitable multiobjective integer programming problems," Annals of Operations Research, Springer, vol. 311(2), pages 967-995, April.
    7. Klamroth, Kathrin & Stiglmayr, Michael & Sudhoff, Julia, 2023. "Ordinal optimization through multi-objective reformulation," European Journal of Operational Research, Elsevier, vol. 311(2), pages 427-443.
    8. Maciej Nowak & Tadeusz Trzaskalik, 2022. "A trade-off multiobjective dynamic programming procedure and its application to project portfolio selection," Annals of Operations Research, Springer, vol. 311(2), pages 1155-1181, April.
    9. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.

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