Tolerance synthesis by neural learning and nonlinear programming

Article Abstract:

The tolerance design directly influences the functionality of products and related production costs. Tolerance synthesis is a procedure that distributes assembly tolerances between components or distributes final part design tolerances between related tolerances. In order to make a reliable trade-off between design tolerances and costs, it is necessary to obtain the cost-tolerance relationships. Various operations such as turning, milling, drilling, grinding, casting, etc., have different cost-tolerance relationships. Previous studies have usually established cost-tolerance functions for various manufacturing operations by regression analysis using the empirical data. Using traditional methods of regression analysis, people must make assumptions about the form of the regression equation or its parameters, which may not be valid. The neural network recently has been reported to be an effective statistical tool for determining the relationships between input factors and output responses. This study deals with the optimal tolerance design for an assembly simultaneously considering manufacturing cost and quality loss. In this paper, a backpropagation (BP) network is applied to fit the cost-tolerance relationship. Once the cost-tolerance functions have been generated, mathematical models for tolerance synthesis can be built. By solving the formulated mathematical models, the optimal tolerance allocation can be generated. An optimization method based on simulated annealing (SA) is then used to locate the combination of controllable factors (tolerances) to optimize the output response (manufacturing cost plus quality loss) using the equations stemming from the trained network. A tolerance synthesis problem for a motor assembly is used to investigate the effectiveness and efficiency of the proposed methodology. [C] 2001 Elsevier Science B.V. All rights reserved. Keywords: Tolerance synthesis; Cost-tolerance relationship: Optimization; Neural network

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Minimizing the expected total value of shortages for a population of items subject to practical restrictions on the reorder points

Article Abstract:

We address a problem of setting reorder points (expressed as time supplies) of a population of items, subject to a restricted set of possible time supplies as well as a budget on the total amount of safety stocks, both important practical constraints. We provide a branch-and-bound algorithm for obtaining the optimal solution. In addition, a simple and efficient heuristic algorithm has been developed. Computational experiments show that the performance of the heuristic is excellent based on a set of realistic examples. However, the typical set of possible time supplies may significantly degrade performance compared with the situation where a continuum of choices are possible. [C] 2001 Elsevier Science B.V. All rights reserved. Keywords: Inventory; Safety stock; Lower bound; Branch and bound; Heuristic

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