1 Introduction

In the recent decades, global pandemics, international conflicts, economic downturns, and other adverse factors have posed significant logistical challenges across various industries. Spurred on by these factors, the transformation set in motion by advancements in information technologies has become an inescapable reality. Moreover, the rising order quantities coupled with decreasing order volumes has emphasized the need for companies to optimize order delivery times and improve customer satisfaction, especially as customers increasingly expect the same-delivery at an affordable cost. Therefore, companies have been compelled to reevaluate and reconfigure their logistics systems and strategies. Consequently, a prominent goal for companies is to innovate and implement faster and more efficient delivery strategies to meet customer expectations and secure a competitive advantage. Accordingly, logistics systems have made significant advancements over the past decade, largely propelled by the emergence and widespread adoption of automated or autonomous systems.

Automated storage and retrieval systems (AS/RSs) were initially employed in Europe and gradually became more prevalent worldwide over time [37]. Nevertheless, alternative systems have gained popularity in recent years, primarily driven by the limited throughput capacity associated with AS/RS, where a single crane manages loads across all vertical levels within a designated storage aisle. The fundamental design characteristics of such an alternative system, the Autonomous Vehicle Storage and Retrieval System (AVS/RS), are detailed in Malmborg [29]. As a result, AVS/RS has attracted attention for its capacity to effectively address and overcome throughput constraints, providing a substantially higher retrieval capacity. Compared to traditional AS/RSs, AVS/RSs offer the advantage of flexibility in allocating varying numbers of autonomous vehicles (AVs) and lifts to align with demand [20]. Furthermore, AVS/RSs provide the distinct advantage of adjusting the locations of AVs according to warehouse needs, facilitating sequential movement in both horizontal and vertical directions. Vertical movement is managed by lifts, while horizontal movement is facilitated by AVs. In contrast to AS/RSs, which typically store uniform palletized products, AVS/RSs enable the storage of items with diverse sizes and types.

Accurate models are crucial for the performance estimation because substantial investment required for the design and implementation of the AVS/RS [5]. As a result, recent research has shown a growing interest in the AVS/RS, with the aim of understanding the impact of various design factors on the performance measures. This study conducts a comprehensive exploration and examination of design factors associated with the AVS/RS, along with performance measures. Accordingly, the purpose of this study is to provide a roadmap for researchers intending to explore topics related to AVS/RS. Therefore, this paper summarizes the existing literature and points out potential directions for future research. The contributions are outlined as follows:

  • A bibliometric analysis is utilized for quantitative analysis to identify trends in publications, distribution of studies, citations per year, and the formation of keywords.

  • A systematic analysis is conducted to provide a comprehensive overview of the current studies by categorizing mathematical and simulation models while emphasizing design factors and performance measures.

This paper is organized into five sections. Section 2 outlines the research methodology including paper selection process and filtering techniques. Section 3 presents bibliometric and bibliographic information about the studies. Section 4 provides a comprehensive overview of studies, summarizing key design factors or performance measures found in the existing literature concerning mathematical or simulation models. The last section concludes the paper and offers suggestions for future research.

2 Methodology

A systematic literature review is a robust method for conducting a comprehensive and unbiased examination of a research topic. Such a review encompasses all accessible studies by applying specific search criteria in relevant databases. Moreover, enhanced reliability in results can be achieved with a transparent and reproducible analysis that remains unaffected by subjective judgments. Therefore, it becomes possible to gain a comprehensive understanding of the existing knowledge within the relevant field, detect emerging trends and unveil potential avenues for further research.

This section provides an overview of the studies in the literature, the methods employed to access to these studies, and the results of the bibliometric analysis conducted on the selected studies. We conduct a comprehensive review of articles focusing on AVS/RS. To do so, we examine studies published between 2002 and 2023 by utilizing the Scopus database. Following an eight-level research screening process (see Fig. 1), we include articles and book chapters written in English among the studies published during this timeframe. We further categorize the studies into different methodology groups. The selected articles within the scope of this study are then subjected to a bibliometric analysis, exploring various aspects such as trends, distribution patterns, citations, and keywords in the studies.

