Article Abstract:
The problem of choosing a subset of N projects under multiple sequence-dependent resource constraints is considered. Known as the project selection problem, it is a nonlinear (0-1) integer problem that seeks to maximize the net present value of total returns. To solve it, two heuristics that converge to near solutions within O(N3K) and O(N4K) time are described. The first refines a feasible solution derived by a greedy procedure while the second combines it with steps zero and one of the M heuristic.
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Article Abstract:
A dynamic programming approach to the interval cutting problem encountered in the textile industry is presented. Specifically, it is shown that a small change to a dynamic programming method for solving the unperturbed instance of the two-parametric discrete optimization problem yields more information about the regions of stability of an optimal solution. In addition, a dynamic programming algorithm for determining the problem's optimal value function is proposed.
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Article Abstract:
The problem of minimizing the cutting sequence length or total time required for making guillotine cuts of a given convex shape from a given piece of material of a different convex design is investigated. Specifically, a dynamic programming-based polynomial approximation for deriving optimal solutions in the algebraic extension of the input data field is introduced. Its application to the case of non-convex polygons is also studied.
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