In this paper, we deal with the optimal I\/O point location in an automated parking system. In this system, the S\/R machine (storage and retrieve machine) travels independently in vertical and horizontal directions. Based on the characteristics of the parking system and the basic principle of AS\/RS system (Automated Storage and Retrieval System), we obtain the continuous model in units of time. For the single command cycle using the randomized storage policy, we calculate the probability density function for the system travel time and thus we develop the travel time model. And we confirm that the travel time model shows a good performance by comparing with discrete case. Finally in this part, we establish the optimal model by minimizing the expected travel time model and it is shown that the optimal location of the I\/O point is located at the middle of the left-hand above corner.<\/p>\r\n","references":"[1]\tNational Bureau of statistics. China Statistical Yearbook [J]. Beijing: China Statistics Press, 2000~2014\r\n[2]\tW. H. Hausman, L. B. Schwarz, and S. C. Graves, \u201cOptimal Storage Assignment in Automatic Warehousing Systems\u201d, Management Science, vol. 22, no. 2, pp. 629-638, 1976.\r\n[3]\tS. C. Graves, W. H. Hausman, and L. B. Schwarz, \u201cStorage-Retrieval Interleaving in Automatic Warehousing Systems\u201d, Management Science, vol. 23, no. 9,pp. 935-945, 1977.\r\n[4]\tL. B. Schwarz, S. C. Graves, and W. H. Hausman, \u201cScheduling Policies for Automatic Warehousing Systems: Simulation Results\u201d, IIE Transactions, vol. 10, no. 3, pp. 260-27, 1978.\r\n[5]\tY. A. Bozer and J. A. White, \u201cTravel Time Models for Automated Storage\/Retrieval Systems\u201d, IIE Transactions, vol. 16, no. 4, pp. 329-338, 1984.\r\n[6]\tZaerpour, Nima, Y. Yu and R. B. M. D. Koster, \u201cSmall is Beautiful: A Framework for Evaluating and Optimizing Live-Cube Compact Storage Systems\u201d, Transportation Science, 2015.\r\n[7]\tS. G. Koh, B. S. Kim, and B. N. Kim, \"Travel time model for the warehousing system with a tower crane S\/R machine\", Computers & Industrial Engineering, vol. 43, no. 3, pp. 495-507, 2002.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 146, 2019"}