Fig. 1
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The flow of methodology process

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In the study, the first step was to define the scope of the research, followed by the consideration of all relevant keywords. During this process, the Scopus database was examined, and the keywords were refined through simultaneous checks. After defining the research scope, all relevant keywords were taken into consideration. Subsequently, a search was conducted using different combinations of the identified keywords in accordance with the search criteria. All articles obtained throught the database search were read, and summaries were prepared. Eventually, the database research, article examination, and classification processes were integrated. Moreover, tables were created to facilitate both the examination of the selected articles and comprehension for the reader. The inferences drawn from these tables were used to evaluate research gaps for future studies, ultimately concluding the reviewing process. The study’s workflow is summarized in Fig. 1.

2.1 Determining the Scope of Study

The first step involves identifying the articles to be reviewed in relation to the scope of the research. To access the relevant literature covering the subject of this article, a search is performed in the Scopus database by entering the keywords “autonomous” AND “storage-retrieval” OR “storage/retrieval” OR “storage retrieval” OR “storage and retrieval”. The Scopus database is opted in our research due to its extensive access to peer-reviewed articles and book chapters. The chosen keywords are set to search within the title, abstract, or article keywords, ensuring the retrieved studies are directly related to AVS/RS rather than referencing these terms briefly.

2.2 Determination of Research Criteria

A four-criteria approach is employed to examine and understand the literature in detail, with a specific focus on identifying original and innovative aspects within the studies.

  1. 1.

    Identification: the scope of the study is specified. Hence, specific keywords are entered to be searched in the title, abstract, and keywords, rather than conducting a general search.

  2. 2.

    Screening: the type and time frame of publication to be included are established. Conference proceedings, review papers and short surveys are excluded from the search results, and only studies published from 2002 onwards are considered.

  3. 3.

    Eligibility: studies are evaluated based on their abstracts. Articles that are pertinent to the research topic are included from the accessed articles.

  4. 4.

    Inclusion: the selected studies are thoroughly read and examined. The articles are chosen for a comprehensive examination and analysis.

Figure 2 provides a visual representation of the criteria utilized for selecting the studies included in the review article from the Scopus database. This method serves as an effective approach to guarantee the careful selection of studies and to improve the reliability of the research.

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Selection criteria employed for studies featured in the review article

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3 Bibliometric Analysis

Bibliometry is a method commonly used to gain a comprehensive perspective, particularly in systematic literature reviews [7]. On the other hand, bibliometric analysis is a research method that employs quantitative analysis to examine various characteristics of studies within a specific field. This includes the analysis of features such as journals, subjects, the number of authors, and publication information [2].

In this section, a quantitative analysis and data visualization of the studies are presented based on the number of publications per year, publication types, the distribution of studies across journals and countries of publication, the number of citations received by the studies, connections among authors working in the field, and keyword analysis criteria.

3.1 Number of Publications by Years

The yearly publication numbers of the selected studies on AVS/RS between 2002 and 2023 are presented in Fig. 3. As can be seen from the figure, the first study on AVS/RS was published in 2002. It appears that no articles were published directly with AVS/RS between 2004 and 2006. This may be because the shuttle-based storage and retrieval system (SBS/RS) was more popular during those years, and there was insufficient information available about the AVS/RS. Only 1 article was published in 2007, then the number of studies increased and the average number of studies increased to 2 per year in 2008 and 2009. Between 2010 and 2014, the number of articles was 2 or 4. It is seen that the number of publications on AVS/S decreased after 2015. The reason for this decrease, in addition to the previous reasons, may be the prolongation of the publication process of articles or the shift of interest in the AVS/RS system to a different field. There was an increase in the number of publications in 2019. 3 articles were published in 2021. Although there has been a decrease in the number of studies on an annual basis in some years, it can be said that interest in AVS/RS continues in the academic field in general.

