Automated warehouse systems are increasingly adopted in supply chains to meet diverse customer demands driven by global e-commerce growth. It is supported by the adoption of Automated Storage and Retrieval System (AS/RS), designed to enhance not only efficiency but also accuracy and safety of material handling. However, the automation nature of AS/RS explodes the need for energy consumption which has become a global concern. Whereas, reducing energy usage may lead to contradiction with other objectives, making it more challenging to be improved. Further, the dynamic complexity inherent in AS/RS operations requires an advanced modeling tool for accurate estimation. Literature review shows that most previous studies in AS/RS still focus on efficiency metrics assessed by traditional travel time models, showing the gap in green AS/RS. Therefore, the purpose of this research is to propose a multi-objective simulation-optimization framework for designing a low-energy AS/RS while maintaining the efficiency under different decision levels. The comprehensive AS/RS energy consumption formulation is first proposed. Then, a real automated warehouse is modeled based on Discrete-Event Simulation using FlexSim for imitating the end-to-end AS/RS operations and building the user interface. Finally, three applications are given. First, AS/RS integrated planning is proposed based on Simheuristics. The results produce non-dominated solutions informing near-optimal AS/RS configurations from the greenest to the fastest ones that are further categorized into 4 classes via a clustering algorithm which can be very useful for global AS/RS design either at the establishment or reconfiguration stages. Second, AS/RS multi-speed configuration is proposed based on metamodeling and desirability function under different storage assignment methods. The near-optimal speed configuration is achieved efficiently comprising four speed variables: horizontal (x), vertical (y), depth (z), and acceleration/deceleration. Lastly, AS/RS dynamic scheduling is proposed based on multi-objective deep reinforcement learning which can provide real-time decision. The result statistically reduces both energy usage and waiting time compared to other well-known AS/RS scheduling policies. In addition, AS/RS idle rate becomes higher indicating more robust performance to cope with supply and demand uncertainties. Overall, all proposed frameworks allow logistics managers to make better decisions in designing and managing green AS/RS toward sustainable warehousing.

[1] F. Z. B. Moussa, R. D. Guio, S. Dubois, I. Rasovska, and R. Benmoussa, “Study of an innovative method based on complementarity between ARIZ, lean management and discrete event simulation for solving warehousing problems,” Computers and Industrial Engineering, vol. 132, pp. 124–140, 2019, doi: 10.1016/j.cie.2019.04.024.
[2] R. K. Singh, N. Chaudhary, and N. Saxena, “Selection of warehouse location for a global supply chain: A case study,” IIMB Management Review, vol. 30, no. 4, pp. 343–356, 2018, doi: 10.1016/j.iimb.2018.08.009.
[3] L. Zhen and H. Li, “A literature review of smart warehouse operations management,” Frontiers of Engineering Management, vol. 9, no. 1, pp. 31–55, 2022, doi: 10.1007/s42524-021-0178-9.
[4] J. Kembro and A. Norrman, “The transformation from manual to smart warehousing: an exploratory study with Swedish retailers,” International Journal of Logistics Management, vol. 33, no. 5, pp. 107–135, 2022, doi: 10.1108/IJLM-11-2021-0525.
[5] J. Walker, “Warehouse automation market to expand to over $69bn by 2025,” Interact Analysis. Accessed: Aug. 20, 2023. [Online]. Available: https://interactanalysis.com/warehouse-automation-market-to-expand-to-over-69bn-by-2025/
[6] A. Edouard, Y. Sallez, V. Fortineau, S. Lamouri, and A. Berger, “Automated storage and retrieval systems: An attractive solution for an urban warehouse’s sustainable development,” Sustainability, vol. 14, no. 15, 2022, doi: 10.3390/su14159518.
[7] A. Fenercioğlu, M. Soyaslan, and C. Kozkurt, “Automatic storage and retrieval system (AS/RS) based on cartesian robot for liquid food industry,” 12th International Workshop on Research and Education in Mechatronics, no. January, pp. 283–287, 2011.
[8] T. Settey, J. Gnap, D. Beňová, M. Pavličko, and O. Blažeková, “The growth of e-commerce due to COVID-19 and the need for urban logistics centers using electric vehicles: Bratislava case study,” Sustainability, vol. 13, no. 10, 2021, doi: 10.3390/su13105357.
