An Efficient Point Algorithm for a Linear Two-State Optimization Problem

Article Abstract:

An algorithm using sensitivity analysis to solve a linear two-stage optimization problem is presented. The underlying theory rests on a set of first order optimality conditions. The conditions parallel the Kuhn-Tucker conditions associated with a one-dimensional parametric linear program. The solution to the original problem is uncovered by systematically varying the parameter over the unit internal. The corresponding linear program is then solved. Finite convergence is established under nondegenerate assumptions. Other solution techniques such as branch and bound and vertex enumeration are discussed. Examples are given. Finally, a comparison is drawn between bicriteria and bilevel programming. A table of computational results using a grid search algorithm is shown. A comparison of several results of several algorithms is also presented.

Mathematical models, Optimization, Systems, Mathematical Programming, Sensitivity Analysis, Theory, Branch and Bound

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Implementation and Testing of a Primal-Dual Algorithm for the Assignment Problem

Article Abstract:

State-of-the-art computational results have shown that primal simplex algorithms are more efficient than primal-dual algorithms for general minimum cost network flow problems. There is, however, some controversy concerning their relative merits for solving assignment problems. A detailed development for a computationally efficient primal-dual algorithm and extensive computational comparisons to primal simplex algorithms. A graph of solution times for NETGEN benchmarks adjusted to the CDC 6600, RUN equivalent is included.

Simplexes (Mathematics), Efficiency, Simplex Method

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A Weighted Selection Algorithm for Certain Tree-Structured Linear Programs

Article Abstract:

Linear programming problems with tree-structured constraint matrices are solved. These problems occur in portfolio selection, placement of advertisements, and multiperiod productions and inventory decisions. The problem is separated into a sequence of continuous knapsack problems. Each needs linear time to solve. Diagrams illustrate concepts and a table of results is included.

Modeling, Data modeling software, Scientific Research, Tree Structures, NP-Complete Problems

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