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Ensuring the economic efficiency of enterprises by multi-criteria selection of the optimal manufacturing process

Kotliar Alexey, Basova Yevheniia, Ivanov Vitalii, Murzabulatova Olena, Vasyltsova Svitlana, Litvynenko Mariia, Zinchenko Olena

Management and Production Engineering Review

2020

Vol. 11, No. 1

52--61

Technological assurance and improvement of the economic efficiency of production are the first-priority issues for the modern manufacturing engineering area. It is possible to achieve a higher value of economic efficiency in multiproduct manufacturing by multicriteria optimization. A set of optimality criteria based on technological and economic indicators was defined with the aim of selecting the optimal manufacturing process. Competitive variants and a system of optimization were developed and investigated. A comparative analysis of the optimality criteria and their influence on the choice of optimal machining processes was carried out. It was determined that the batch of parts made an impact on the selection of the manufacturing process.

Fixed-point iteration based algorithm for a class of nonlinear programming problems

Belegundu A. D.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 2

29--41

A fixed-point algorithm is presented for a class of singly constrained nonlinear programming (NLP) problems with bounds. Setting the gradient of the Lagrangian equal to zero yields a set of optimality conditions. However, a direct solution on general problems may yield non-KKT points. Under the assumption that the gradient of the objective function is negative while the gradient of the constraint function is positive, and that the variables are positive, it is shown that the fixed-point iterations can converge to a KKT point. An active set strategy is used to handle lower and upper bounds. While fixed-point iteration algorithms can be found in the structural optimization literature, these are presented without clearly stating assumptions under which convergence may be achieved. They are also problem specific as opposed to working with general functions f, g. Here, the algorithm targets general functions which satisfy the stated assumptions. Further, within this general context, the fixed-point variable update formula is given physical significance. Unlike NLP descent methods, no line search is involved to determine step size which involves many function calls or simulations. Thus, the resulting algorithm is vastly superior for the subclass of problems considered. Moreover, the number of function evaluations remains independent of the number of variables allowing the efficient solution of problems with a large number of variables. Applications and numerical examples are presented.