[9] K. J. Roodbergen and I. F. A. Vis, “A survey of literature on automated storage and retrieval systems,” European Journal of Operational Research, vol. 194, no. 2, pp. 343–362, 2009, doi: 10.1016/j.ejor.2008.01.038.
[10] D. Popović, M. Vidović, and N. Bjelić, “Application of genetic algorithms for sequencing of AS/RS with a triple-shuttle module in class-based storage,” Flexible Services and Manufacturing Journal, vol. 26, no. 3, pp. 432–453, 2014, doi: 10.1007/s10696-012-9139-2.
[11] A. Meneghetti, E. D. Borgo, and L. Monti, “Decision support optimisation models for design of sustainable automated warehouses,” International Journal of Shipping and Transport Logistics, vol. 7, no. 3, pp. 266–294, 2015, doi: 10.1504/IJSTL.2015.069127.
[12] M. Bartolini, E. Bottani, and E. H. Grosse, “Green warehousing: Systematic literature review and bibliometric analysis,” Journal of Cleaner Production, vol. 226. pp. 242–258, 2019. doi: 10.1016/j.jclepro.2019.04.055.
[13] T. Liu and X. Feng, “The simulation and optimization of automated storage and retrieve system based on flexsim,” in CSAE 2012 - Proceedings, 2012 IEEE International Conference on Computer Science and Automation Engineering, 2012, pp. 692–697. doi: 10.1109/CSAE.2012.6272687.
[14] Y. Wang, J. Pan, P. Zhang, and D. T. Semere, “Application on automated warehouse simulation system in location optimization,” in The First International Symposium on Management and Social Sciences, 2019, pp. 97–101. doi: 10.2991/ismss-19.2019.20.
[15] A. R. Nia, H. Haleh, and A. Saghaei, “Dual command cycle dynamic sequencing method to consider GHG efficiency in unit-load multiple-rack automated storage and retrieval systems,” Computers and Industrial Engineering, vol. 111, pp. 89–108, 2017, doi: 10.1016/j.cie.2017.07.007.
[16] H. P. Hsu, C. N. Wang, and T. T. Dang, “Simulation-based optimization approaches for dealing with dual-command crane scheduling problem in unit-load double-deep AS/RS considering energy consumption,” Mathematics, vol. 10, no. 21, 2022, doi: 10.3390/math10214018.
[17] G. Zhou and L. Mao, “Design and simulation of storage location optimization module in AS/RS based on FLEXSIM,” International Journal of Intelligent Systems and Applications, vol. 2, no. 2, pp. 33–40, 2010, doi: 10.5815/ijisa.2010.02.05.
[18] T. Lerher, M. Edl, and B. Rosi, “Energy efficiency model for the mini-load automated storage and retrieval systems,” International Journal of Advanced Manufacturing Technology, vol. 70, no. 1–4, pp. 97–115, 2014, doi: 10.1007/s00170-013-5253-x.
[19] H. M. Hameed, K. A. A. Amry, and A. T. Rashid, “The automatic storage and retrieval system: An overview,” International Journal of Computer Applications, vol. 177, no. 16, pp. 36–43, 2019, doi: 10.5120/ijca2019919603.
[20] W. H. Hausman, L. B. Schwarz, and S. C. Graves, “Optimal storage assignment in automatic warehousing systems,” Management Science, vol. 22, no. 6, pp. 629–638, 1976, doi: 10.1287/mnsc.22.6.629.
[21] S. C. Graves, W. H. Hausman, and L. B. Schwarz, “Storage-retrieval interleaving in automatic warehousing systems,” Management Science, vol. 23, no. 9, pp. 935–945, 1977, doi: 10.1287/mnsc.23.9.935.
[22] Y. A. Bozer and J. A. White, “Travel-time models for automated storage/retrieval systems,” IIE Transactions, vol. 16, no. 4, pp. 329–338, 1984, doi: 10.1080/07408178408975252.
[23] J. P. Gagliardi, J. Renaud, and A. Ruiz, “Models for automated storage and retrieval systems: A literature review,” International Journal of Production Research, vol. 50, no. 24, pp. 7110–7125, 2012, doi: 10.1080/00207543.2011.633234.
