2011
HMS 2011 Proceeding
Convex Extension of Discrete-Convex Functions and Applications in Optimal Design of Complicated Logistic, Manufacturing and Processing Environments
Authors: Tiit Riismaa
Abstract
A method of description and optimal design of the structure of complicated multi-level processing systems is presented. The set of feasible structures for such class of systems is defined. The representation of this set is constructed in terms of the graph theory. For the reduced statement two types of variable parameters are defined for the level size and for the relations of adjacent levels. The choice of variable parameters guarantees the discrete-convexity of objective function. A class of iteration methods for solving the discrete- convex programming problem is derived. The method based on the extension of discrete-convex function to the convex function and on extension of discrete- convex programming problem to the convex programming problem. On each step of the iteration the calculation of the value of objective function is required only on some vertices of unit cube. The considered approach is illustrated by an academic example of modelling and optimal design of the multi-level manufacturing system.
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