Vehicle fleet sizing for automated material handling systems to minimize cost subject to time constraints

Vehicle fleet sizing for an Automated Material Handling System (AMHS) is an important but challenging problem due to the complexity of AMHS design and uncertainty involved in the production process; e.g., random processing time. For a complex manufacturing system such as semiconductor manufacturing, the problem is even more complex. This article studies the vehicle fleet sizing problem in semiconductor manufacturing and proposes a formulation and solution method, called Simulation Sequential Metamodeling (SSM), to facilitate the determination of the optimal vehicle fleet size that minimizes the vehicle cost while satisfying time constraints. The proposed approach is to sequentially construct a series of metamodels, solve the approximate problem, and evaluate the quality of the resulting solution. Once the resulting solution is satisfactory, the algorithm is terminated. Compared with the existing metamodeling approaches that employ a large number of observations for one time, the sequential nature of SSM allows it to achieve much better computational efficiency. Furthermore, a newly developed estimation method enables SSM to quantify the quality of the resulting solution. Extensive numerical experiments show that SSM outperforms the existing methods and the computational advantage of SSM is increasing with the problem size and the level of the variance of response variables. An empirical study based on real data is conducted to validate the viability of SSM in practical settings.