Gilmore and Gomory: generate useful cutting patterns instead of listing them all

What changed

An implicit-pattern LP formulation made computationally usable by knapsack pricing, with a small working basis and an explicit distinction between finding a column heuristically and certifying no improving column.

Scientific scope

An implicit-pattern LP formulation made computationally usable by knapsack pricing, with a small working basis and an explicit distinction between finding a column heuristically and certifying no improving column. matrix/formula glyphs are damaged, not certified transcriptions. Unlimited stock of specified lengths and costs; one-dimensional cutting patterns and order demands. Page 851 explicitly restricts this report to the continuous LP relaxation; integer pattern counts can remain fractional and rounding may be suboptimal. An integer knapsack pricing subproblem does not make the LP master integer. Heuristic pricing can find useful columns; failure requires the complete dynamic-programming check across stock types before claiming LP optimality. Degeneracy/anti-cycling treatment is discussed, not ignored. The worked example has stock lengths 5,6,9 costs 6,7,10 and demands 20,10,20 for lengths 2,3,4; its integer cost 170 is explicitly called fortuitous. This example is not a general benchmark. Ford/Fulkerson, Dantzig/Wolfe and knapsack/dynamic-programming predecessors retain credit. Part II 1963 and later integer/branch-and-price/multidimensional methods are separate. Original reprint says November 1961; Crossref deposits December 1961; only year and issue are used, without silently resolving the discrepancy. The editorial account uses the publication year and does not assert a manuscript receipt date. The complete implementation and cost-model results have not been independently certified here.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• P. C. Gilmore · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
• R. E. Gomory · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• Gilmore and Gomory: generate useful cutting patterns instead of listing them all; exact original technical paper
• Publisher-deposited identity for gilmore-gomory-pattern-column-generation-1961

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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