Fig. 3
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Article published by years

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3.2 Distribution of Studies According to Journals and Countries of Publication

The charts presented in Figs. 4 and 5 are prepared with a focus on the number of publications in each journal and the countries in which the selected articles were studied. As seen in Fig. 4, a total of 44 articles were published across 13 different journals. The majority of these studies (33%) appeared in the ‘International Journal of Production Research,’ followed by ‘International Journal of Advanced Manufacturing Technology’ at 9% and ‘European Journal of Operational Research’ at 7%.

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Distribution of articles by journals published

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Fig. 5
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Distribution of studies by country

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When we look at the countries based on the corresponding authors of the articles, as illustrated by the treemap in Fig. 5, the ‘United States of America’ leads the way, making the most significant contributions to the literature with 15 studies. The figure clearly demonstrates the global interest in AVS/RS through the number of academic studies conducted by each country. Following the United States of America, ‘Italy’ has contributed with 8 studies, ‘Turkey’ with 6 studies, and ‘India’ with 6 studies, making substantial contributions to the field.

3.3 Citations Analysis

The graph containing the total number of citations received by 44 academic studies is given in Fig. 6. As can be seen from the figure, studies started to receive citations after the year they were first published. It can be said that the number of citations of the studies increased with the increase in the popularity of AVS/RS.

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Total and cumulative citation numbers of studies by years

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Upon analyzing the citation numbers presented in Fig. 7, it is evident that Malmborg’s [29] pioneering work on AVS/RS stands out as the most frequently cited study. This observation underscores the enduring relevance and foundational nature of Malmborg’s [29] research. Subsequent to Malmborg [29], Kuo et al. [26] and Marchet et al. [33] emerge as the most cited studies, highlighting the lasting impact of queueing network methodologies, especially in the context of cycle time estimation. While there is a slight decrease in citation numbers for newer studies, the cumulative citations over the years reveal a consistent upward trend (see Fig. 6). Consequently, it can be inferred that interest in AVS/RS technology remains robust.

Fig. 7
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Citation numbers of published articles (Scopus)

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3.4 Relationship Diagrams of Authors and Keywords

The relationship diagram showing the connections of the authors working on the subject is given in Fig. 8. As seen in the relationship diagram, most of the studies in the literature were done by C.J. Malmborg, S.S. Heragu and B.Y. Ekren and these authors have published work with each other to contribute to the development of AVS/RS. Apart from these authors, D. Roy, I. Zhang, P. Kuo, T. Lerher, X. Cai and M. Fukunari are also authors who have contributed significantly to the literature.

Fig. 8
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Relationship diagram of the authors working on the subject (produced with VOSviewer)

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Utilizing 44 selected articles for analysis, the diagram in Fig. 9 is created to illustrate the connections between keywords. The terms most frequently used in the network map, as generated with VOS Viewer, include ‘autonomous vehicle storage and retrieval system,’ ‘simulation,’ and ‘storage and retrieval’.

Fig. 9
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Keyword formation and relationship map (produced with VOSviewer)

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In network visuliation, the size of the circles indicates the density of the keyword, and the proximity of the keywords indicates the strength of the relationship between them. In studies on AVS/RS, it is seen that the strongest keyword is “autonomous vehicle storage and retrieval system”. Moreover, it can be said that it has an intense relationship with many keywords such as “storage and retrieval”, “autonomous vehicles” and “AVS/RS”.

4 Literature Analysis

A total of 44 studies related to AVS/RS are reviewed and organized into two categories depending on their solution approaches, namely Analytical and Simulation Models. Moreover, these studies are scrutinized based on performance measures, along with the physical and operational design factors.

