Solution of a tinned iron purchasing problem by Lagrangean relaxation

Article Abstract:

A tin factory encounters production and purchasing problems when tinned iron sheets demanded by clients require variant specifications. Thus, the factory has to develop a production program that minimizes purchase costs while meeting customer specifications. Such a program may integrate quantity discounts for large, one-size orders. The program is integrated as a combinatorial optimization problem and solved using Lagrangean relaxation techniques.

Production management

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Lagrangean methods for the 0-1 quadratic knapsack problem

Article Abstract:

Lagrangean decomposition and Lagrangean relaxation are compared in terms of their performance when used in branch-and-bound algorithms. Decomposition and relaxation are used to solve the 0-1 Quadratic Knapsack problem. Lagrangean decomposition is found to improve CPU time and the number of nodes. Decomposition provides tighter upper and lower bounds which fix more variables and reduce the number of nodes in a branch-and-bound scheme.

Quadratic programming, Branch and bound algorithms

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Minmax combinatorial optimization

Article Abstract:

The minmax combinatorial optimization problem (MMCOP) has applications in multi-criteria optimization, categorized assignment scheduling, band width minimization in matrices and graphs, spanning tree and bipartite matching problems. MMCOP solutions require enumerative techniques or approximations from heuristic algorithms. Lagrangean relaxation generates good upper and lower bounds for enumerative solutions to MMCOP.

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