(373aq) Enhancing Productivity of Multi-Process Production System By Machine Combination Optimization

In a multi-process production system such as a semiconductor manufacturing process, products are manufactured through multiple stages, and each stage has parallel machines. In such a production system, machine combinations in different stages, i.e. paths, may strongly affect the quality of the final products. Clearly, low-performance machines should not be used for manufacturing high-quality products. When such machines are used in different stages, however, the product quality may not necessarily degrade. For example, the total machining error may be reduced when machining errors occur in the opposite direction in two stages. Such two machines are said to be compatible with each other. In addition, the use of particular two machines, each of which is not bad, may lower the product quality when they are incompatible with each other. Thus, taking account of the interaction of machines is crucial for improving the productivity.

Although the effect of machine combinations on product quality has been empirically considered in manufacturing plants, it has not been systematically revealed. For further productivity improvement, there is a strong demand for the optimal use of machine combinations; machine combinations need to be selected and used according to their goodness or compatibility. The objective of this research is to develop a new method for machine combination optimization.

For optimizing machine combinations, it is ideal all machine combinations are ranked according to the quality criteria of final products such as the yield rate. In a complex system, however, many combinations have not been used, and therefore no data on their yield rates are available. If the goodness of unused machine combinations can be estimated using observed data, machine combinations can be optimized by taking account of all combinations. Hence, we propose a modeling method that can estimate the yield rate that depends on machine combinations. In addition, using the constructed model, we aim to identify which machine pairs affect product quality significantly to evaluate the goodness of machine combinations in more detail. To cope with the interactions of machines, we focus on nonlinear regression models: support vector regression (SVR), Gaussian process regression (GPR), and Random Forest (RF). In addition, it is necessary to construct a regression model with a small amount of training data because the available data is typically sparse in the case of a large-scale multi-process production system where the number of machine combinations is enormous. For this reason, we also examine Factorization Machines (FM) and Field-aware Factorization Machines (FFM), which are reported to have high estimation accuracy even in sparse settings. FM is a supervised learning method that can use feature combinations efficiently even when the data is very high-dimensional. However, latent vectors of FM are shared by all input variables (features), therefore useless interaction features will introduce noise in learning latent vectors. To solve this problem, FFM introduces the concept of fields for input variables to FM. The fields represent categories where input variables are classified according to their common attribute. FFM learns a different set of latent vectors for every pair of fields. In other words, each feature uses a different latent vector to interact with other features from a different field. In this work, stages are regarded as fields; that is, machines at the same stage belong to the same field. Thus, the interaction coefficient of machines that belong to the same field, i.e. stage, becomes zero automatically. This enhances the estimation performance of FFM in comparison with FM. In addition, as with FM, the importance of machine pairs can be evaluated by using the interaction coefficients of FFM.

To improve the productivity, it is necessary not only to increase the yield rate but also to decrease the makespan, which is the maximum completion time of all jobs. In the field of production scheduling, many studies have tackled the problem of determining an optimal schedule to minimize the makespan, and various approaches with exact solutions or metaheuristic have been proposed. However, the influence of machine combinations on the product quality has not been considered. This motivated us to develop a scheduling method that minimizes the makespan and maximizes the yield rate simultaneously.

In this work, we proposed a modeling method that can estimate the yield rates achieved by unused machine combinations and a production scheduling method that can optimally select machine combinations by taking account of the yield rates depending on the combinations. A case study showed that field-aware factorization machines (FFM) achieved the best estimation performance in comparison with support vector regression, gaussian process regression, random forest, and factorization machines. Even when yield rates are available in only 20% of all machine combinations, the coefficient of determination was 0.967. In addition, almost all important machine pairs which significantly affect product quality were identified using the interaction coefficients of FFM. Furthermore, we developed a multi-objective scheduling method using non-dominated sorting genetic algorithm II (NSGA-II) with novel dispatching rules. Another case study demonstrated that the proposed method improved the throughput by 12% comparing to the conventional method. The present study confirmed that the productivity can be improved with the proposed machine combination optimization framework.