Typically, physical design factors consist of four key aspects. Among these, the performance of an AVS/RS system is notably relient on the storage capacity (NS). Depending on the value of NS, various rack configurations are taken into consideration. When exploring alternative AVS/RS designs, most studies evaluated the system performance as a function of the rack configuration. Accordingly, different number of lanes in an aisle (Single, S or Multiple, M), aisles (A), columns or bays (C), tiers (T), zones in a tier (Z) are evaluated to find the optimal rack configuration. Additionally, researchers investigate various rack width, length and height to determine the optimal rack dimensions (R). Last but not the least, alternative layout (LC) and input/output point configurations (PC) are compared.

In accordance with the physical design factors, the operational design factors primarily concentrate on four key aspects. Within these aspects, the AVS/RS performance is assessed under various arrival rates (AR) for storage and/or retrieval operations. Depending on the number of operations executed within each cycle, single-command (either a single storage or retrieval operation is performed in a cycle, SC), dual-command (a storage operation is paired with a retrieval operation in a cycle, DC) or a combination of both commands is investigated. Depending on the vehicle assignment to tiers, vehicles can either access any aisle in any tier (Tier-To-Tier, T-T) or a specific tier (Tier-Captive, T-C). Moreover, vehicle assignment policy will impact the number of vehicles (NV) or lifts (NL) in the system. In addition to NV and NL, the acceleration/decelaration rate (AD) of vehicles or lifts is taken into consideration. Furthermore, several dwell point (DP) policies are studied to determine where idle vehicles or lifts should be positioned after the completion of each operation cycle. Different storage policies (SP) are implemented to assign Unit-Loads (ULs) to storage locations. Finally, task scheduling (TS) is considered to reduce the overall task completion time.

Identifying the impact of physical and/or operational design factors, several performance measures are taken into account. In the vast majority of research efforts, the key performance measure revolves around time minimization (TM), specifically focusing on cycle time or throughput (which represents the inverse of the cycle time). Besides TM, many studies also contemplate economic (CM–cost reduction), energy-related (EM–energy conservation), and environmental objectives (EIM–environmental impact mitigation), although not as frequently. In addition to the objectives of analytical models, additional information is available in queueing models, emphasizing resource utilization (RU) and the reduction of queue lengths (QL) or waiting times (WT).

The detailed results of the reviewed literature based on the design factors (physical or operational) and performance measures are presented in the following two subsections. While the former subsection focuses on the examination of mathematical models, the latter section delves into the detailed exploration of simulation models.

4.1 Mathematical Models

Mathematical models are frequently used to assess the impact of various design factors on the performance measures. Typically, models are expressed through equations, formulations, or algorithms. When developing models, the initial step involves a precise definition of the problem, along with clearly stated assumptions and important factors like variables and parameters. Following the initial step, expressions are formulated to represent the relationships among important factors. After ensuring the accurate representation of the model to real system, constraints are imposed to limit the solution space. Then, the model is solved either analytically or numerically. Eventually, the model is validated and verified by simulation (VbS) models or real data (VbR) obtained from material handling providers. This section provides an in-depth review of studies utilizing mathematical models for the analysis of the AVS/RS performance.

Malmborg [29] was recognized as the first researcher who led the way in analyzing the performance of an AVS/RS. He developed mathematical models based on state equations to estimate how efficiently the AVS/RS utilizes vehicles and handles its throughput capacity for SC or DC operations. His analysis took into account various design factors, the number of aisles, columns, tiers, vehicles and lifts. Taking cost factors into consideration, Malmborg 30 proposed an integrated model to evaluate the trade-offs between system cost and performance measures while adhering a budget limitation. Malmborg 31 extended his early models by predicting the proportion of DC operations to evaluate SC/DC cycle times and vehicle utilization for alternative AVS/RS design configurations. Highlighting the ecological impact of autonomous warehouses, Tappia et al. [43] observed that the evaluation of the environmental performance of automated warehouses was deficient. Accordingly, they proposed a mathematical model to evaluate the energy consumption and environmental impact of the AVS/RS. Manzini et al. [32] introduced a collection of mathematical models for deep-lane AVS/RS with the aim of calculating travel distance or time by considering alternative layout and design configurations. D’Antonio et al. 6 incroporated the allocation criteria as a variable within the model to achieve a more precise estimation of both the average and variability of cycle time. Moreover, they considered the capability of both the shuttle and the satellite to concurrently execute different tasks and move multiple ULs. D’Antonio and Chiabert 5 evaluated the operational efficiency of the AVS/RS with a lift and various number of shuttles, as they interacted with a rack of arbitrary depth. Lerher et al. [28] developed SC/DC travel time models to evaluate various rack configurations in an AVS/RS with multi-level shuttle, which possesses the capability to move both horizontally and vertically across multiple levels within each tier.