[24] Z. Zhang, X. Wang, S. Yang, Y. Wu, and J. Du, “Simulation and analysis of the complex dynamic behavior of supply chain inventory system from different decision perspectives,” Complexity, vol. 2020, 2020, doi: 10.1155/2020/7393848.
[25] L. J. Hong and X. Zhang, “Surrogate-based simulation optimization,” INFORMS TutORials in Operations Research, pp. 287–311, 2021, doi: 10.1287/educ.2021.0225.
[26] B. Dengiz, T. Bektas, and A. E. Ultanir, “Simulation optimization based DSS application: A diamond tool production line in industry,” Simulation Modelling Practice and Theory, vol. 14, no. 3, pp. 296–312, 2006, doi: 10.1016/j.simpat.2005.07.001.
[27] J. Karnon, J. Stahl, A. Brennan, J. J. Caro, J. Mar, and J. Möller, “Modeling using discrete event simulation: A report of the ISPOR-SMDM modeling good research practices task force-4,” Value in Health, vol. 15, no. 6, pp. 821–827, 2012, doi: 10.1016/j.jval.2012.04.013.
[28] M. Pidd, Computer Simulation in Management Science, 5th ed. Wiley, 2004.
[29] A. M. Law, Simulation Modeling and Analysis, 5th ed. New York: McGraw-Hill Education, 2015.
[30] N. Prajapat and A. Tiwari, “A review of assembly optimisation applications using discrete event simulation,” International Journal of Computer Integrated Manufacturing, vol. 30, no. 2–3, pp. 215–228, 2017, doi: 10.1080/0951192X.2016.1145812.
[31] E. Aretoulaki, S. T. Ponis, G. Plakas, and D. Tzanetou, “(DT4Smart) discrete event simulation and Digital Twins in warehouse logistics: A bibliometric and content analysis-based systematic literature review,” International Journal of Computer Integrated Manufacturing, pp. 1–28, 2024, doi: 10.1080/0951192X.2024.2314772.
[32] W. B. Nordgren, “Flexsim simulation environment,” in Winter Simulation Conference Proceedings, 2003, pp. 250–252. doi: 10.1109/wsc.2003.1261424.
[33] C. B. Morgan, “Discrete-event system simulation,” Technometrics, vol. 26, 1984, doi: 10.2307/1268124.
[34] S. Luściński, “Digital twinning for smart industry,” in InMMS 2018: 3rd EAI International Conference on Management of Manufacturing Systems, 2018. doi: 10.4108/eai.6-11-2018.2279986.
[35] M. B. Shim, M. W. Suh, T. Furukawa, G. Yagawa, and S. Yoshimura, “Pareto-based continuous evolutionary algorithms for multiobjective optimization,” Engineering Computations, vol. 19, no. 1, pp. 22–48, 2002, doi: 10.1108/02644400210413649.
[36] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002, doi: 10.1109/4235.996017.
[37] G. Subashini and M. C. Bhuvaneswari, “Comparison of multi-objective evolutionary approaches for task scheduling in distributed computing systems,” Sadhana, vol. 37, no. 6, pp. 675–694, 2012, doi: 10.1007/s12046-012-0102-4.
[38] A. P. Guerreiro, C. M. Fonseca, and L. Paquete, “The hypervolume indicator: Computational problems and algorithms,” ACM Computing Surveys, vol. 54, no. 6, pp. 1–42, 2021, doi: 10.1145/3453474.
[39] A. Auger, J. Bader, D. Brockhoff, and E. Zitzler, “Hypervolume-based multiobjective optimization: Theoretical foundations and practical implications,” Theoretical Computer Science, vol. 425, pp. 75–103, 2012, doi: 10.1016/j.tcs.2011.03.012.
[40] S. Amaran, N. V. Sahinidis, B. Sharda, and S. J. Bury, “Simulation optimization: A review of algorithms and applications,” Annals of Operations Research, vol. 240, no. 1, pp. 351–380, 2016, doi: 10.1007/s10479-015-2019-x.
[41] A. A. Juan, J. Faulin, S. E. Grasman, M. Rabe, and G. Figueira, “A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems,” Operations Research Perspectives, vol. 2, pp. 62–72, 2015, doi: 10.1016/j.orp.2015.03.001.
