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A Linear Programming Approach to the Cutting Stock Problem—Part II
Abstract
In this paper, the methods for stock cutting outlined in an earlier paper in this Journal [Opns Res 9, 849–859 (1961)] are extended and adapted to the specific full-scale paper trim problem. The paper describes a new and faster knapsack method, experiments, and formulation changes. The experiments include ones used to evaluate speed-up devices and to explore a connection with integer programming. Other experiments give waste as a function of stock length, examine the effect of multiple stock lengths on waste, and the effect of a cutting knife limitation. The formulation changes discussed are (i) limitation on the number of cutting knives available, (n) balancing of multiple machine usage when orders are being filled from more than one machine, and (m) introduction of a rational objective function when customers' orders are not for fixed amounts, but rather for a range of amounts. The methods developed are also applicable to a variety of cutting problems outside of the paper industry.
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Cited by
Approximation Algorithms for Bin-Packing — An Updated Survey
Coffman, E. G., Garey, M. R., & Johnson, D. S. (1984) · CISM International Centre for Mechanical Sciences · doi:10.1007/978-3-7091-4338-4_3 · Cited by 433
Bin Packing Approximation Algorithms: Survey and Classification
Coffman, E. G., Csirik, J., Galambos, G., Martello, S., & Vigo, D. (2013) · Handbook of Combinatorial Optimization · doi:10.1007/978-1-4419-7997-1_35 · Cited by 289
A technical review of column generation in integer programming
Wilhelm, W. E. (2001) · Optimization and Engineering · doi:10.1023/a:1013141227104 · Cited by 108
Robust earth observation satellite scheduling with uncertainty of cloud coverage
Wang, X., Song, G., Leus, R., & Han, C. (2020) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2019.2947978 · Cited by 70
Scheduling multiple agile Earth observation satellites with multiple observations
Wang, X., Han, C., & Leus, R. (2026) · Advances in Space Research · doi:10.1016/j.asr.2025.10.042 · Cited by 24
Metadata
- Authors
- Gilmore, P. C., & Gomory, R. E.
- Venue
- Operations Research
- Published
- 1963-12
- Volume
- 11
- Issue
- 6
- Pages
- 863-888
- ISSN
- 0030-364X (ISSN-L)
- 1526-5463
- OpenAlex
- W2085478109
- Cited by
- 1,119
- References
- 0
- FWCI
- 134.67
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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