Mathematical models suffers to offer additional insights into waiting times, queue lengths, and related performance measures. Therefore, numerous papers employed queuing theory to provide additional information. Indeed, queuing network (QN) models are employed to encompass a collection of service stations in the AVS/RS. Several studies explored nested QN (NQN) models, in which queues for certain resources are nested within queues for other resources. It is worth noting that the AVS/RS exhibits characteristics of both open and closed QN (OQN and CQN) since storage or retrieval requests come from the outside and eventually leave the system; whereas, incoming requests are constrained by the availability of resources to handle them. Therefore, a significant portion of research focused on semi-open QN (SOQN).

Kuo et al. [26] introduced an NQN model to predict task waiting times, cycle durations and resource utilization. They envisioned the vehicle system using a queuing model, where tasks were regarded as customers and vehicles as service stations. Within this framework, they further embedded a distinct lift queueing system, where vehicles were treated as customers and lifts functioned service stations. Fukunari and Malmborg [20] enhanced earlier models by incorporating opportunistic interleaving, which involved pairing storage and retrieval tasks to improve the overall system performance. Acknowledging the shortcomings of earlier models in estimating task waiting times, Zhang et al. [45] proposed an approach to select between queueing approximations based on the variability in task inter-arrival times. In a follow-up paper, Zhang et al. [46] relaxed the constraint of having an equal number of lifts to the number of vehicles.

Heragu et al. [23] developed an OQN model to compare the performance of AS/RS with AVS/RS. They utilized a manufacturing performance analyser (MPA) tool to solve their models and emphasized the effectiveness of mathematical models compared to simulation in rapidly evaluating hundreds of alternative configurations. Marchet et al. [33] devised a model for the effective estimation of the average cycle time, which encompassed both traveling times for vehicles and lifts as well as waiting times for lifts. Ozaki et al. [36] proposed a quantitative assessment method for designing the AVS/RS while considering operational constraints such as group shipments, buffer sizes, and task fluctuations. Epp et al. [18] introduced a discrete-time OQN approach for deriving not only expected values and variances but also quantiles of performance measures. They observed a high level of accuracy with their models in system configurations with Poisson arrivals. Despite the lower approximation quality with non-Poisson arrivals, their approach yielded lower average errors compared to the MPA.

Kuo et al. [27] asserted that implementing a class-based storage policy is a practical solution for addressing slow lift movements, as it reduces the extent of vertical travel. Therefore, they proposed a CQN model to investigate the effect of demand skewness on cycle time while incorporating alternative class-based storage policies. Fukunari and Malmborg [21] introduced a model to estimate the reseource utilization by determining the proportion of single- and dual-command operations based on their operating assumptions. Zou et al. [47] investigated the impact of parallel processing policy, wherein a lift and a vehicle can concurrently perform a task simultaneously instead of doing so sequentially.