[42] J. V. S. D. Amaral, J. A. B. Montevechi, R. D. C. Miranda, and W. T. D. S. Junior, “Metamodel-based simulation optimization: A systematic literature review,” Simulation Modelling Practice and Theory, vol. 114, 2022, doi: 10.1016/j.simpat.2021.102403.
[43] K. H. Chang and T. L. Chen, “Simulation learning and optimization: Methodology and applications,” Asia-Pacific Journal of Operational Research, 2024, doi: doi.org/10.1142/S0217595924400086.
[44] A. Ghasemi, A. Ashoori, and C. Heavey, “Evolutionary learning based simulation optimization for stochastic job shop scheduling problems,” Applied Soft Computing, vol. 106, 2021, doi: 10.1016/j.asoc.2021.107309.
[45] J. Qiu, Q. Wu, G. Ding, Y. Xu, and S. Feng, “A survey of machine learning for big data processing,” Eurasip Journal on Advances in Signal Processing, vol. 27, pp. 327–336, 2016, doi: 10.1186/s13634-016-0355-x.
[46] M. Z. Hossain, M. N. Akhtar, R. B. Ahmad, and M. Rahman, “A dynamic K-means clustering for data mining,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 13, no. 2, pp. 521–526, 2019, doi: 10.11591/ijeecs.v13.i2.pp521-526.
[47] S. Wang, M. Li, N. Hu, E. Zhu, J. Hu, X. Liu, and J. Yin, “K-Means clustering with incomplete data,” IEEE Access, vol. 7, pp. 69162–69171, 2019, doi: 10.1109/ACCESS.2019.2910287.
[48] M. I. Radaideh, K. Du, P. Seurin, D. Seyler, X. Gu, H. Wang, and K. Shirvan, “NEORL: NeuroEvolution Optimization with Reinforcement Learning—Applications to carbon-free energy systems,” Nuclear Engineering and Design, vol. 412, 2023, doi: 10.1016/j.nucengdes.2023.112423.
[49] M. Uzair and N. Jamil, “Effects of hidden layers on the efficiency of neural networks,” in 2020 IEEE 23rd international multitopic conference (INMIC), 2020, pp. 1–6. doi: 10.1109/INMIC50486.2020.9318195.
[50] X. Yan, Z. Zhang, Q. Liu, C. Lv, L. Zhang, and S. Li, “An NSABC algorithm for multi-aisle AS/RS scheduling optimization,” Computers and Industrial Engineering, vol. 156, 2021, doi: 10.1016/j.cie.2021.107254.
[51] S. Roh, H. H. Lin, and H. Jang, “Performance indicators for humanitarian relief logistics in Taiwan,” Asian Journal of Shipping and Logistics, vol. 38, no. 3, pp. 173–180, 2022, doi: 10.1016/j.ajsl.2022.06.002.
[52] M. Beaverstock, A. Greenwood, and W. Nordgren, Applied Simulation: Modeling and Analysis Using FlexSim, 5th ed. BookBaby, 2018.
[53] S. U. Randhawa, E. D. McDowell, and W. T. Wang, “Evaluation of scheduling rules for single- and dual-dock automated storage/retrieval system,” Computers and Industrial Engineering, vol. 20, no. 4, pp. 401–410, 1991, doi: 10.1016/0360-8352(91)90012-U.
[54] A. Meneghetti and L. Monti, “Sustainable storage assignment and dwell-point policies for automated storage and retrieval systems,” Production Planning and Control, vol. 24, no. 6, pp. 511–520, 2013, doi: 10.1080/09537287.2011.637525.
[55] J. P. Gagliardi, J. Renaud, and A. Ruiz, “On storage assignment policies for unit-load automated storage and retrieval systems,” International Journal of Production Research, vol. 50, no. 3, pp. 879–892, 2012, doi: 10.1080/00207543.2010.543939.
[56] P. J. Egbelu and C. T. Wu, “A comparison of dwell point rules in an automated storage/retrieval system,” International Journal of Production Research, vol. 31, no. 11, pp. 2515–2530, 1993, doi: 10.1080/00207549308956880.
[57] L. Yue, Z. Guan, C. He, D. Luo, and U. Saif, “Slotting optimization of automated storage and retrieval system (AS/RS) for efficient delivery of parts in an assembly shop using genetic algorithm: A case study,” in IOP Conference Series: Materials Science and Engineering, 2017. doi: 10.1088/1757-899X/215/1/012002.
