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Practical adaptations of the Gilmore-Gomory approach to cutting stock problems. (English) Zbl 0642.90050
Summary: The delayed pattern generation approach to the solution of cutting stock problems was first proposed by P. C. Gilmore and R. E. Gomory [Oper. Res. 9, 849-859 (1961; Zbl 0096.355); ibid. 11, 863-888 (1963; Zbl 0124.363)]. The most significant barrier to its widespread acceptance in commercial applications is its inflexibility in dealing with objectives other than waste minimization. The adaptations of the basic Gilmore-Gomory approach presented in this article increase its flexibility. The adaptations relate to initial pattern generation, multiple solutions per knapsack problem, explicit valuation of undersupply and oversupply, and waste having a value. While some adaptations improve the basic approach, all adaptations lead to the ability to handle objectives more complex than solely waste minimization.

MSC:
90B30 Production models
90C05 Linear programming
65K05 Numerical mathematical programming methods
90C90 Applications of mathematical programming
90C10 Integer programming
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