Ekren and Heragu 12 introduce a SOQN model functioning as an intermediary approach between OQN and CQN. Accounting for situations where a task might need to wait for a resource or vice versa, their model yielded more precise results. In addition to investigating various design factors, they also conducted a simulation-based regression analysis for different rack configurations. Roy et al. [40] constructed a model for a single tier to investigate trade-offs associated with three key design decisions: tier configuration, the vehicle assignment rule and equal or unequal zone formations. Ekren et al. [15] proposed an analytical approximate solution procedure aimed at rapidly and efficiently evaluating alternative design configurations. Treating different storage/retrieval tasks as different classes of customers, Cai et al. [4] developed a multi-class SOQN, where each customer class adhered to a predetermined path and each server had its own set of customer classes. Ekren et al. [16] introduced a model built upon three stations within the network. To make use of a matrix-geometric method (MGM) solution, they streamlined the network by merging the last two stations, as the MGM solution becomes unattainable when dealing with a network comprising more than two stations. Consequently, they employed the MGM solution on the reduced network to investigate various warehouse configurations. Considering the occurrence of blocking within an aisle, cross-aisle, and at the intersection of an aisle and cross-aisle, Roy et al. [41] analyzed the impact of blocking delays in a tier on cycle time while implementing protocols to regulate the use of aisles and cross-aisles. Roy et al. 38 developed models for a single tier to explore the selection of vehicle dwell-point locations and cross-aisle position. Roy et al. 39 expanded their early models to evaluate the performance of a conveyor-based multi-tier AVS/RS, employing conveyors to connect individual tiers to each other. In a follow up study, Roy et al. [42] broadened their previous research to evaluate the performance of a tier-captive AVS/RS, employing either a lift and a conveyor system as the vertical transfer mechanism. They developed an integrated model by combining SOQN models for travel within individual tiers with an OQN for the vertical transfers between tiers.

Task Scheduling is yet another crutial operational factor to improve the efficiency of the AVS/RS and minimize the overall time required to complete storage/retrieval tasks. Despite its significance, task scheduling problem garnered relatively little attention from the research community. Fang and Tang [19] tackled the task scheduling problem in an AVS/RS and devised an optimization model. Recognizing the inherent complexity of scheduling problems, they introduced an enhanced artificial fish swarm algorithm (IAFSA) for the solution of large-sized problems. Yu et al. 44 developed a mixed integer programming model to establish the order sequence in which lifts and vehicles retrieve items. They proposed a dynamic programming approach for small-sized problems. Proving the NP-hardness of the problem, they suggested a beam search heursitic to achieve nearly optimal solutions for large-sized problems within a reasonable timeframe.

In summary, Table 1 provides an overview of the connections between design factors (physical and operational) and performance measures studied in the aformentioned research by using mathematical models.

Table 1 A summary of the research employing mathematical models
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Previous studies predominantly focused on single-lane storage racks within the physical design aspect of the AVS/RS, examining different rack configurations such as the number of aisles, columns or bays, and tiers for varying storage capacities. However, limited attention has been given to multi-lane storage rack configurations. Moreover, a small number of studies have explored the limitation of resources to specific zones. Clearly, there is a need for further exploration of different rack dimensions, layout configurations, as well as the number and locations of input/output points.

When considering the operational design aspect, the majority of studies explored varying arrival rates for storage/retrieval transactions, with a notable emphasis on both single- and dual command cycles. Apparently, tier-to-tier designs have garnered more attention compared to tier-captive designs. While the number of vehicles and lifts has been well-studied, the aspects of acceleration and deceleration have often been overlooked. It’s evident that additional research efforts should be directed towards exploring policies like DP, SP and TS to obtain deeper insights.

Regarding performance measures, the primary focus of most researchers has been on time minimization. Nonetheless, there have been a few studies that consider other factors like CM, EM and EIM. It is crucial to further advance research in these alternative performance measures. Queueing network models have been extensively used to examine resource utilization, as well as parameters like QL and WT. However, it’s important to note that the solutions of some models are approximated, and certain studies have documented substantial percentage errors. Therefore, there is a need to explore more precise approaches.