[58] M. H. Han, L. F. McGinnis, J. S. Shieh, and J. A. White, “On sequencing retrievals in an automated storage/retrieval system,” IIE Transactions, vol. 19, no. 1, pp. 56–66, 1987, doi: 10.1080/07408178708975370.
[59] H. F. Lee and S. K. Schaefer, “Sequencing methods for automated storage and retrieval systems with dedicated storage,” Computers and Industrial Engineering, vol. 32, no. 2, pp. 351–362, 1997, doi: 10.1016/s0360-8352(96)00298-7.
[60] C. Murphy and C. Michelle L.F., “Identification of demand through statistical distribution modeling for improved demand forecasting,” arXiv, pp. 1–14, 2011.
[61] A. Beck, “Simulation: the practice of model development and use,” Journal of Simulation, vol. 2, no. 1, pp. 67–67, 2008, doi: 10.1057/palgrave.jos.4250031.
[62] R. G. Sargent, “Verification and validation of simulation models,” in Proceedings - Winter Simulation Conference, 2010, pp. 166–183. doi: 10.1109/WSC.2010.5679166.
[63] L. Cassettari, F. Currò, M. Mosca, R. Mosca, R. Revetria, S. Saccaro, and G. Galli, “A 4.0 automated warehouse storage and picking system for order fulfillment,” in Proceedings of the World Congress on Engineering, 2021.
[64] M. Baghel, S. Agrawal, and S. Silakari, “Survey of metaheuristic algorithms for combinatorial optimization,” International Journal of Computer Applications, vol. 58, no. 19, pp. 21–31, 2012, doi: 10.5120/9391-3813.
[65] Y. Carson and A. Maria, “Simulation optimization: Methods and applications,” Proceedings of the 1997 Winter Simulation Conference Healy and Kilgore, pp. 118–126, 1997.
[66] F. Azadivar, “A simulation optimization approach to optimum storage and retrieval policies in an automated warehousing system,” in Winter Simulation Conference Proceedings, 1984, pp. 206–214.
[67] L. Ghomri and Z. Sari, “Mathematical modeling of retrieval travel time for flow-rack automated storage and retrieval systems,” in IFAC-PapersOnLine, 2015, pp. 1906–1911. doi: 10.1016/j.ifacol.2015.06.365.
[68] M. Rajković, N. Zrnić, N. Kosanić, M. Borovinšek, and T. Lerher, “A Multi-objective optimization model for minimizing cost, travel time and CO2 emission in an AS/RS,” FME Transactions, vol. 45, no. 4, pp. 620–629, 2017, doi: 10.5937/fmet1704620R.
[69] H. Yılmaz and A. Tuncer, “Genetic algorithm based storage and retrieval system optimization considering operational constraints in a multidimensional warehouse,” International Journal of Applied Mathematics Electronics and Computers, vol. 8, no. 4, pp. 148–153, 2020, doi: 10.18100/ijamec.802125.
[70] K. Lewczuk, “The study on the automated storage and retrieval system dependability,” Eksploatacja i Niezawodnosc, vol. 23, no. 4, pp. 709–718, 2021, doi: 10.17531/ein.2021.4.13.
[71] H. Yu and Y. Yu, “Optimising two dwell point policies for AS/RSs with input and output point at opposite ends of the aisle,” International Journal of Production Research, vol. 57, no. 21, pp. 6615–6633, 2019, doi: 10.1080/00207543.2019.1570377.
[72] X. Li, L. Wang, and X. Zhu, “Simulation and optimization of automated warehouse based on flexsim,” in LISS 2020: Proceedings of the 10th International Conference on Logistics, Informatics and Service Sciences, 2021, pp. 245–261. doi: 10.1007/978-981-33-4359-7_18.
[73] S. Brezovnik, J. Gotlih, J. Balič, K. Gotlih, and M. Brezočnik, “Optimization of an automated storage and retrieval systems by swarm intelligence,” in Procedia Engineering, 2015, pp. 1309–1318. doi: 10.1016/j.proeng.2015.01.498.
[74] D. Arthur and S. Vassilvitskii, “K-means++: The advantages of careful seeding,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 2007, pp. 1027–1035.
