Modeling parallel movement of lifts and vehicles in tier-captive vehicle-based warehousing systems

This paper models and analyzes tier-captive autonomous vehicle storage and retrieval systems. While previous models assume sequential commissioning of the lift and vehicles, we propose a parallel processing policy for the system, under which an arrival transaction can request the lift and the vehicle simultaneously. To investigate the performance of this policy, we formulate a fork-join queueing network in which an arrival transaction will be split into a horizontal movement task served by the vehicle and a vertical movement task served by the lift. We develop an approximation method based on decomposition of the fork-join queueing network to estimate the system performance. We build simulation models to validate the effectiveness of analytical models. The results show that the fork-join queueing network is accurate in estimating the system performance under the parallel processing policy. Numerical experiments and a real case are carried out to compare the system response time of retrieval transactions under parallel and sequential processing policies. The results show that, in systems with less than 10 tiers, the parallel processing policy outperforms the sequential processing policy by at least 5.51 percent. The advantage of parallel processing policy is decreasing with the rack height and the aisle length. In systems with more than 10 tiers and a length to height ratio larger than 7, we can find a critical retrieval transaction arrival rate, below which the parallel processing policy outperforms the sequential processing policy.

[1]  Charles J. Malmborg,et al.  Variance-based approximations of transaction waiting times in autonomous vehicle storage and retrieval systems , 2009 .

[2]  Yang Liu,et al.  Modeling and evaluating the AVS/RS with tier-to-tier vehicles using a semi-open queueing network , 2014 .

[3]  Charles J. Malmborg,et al.  A network queuing approach for evaluation of performance measures in autonomous vehicle storage and retrieval systems , 2009, Eur. J. Oper. Res..

[4]  Charles J. Malmborg,et al.  Simulation based experimental design to identify factors affecting performance of AVS/RS , 2010, Comput. Ind. Eng..

[5]  Charles J. Malmborg,et al.  Design models for unit load storage and retrieval systems using autonomous vehicle technology and resource conserving storage and dwell point policies , 2007 .

[6]  Debjit Roy,et al.  Performance analysis and design trade-offs in warehouses with autonomous vehicle technology , 2012 .

[7]  Wen-Jing Hsu,et al.  Travel time analysis of a new automated storage and retrieval system , 2005, Computers & Operations Research.

[8]  T. Altiok On the Phase-Type Approximations of General Distributions , 1985 .

[9]  Charles J. Malmborg,et al.  Analytical models for analysis of automated warehouse material handling systems , 2011 .

[10]  Arnold O. Allen,et al.  Probability, statistics and queueing theory - with computer science applications (2. ed.) , 1981, Int. CMG Conference.

[11]  Charles J. Malmborg,et al.  Matrix-geometric solution for semi-open queuing network model of autonomous vehicle storage and retrieval system , 2014, Comput. Ind. Eng..

[12]  Charles J. Malmborg,et al.  Design optimization models for storage and retrieval systems using rail guided vehicles , 2003 .

[13]  Charles J. Malmborg Conceptualizing tools for autonomous vehicle storage and retrieval systems , 2002 .

[14]  Gunter Bolch,et al.  Queueing Networks and Markov Chains - Modeling and Performance Evaluation with Computer Science Applications, Second Edition , 1998 .

[15]  Tone Lerher Travel time model for double-deep shuttle-based storage and retrieval systems , 2016 .

[16]  Zaki Sari,et al.  SIMULATION ANALYSIS OF SHUTTLE BASED STORAGE AND RETRIEVAL SYSTEMS , 2015 .

[17]  Debjit Roy,et al.  Queuing models to analyze dwell-point and cross-aisle location in autonomous vehicle-based warehouse systems , 2015, Eur. J. Oper. Res..

[18]  Debjit Roy,et al.  Modeling, Analysis, and Design Insights for Shuttle-Based Compact Storage Systems , 2015, Transp. Sci..

[19]  Goran Dukic,et al.  Travel time model for shuttle-based storage and retrieval systems , 2015 .

[20]  Jing Jia,et al.  Solving Semi-Open Queuing Networks , 2009, Oper. Res..

[21]  Charles J. Malmborg Interleaving dynamics in autonomous vehicle storage and retrieval systems , 2003 .

[22]  Gino Marchet,et al.  Development of a framework for the design of autonomous vehicle storage and retrieval systems , 2013 .

[23]  Gino Marchet,et al.  Analytical model to estimate performances of autonomous vehicle storage and retrieval systems for product totes , 2012 .

[24]  Charles J. Malmborg,et al.  An efficient cycle time model for autonomous vehicle storage and retrieval systems , 2008 .