The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
The Lagrangian Relaxation Method for Solving Integer Programming Problems
Abstract
One of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints. Dualizing the side constraints produces a Lagrangian problem that is easy to solve and whose optimal value is a lower bound (for minimization problems) on the optimal value of the original problem. The Lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm. This approach has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering. This paper is a review of Lagrangian relaxation based on what has been learned in the last decade.
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Cites
A Linear Programming Approach to the Cutting-Stock Problem
Gilmore, P. C., & Gomory, R. E. (1961) · Operations Research · doi:10.1287/opre.9.6.849 · Cited by 2,024
Cornuéjols, G., Fisher, M. L., & Nemhauser, G. L. (1979) · Management Science · doi:10.1287/mnsc.25.8.808 · Cited by 430
Self-citationMathematical Programming: Structures and Algorithms
Ovuworie, G. C., & Shapiro, J. F. (1981) · Journal of the Operational Research Society · doi:10.1057/jors.1981.14 · Cited by 308
Optimal set partitioning, matchings and lagrangian duality
Nemhauser, G. L., & Weber, G. (1979) · Naval Research Logistics Quarterly · doi:10.1002/nav.3800260401 · Cited by 24
Cited by
Emergency Logistics Planning in Natural Disasters
Özdamar, L., Ekinci, E., & Küçükyazici, B. (2004) · Annals of Operations Research · doi:10.1023/b:anor.0000030690.27939.39 · Cited by 819
Latency Minimization for Intelligent Reflecting Surface Aided Mobile Edge Computing
Bai, T., Pan, C., Deng, Y., Elkashlan, M., Nallanathan, A., & Hanzo, L. (2020) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2020.3007035 · Cited by 528
A comparison of reserve selection algorithms using data on terrestrial vertebrates in Oregon
Csuti, B., Polasky, S., Williams, P. H., Pressey, R. L., Camm, J. D., Kershaw, M., Kiester, A. R., Downs, B., Hamilton, R., Huso, M., et al. (1997) · Biological Conservation · doi:10.1016/s0006-3207(96)00068-7 · Cited by 448
Relaxations of Weakly Coupled Stochastic Dynamic Programs
Adelman, D., & Mersereau, A. J. (2008) · Operations Research · doi:10.1287/opre.1070.0445 · Cited by 198
Quinton, F. A., Myhr, P. A. S., Barani, M., Crespo del Granado, P., & Zhang, H. (2025) · Scientific Reports · doi:10.1038/s41598-025-96220-2 · Cited by 46
Metadata
- Authors
- Fisher, M. L.
- Venue
- Management Science
- Published
- 1981-01
- Volume
- 27
- Issue
- 1
- Pages
- 1-18
- ISSN
- 0025-1909 (ISSN-L)
- 1526-5501
- OpenAlex
- W4236384091
- Cited by
- 2,109
- References
- 4
- FWCI
- 18.19
- Type
- journal article
- Language
- en
- Open access
- closed
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