[75] Q. Wang, L. Wang, W. Huang, Z. Wang, S. Liu, and D. A. Savić, “Parameterization of NSGA-II for the optimal design of water distribution systems,” Water, vol. 11, no. 5, 2019, doi: 10.3390/w11050971.
[76] P. A. Lachenbruch and J. Cohen, “Statistical Power Analysis for the Behavioral Sciences (2nd ed.).,” Journal of the American Statistical Association, 1989, doi: 10.2307/2290095.
[77] S. Gupta, P. S. Kushwaha, U. Badhera, P. Chatterjee, and E. D. R. S. Gonzalez, “Identification of benefits, challenges, and pathways in E-commerce industries: An integrated two-phase decision-making model,” Sustainable Operations and Computers, vol. 4, pp. 200–218, 2023, doi: 10.1016/j.susoc.2023.08.005.
[78] U. P. Wen, D. Chang, and S. Chen, “The impact of acceleration/deceleration on travel-time models in class-based automated S/R systems,” IIE Transactions, vol. 33, no. 7, pp. 599–608, 2001, doi: 10.1080/07408170108936857.
[79] P. Yang, L. Miao, Z. Xue, and L. Qin, “Optimal storage rack design for a multi-deep compact AS/RS considering the acceleration/deceleration of the storage and retrieval machine,” International Journal of Production Research, vol. 53, no. 3, pp. 929–943, 2015, doi: 10.1080/00207543.2014.942441.
[80] P. Yang, L. Miao, L. Qin, and Z. Xue, “The impact on designing storage rack for a multi-deep compact AS/RS on the speed profile of the storage and retrieval machine,” in Proceedings of 2013 6th International Conference on Information Management, Innovation Management and Industrial Engineering, ICIII 2013, 2013, pp. 209–212. doi: 10.1109/ICIII.2013.6702911.
[81] D. T. Chang, U. P. Wen, and J. T. Lin, “The impact of acceleration/deceleration on travel-time models for automated storage/retrieval systems,” IIE Transactions, vol. 27, no. 1, pp. 108–111, 1995, doi: 10.1080/07408179508936723.
[82] R. Ertl and W. A. Günthner, “Meta-model for calculating the mean energy demand of automated storage and retrieval systems,” Logistics Journal, vol. 2, pp. 9–14, 2016.
[83] X. Xu, Y. Gong, X. Fan, G. Shen, and B. Zou, “Travel-time model of dual-command cycles in a 3D compact AS/RS with lower mid-point I/O dwell point policy,” International Journal of Production Research, vol. 56, no. 4, pp. 1620–1641, 2018, doi: 10.1080/00207543.2017.1361049.
[84] R. D. Meller and A. Mungwattana, “AS/RS dwell‐point strategy selection at high system utilization: A simulation study to investigate the magnitude of the benefit,” International Journal of Production Research, vol. 43, no. 24, pp. 5217–5227, 2005, doi: 10.1080/00207540500215617.
[85] R. R. Barton, “Tutorial: Metamodeling for Simulation,” in Proceedings - Winter Simulation Conference, 2020, pp. 1102–1116. doi: 10.1109/WSC48552.2020.9384059.
[86] A. Parnianifard, A. S. Azfanizam, M. K. A. Ariffin, M. I. S. Ismail, and N. A. Ebrahim, “Recent developments in metamodel based robust black-box simulation optimization: An overview,” Decision Science Letters, vol. 8, no. 1, pp. 17–44, 2019, doi: 10.5267/j.dsl.2018.5.004.
[87] J. C. Chen, T. L. Chen, and Y. C. Teng, “Meta-model based simulation optimization for automated guided vehicle system under different charging mechanisms,” Simulation Modelling Practice and Theory, vol. 106, 2021, doi: 10.1016/j.simpat.2020.102208.
[88] Y. Kuo, T. Yang, B. A. Peters, and I. Chang, “Simulation metamodel development using uniform design and neural networks for automated material handling systems in semiconductor wafer fabrication,” Simulation Modelling Practice and Theory, vol. 15, no. 8, pp. 1002–1015, 2007, doi: 10.1016/j.simpat.2007.05.006.
