A Class of Variance Constrained Problems

Article Abstract:

A Lagrange multiplier solution procedure is developed for a class of variance-constrained problems. The method, based on the separation of the variance and an algorithm for determining the optimal value of the mean, relies on the availability of a method of solving a modified problem in which the variance operation is replaced by the generalized variance operator. It is indicated that the procedure can be used in conjuction with dynamic programming to solve a variety of variance-constrained problems which allow the consideration of adaptive strategies. The procedure is demonstrated by a simple numerical example.

Analysis of variance, Dynamic programming, Decision theory, Dynamic Systems, Stochastic Model

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The Solution of Distance Constrained Mini-Sum Location Problems

Article Abstract:

Some facility location problems have the dual objective of both minimizing service costs and ensuring that all customers receive adequate service. Plants manufacturing perishable goods, schools, or service centers must be located so that travel time is not excessive. Methods for solving the single-facility case are extended to cover the multifacility case. The method uses a partial enumerative graph-coloring algorithm. Also presented is a fast heuristic which is based upon a location-allocation method. Tables present computational results.

Service Centers, Facility Location, Heuristic Methods, Iteration

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Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems

Article Abstract:

Two combinatoric methods that generate constrained cutting patterns by successive horizontal and vertical builds of ordered rectangles are proposed. Each of the algorithms uses a parameter to bound the maximum acceptable percentages of waste they create. Error bounds measure how close the pattern wastes are to the waste of the optimal solution. Computational results and applications of the methods to a general cutting stock problem are also discussed. Normalized and not normalized guillotine patterns are shown.

Integer programming, Numerical analysis, Materials handling, Optimization, Approximation, Combinatorics

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