4.2 Simulation Models

Analytical models are favored over simulation models in the physical design process because the former allow the assessment of numerous warehouse configurations efficiently. However, analytical models are often deemed inadequate for fully capturing the complexity inherent in the AVS/RS. Therefore, an approach based on simulation techniques is preferred. We acknowledge that simulation will ultimately be required to validate the effectiveness of the chosen configuration. Although many studies have employed simulation models to validate analytical models, some researchers have utilized simulation models to explore the influence of design factors on performance measures for a limited range of designs.

Ekren et al. [14] conducted a simulation-driven experimental study with the aim of identifying the most effective combinations of design factors, including PC, SC/DC, DP and ST. Selecting the best combination of the number of vehicles and lifts from a pre-defined set of scenarios, they implemented the principles of design of experiments (DOE) to determine the relative significance of the design factors and their interactions across various arrival rates. Ekren [8] delved into further performance measures, including waiting times and queue lengths, across a range of pre-defined design scenarios. Additionally, they conducted assessments of the system cost associated with each of these design scenarios. Ekren and Heragu [11] carried out a performance analysis through simulation model to explore how predetermined rack configurations relate to various combinations of vehicle/lift numbers in terms of cycle time and resource utilization. In an extension of their previous research, Ekren and Heragu 13 performed a comparative analysis of the AVS/RS and AS/RS by considering cost, cycle time and resource utilization across two different arrival rate scenarios. Marchet et al. [34] assessed performance measures in a tier-captive AVS/RS and compared design outcomes with the AVS/RS featuring a tier-to-tier configuration. Kumar et al. [25] introduced a zone-captive AVS/RS by combining the characteristics of both tier-to-tier and tier-captive configurations. Moreover, they investigated the impact of zoning in both horizontal and vertical directions. Unlike previous studies, Akpunar et al. [1] focused on evaluating various designs with the objective of minimizing the energy consumption per task in the AVS/RS. Taking into account the implementation of regenerative braking systems in lifts to recapture energy during braking, Taking into account the incorporation of regenerative braking systems in lifts for energy recovery during breaking, Guerrazzi et al. [22] evaluated the energy performance in a deep-lane AVS/RS. Ekren [9] proposed a multi-objective optimisation to jointly optimize vehicle utilization and energy consumption per task. Noting the absence of a single solution to optimize both objectives simultaneously, pareto-optimal solutions were presented to quantify the trade-offs between objectives. Jerman et al. [24] introduced a new AVS/RS design featuring movable lifts as an alternative to traditional aisle-captive lifts. They performed simulations with various rack configurations and vehicle quantities while eximining two alternative input/output location designs. Considering random, depth-first and nearest neighbour assignment strategies for storage/retrieval operations, Marolt et al. [35] evaluated nine different combinations of strategies for five different multiple-deep aisle-captive AVS/RS designs. Further, they explored the impact of varying occupancy levels in multi-deep lanes. Ekren et al. [17] formulated collision prevention regulations for both vehicles and lifts within an AVS/RS design with movable lifts.

Ekren and Heragu [10] conducted a simulation-based regression analysis to investigate different rack configurations under three vehicle/lift combination and two demand rate scenarios. Their objective was to gain a deeper understanding of the relationship between performance measures and design factors. Finally, going beyond the limitations of both analytical and simulation-based methods, Battara et al. 3 introduced a hybrid model by combining an analytical approach to evaluate travel times for storage/retrieval tasks with a simulation-based approach to analyze interactions among various components of a deep-lane multi-satellite AVS/RS system. In essence, Table 2 presents a summary of the relationships between design factors and performance measures investigated in the aforementioned research, utilizing simulation models.

