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This paper investigates the problem of obtaining the best arrangement for cutting stock patterns in the presence of defective material in the paper, which is a common problem in the industry. This problem is modeled as a multiple subset sum problem and its structure is exploited in order to obtain a practical solution procedure. The solution methodology employs the subset sum problem as a subprocedure. Computational results are reported. [ABSTRACT FROM AUTHOR]

The main idea of conditional ordering is to sharpen the ordering results in such a way that even conditionally on some kind of additional information on the underlying ‘experiment’ the ordering is valid. In this paper, some sufficient conditions for conditional variability and conditional dispersion orderings are established. The main idea is to find sufficient assumptions which are stable by conditioning. [ABSTRACT FROM AUTHOR]