Tighter relaxations for the cutting stock problem

Article Abstract:

A study was conducted to characterize a nonlinear framework of the cutting stock problem which supports tighter linear programming relaxations compared with conventional continuous relaxation. Theoretical and numerical studies were carried out to analyze the effectiveness of the nonlinear framework. It was also shown that the bound resulting from the proper relaxation supports an optimal value. Results indicated that the tighter relaxation can be utilized to determine solutions for verifying optimality.

Operations Research, Simulated annealing (Mathematics)

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A new procedure for identifying the frame of the convex hull of a finite collection of points in multidimensional space

Article Abstract:

A new method for identifying the frame of the convex hull of a finite set of points is proposed. The method is based on solving linear programs, although with one main advantage: the size of the linear program is initially small and grows in columns that do not exceed the number of elements in the frame. The method promises to boost performance in areas ranging from linear programming redundancy to data envelopment analysis.

Finite groups, Convex sets

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On consistency in probabilistic logic for logical formulas represented by B-hypertrees

Article Abstract:

The case of probabilistic logic was investigated, particularly with regards to ways of consistently designating probabilities in logical formulas. A need to satisfy a group of conditions necessary to consistently designate probabilities to the logical formulas was established. Such conditions are vital to resolve three sets of inequalities present during designation of probabilities.

Research and Development in the Physical, Engineering, and Life Sciences, Mathematics, Probabilities, Probability theory

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