Table 2 A summary of the research employing simulation models
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Different from mathematical models, the majority of studies have predominantly centered on a restricted range of storage capacity and rack configurations, frequently exploring various predefined quantities of aisles, columns, or tiers. Nonetheless, only a scant number of studies have investigated the multi-lane storage racks, and none have taken into account the dimensions of the storage racks. As with mathematical models, there is a necessity for more in-depth exploration of alternative layout configurations, including various designs for number and placement of input/output points. In contrast to mathematical models, a significant number of studies have addressed the aspects of acceleration and deceleration. Last but not least, it is evident that research efforts should be directed toward the examination of operational policies and other performance metrics.

4.3 Density Map of Studies

The studies examined in this article are analyzed based on Physical Design Factors, Operational Design Factors, Performance Measures, and employed Methodologies. The density map of these studies, illustrating the frequency of factors, measures or methodologies within the reviewed papers, is presented in Fig. 10. The total column at the bottom of the figure indicates the frequency of design factors and performance measures, while the rightmost column shows the frequency of usage of the respective methodologies employed. A color scale from green to red is applied to this density map, and the number of occurrence for each criterion are displayed in the respective cell. Consequently, a green-colored or low-numbered cell signifies that the associated criterion is not utilized at all, whereas a dark red color or a large number indicates its most frequent usage.

Fig. 10
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Density map of studies

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In the realm of physical design factors, the Single (S) rack configuration with Aisle (A) and Column/Bay (C) structures stood out as the most favored choices. Conversely, Rack Dimension (R), Layout Configuration (LC), and Input/Output Point Configuration (PC) were among the less frequently employed physical design factors. Shifting focus to operational design factors, Single Command (SC) and Arrival Rate (AR) emerged as the top preferences, while Dwell Point Policy (DP), Storage Policy (SP), and Task Scheduling (TS) were found to be less favored. Regarding performance outcomes, Time Minimization (TM) and Resource Utilization (RU) took the lead as the most preferred metrics. In contrast, Energy Minimization (EM) and Environmental Impact Minimization (EIM) were identified as the least utilized criteria.

Upon analyzing the methodologies employed, it becomes apparent that the Simulation and Semi-Open Queueing Network approach is the most frequently utilized. In contrast, the Improved Artificial Fish Swarm Algorithm, Dynamic Programming, and Beam Search methods are observed to be the least commonly applied techniques.

5 Conclusion

This paper presents an extensive review of research dedicated to autonomous vehicle storage and retrieval systems (AVS/RS) and conducts a comprehensive analysis of current studies to identify potential future research directions. Relying on a bibliometric analysis, this study places a strong emphasis on quantitative aspects, including trends in studies, distribution patterns, citations, and keywords used in publications. Concurrently, the systematic analysis examines papers while considering design factors and performance measures based on the modeling approaches employed.

This literature review paper serves as a guiding resource for academicians, providing directions for their upcoming research endeavors. Simultaneously, it offers collective information for professionals engaged in Autonomous Vehicle Storage and Retrieval Systems (AVS/RS), including warehouse service providers, designers, and managers. For researchers, it establishes a theoretical framework, laying the groundwork for identifying gaps and facilitating the comparison of methodologies in future studies. Warehouse service providers can access collective information about theoretical studies for the implementation of future AVS/RSs. Designers will find valuable references for comparing physical design configurations, while warehouse managers can compare the performance of their current design factors with other operational design factors. Fundamentally, this comprehensive literature review serves as a pivotal resource, offering valuable insights that not only inform but also guide and propel researchers in academia to explore new research avenues and professionals in business to optimize the physical and operational designs of AVS/RS.

Our review reveals that multi-lane storage rack configurations have received limited attaention, and only a small number of studies have explored the allocation of resources to specific zones. Clearly, there is a need for additional research to explore different rack dimensions, layout configurations, as well as the number and placement of input/output points. Although the aspects of acceleration and deceleration have been extensively explored through simulation models, there is a demand for mathematical models in this domain. Further research efforts should be channeled into exploring operational policies for dwell point, storage and task scheduling to gain a more profound understanding. A vital requirement is to advance research in alternative performance measures, including the minimization of cost, energy, and environmental impact.