An exact algorithm for orthogonal 2-D cutting problems using guillotine cuts

Article Abstract:

A tree-search algorithm for solving the two-dimensional cutting problem is introduced. The problem, which is recast as a dynamic formulation problem, involves minimizing the waste incurred in cutting smaller rectangular pieces of dissimilar size from a stock plate without exceeding the prescribed limit for each pattern size. The algorithm, which was validated by several tests, uses a bound on the size of the tree search to derive an optimal solution to the problem.

Mathematical optimization, Optimization theory

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A suboptimal solution to a hierarchical network design problem using dynamic programming

Article Abstract:

The use of dynamic programming to solve a hierarchical network design problem is demonstrated. The problem, which is characterized by an undirected graph, pertains to networks consisting of a set of nodes with each arc between two nodes having two non-negative costs, namely, primary link cost and secondary link cost. It entails obtaining the shortest path between the source node and the destination node by constructing tree structures from the other nodes.

Trees (Graph theory)

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Expected utility maximization of optimal stopping problems

Article Abstract:

A new study investigates the problem of optimal stopping and expected utility maximization.

Decision theory, Optimal stopping (Mathematical statistics), Utility theory, Utility functions

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