Batch-Sizing and Machinability Data Systems for Milling Operations: An Optimal Sustainable Cost of Quality Approach
Abstract
Because of globalization and high competition in emerging markets, manufacturers strive to produce products with lower machining costs while maintaining high quality, and sustainability must be considered. This research aims to propose a mathematical optimization model that considers the internal quality cost, environmental impact approach, and the effect of buffering for the micro-computer-aided process planning problem (CAPP). The mathematical model is developed for different milling operations: face, side, and peripheral milling to optimize the machining parameters, namely, cutting speed, feed rate, axial depth of cut, radial depth of cut, and nose radius and batch sizing while maximizing profit and meeting customer demand. A Mixed-Integer Nonlinear Programming (MINLP) model is formulated and solved using an Evolutionary Algorithm metaheuristic. Surface roughness is used as a metric to evaluate the desired quality level of a finished machined part type. The normal random variable is used to model the surface roughness of the machined part utilizing a cumulative normal distribution. At the same time, the ratio of rework and scrap is calculated in terms of the surface roughness of the machined part shifting away from the target and exceeding upper and lower specification limits. Hence, the internal failure cost model, including scrap and rework, is developed based on Taguchi's quadratic loss function. Power consumption and carbon dioxide are predicted to establish the relationship between power consumption and machining parameters using a Response Surface Method approach (RSM). The numerical experience illustrates the proposed model adequacy for various milling operations. A small instance of the CAPP problem is solved where a single component type is produced multiple times as part of a single batch using solution procedures, namely, the fminCon and the Genetic Algorithms (GAs) on the MATLAB toolbox. The model is a highly nonlinear mixed-integer formulation; hence, Genetic Algorithms (GAs) are used to solve it. For validation, classical optimization is employed, disregarding the problem's discrete lot-sizing aspect, and exploiting the fact that the problem is convex in its absence. To tackle more intricate buffering and machining optimization scenarios, a larger instance is solved to produce a product-mix consisting of two types of materials. The optimization process focuses on optimizing the buffering size. Due to the complexity of the problem, two different solution algorithms, namely, Xpress Optimizer and Genetic Algorithm (GAs), are used to get optimal or near-optimal solutions. Results show the significance of integrating a well-designed systematic approach for optimizing the machining parameters and batch sizing if both quality and environmental costs are considered. This study reveals that the utilized machining parameters substantially impact the cost components of the objective function as well as the scrap and rework quantities. A stringent quality cost target can force the model to optimize the feed rate and nose radius to minimize the internal failure quality cost while improving the environmental impact model, including direct and indirect power consumption, in addition to CO2 emissions penalty for driving emissions reduction.