[89] I. Potrč, T. Lerher, J. Kramberger, and M. Šraml, “Simulation model of multi-shuttle automated storage and retrieval systems,” in Journal of Materials Processing Technology, 2004, pp. 236–244. doi: 10.1016/j.jmatprotec.2004.09.036.
[90] E. C. Harrington, “The desirability function,” Industrial quality control, vol. 21, no. 10, pp. 494–498, 1965.
[91] J. Chen, S. Y. Chou, T. H. K. Yu, Z. U. Rizqi, and D. T. Hang, “System dynamics analysis on the effectiveness of vaccination and social mobilization policies for COVID-19 in the United States,” PLoS ONE, vol. 17, no. 8, 2022, doi: 10.1371/journal.pone.0268443.
[92] N. Boysen and K. Stephan, “A survey on single crane scheduling in automated storage/retrieval systems,” European Journal of Operational Research, vol. 254, no. 3. pp. 691–704, 2016. doi: 10.1016/j.ejor.2016.04.008.
[93] N. Boysen, S. Emde, and K. Stephan, “Crane scheduling for end-of-aisle picking: Complexity and efficient solutions based on the vehicle routing problem,” EURO Journal on Transportation and Logistics, vol. 11, 2022, doi: 10.1016/j.ejtl.2022.100085.
[94] S. Geng, L. Wang, D. Li, B. Jiang, and X. Su, “Research on scheduling strategy for automated storage and retrieval system,” CAAI Transactions on Intelligence Technology, vol. 7, no. 3, pp. 522–536, 2022, doi: 10.1049/cit2.12066.
[95] J. P. Gagliardi, J. Renaud, and A. Ruiz, “On sequencing policies for unit-load automated storage and retrieval systems,” International Journal of Production Research, vol. 52, no. 4, pp. 1090–1099, 2014, doi: 10.1080/00207543.2013.838331.
[96] Z. Chen, X. Li, and J. N. D. Gupta, “Sequencing the storages and retrievals for flow-rack automated storage and retrieval systems with duration-of-stay storage policy,” International Journal of Production Research, vol. 54, no. 4, pp. 984–998, 2016, doi: 10.1080/00207543.2015.1035816.
[97] L. Baardman, K. J. Roodbergen, H. J. Carlo, and A. H. Schrotenboer, “A special case of the multiple traveling salesmen problem in end-of-aisle picking systems,” Transportation Science, vol. 55, no. 5, pp. 1151–1169, 2021, doi: 10.1287/trsc.2021.1075.
[98] H. Hwang and J. Y. Song, “Sequencing picking operations and travel time models for man-on-board storage and retrieval warehousing system,” International Journal of Production Economics, vol. 29, no. 1, pp. 75–88, 1993, doi: 10.1016/0925-5273(93)90025-G.
[99] F. Dallari, G. Marchet, and R. Ruggeri, “Optimisation of man-on-board automated storage/retrieval systems,” Integrated Manufacturing Systems, vol. 11, no. 2, pp. 87–93, 2000, doi: 10.1108/09576060010313937.
[100] H. P. Hsu and C. N. Wang, “Hybridizing whale optimization algorithm with particle swarm optimization for scheduling a dual-command storage/retrieval machine,” IEEE Access, vol. 11, pp. 21264–21282, 2023, doi: 10.1109/ACCESS.2023.3246518.
[101] C. Zhu, Y. Wu, G. Chen, and S. Wu, “Modelling and scheduling for tier-to-tier multi-shuttle warehousing system,” in Journal of Physics: Conference Series, 2021. doi: 10.1088/1742-6596/1871/1/012106.
[102] J. Lu, L. Xu, J. Jin, and Y. Shao, “A mixed algorithm for integrated scheduling optimization in AS/RS and hybrid flowshop,” Energies, vol. 15, no. 20, 2022, doi: 10.3390/en15207558.
[103] F. S. Panchal and M. Panchal, “Review on methods of selecting number of hidden nodes in artificial neural network,” International Journal of Computer Science and Mobile Computing, vol. 3, no. 11, pp. 455–464, 2014.
[104] Z. U. Rizqi, S. Y. Chou, and W. N. Cahyo, “A simulation-based Digital Twin for smart warehouse: Towards standardization,” Decision Analytics Journal, vol. 12, no. 100509, 2024, doi: 10.1016/j.dajour.2024.100509.