Balancing picking and outbound loading efficiency in an SBS/RS through a digital twin

Abstract

Warehouses are essential elements of almost every Supply Chain and have a significant impact on its performance. However, existing research on warehouse operations mainly aims at maximizing operational performance, neglecting their effect on downstream nodes. In this paper, we propose the use of a digital twin (DT) to support warehouse managers to identify the picking policy that most effectively balances picking and outbound loading efficiencies in an SBS/RS, with the aim of providing both a cost-effective and timely delivery to the subsequent nodes. The problem is set referring to a real case study of the logistics hub of a tire distributor company. The DT was built and validated based on real data from plant sensors and information systems. Afterwards, the DT was used to define three picking strategies that differently impact on both picking and outbound loading efficiency. The DT was then employed on a daily basis and fed with real orders, machine and rack availability to replicate stocking and picking operations and to directly communicate the recommended picking strategy to the warehouse PLC. Several demand scenarios have been considered to extend managerial inferences. Results show that the DT is a valuable tool to support the balancing of picking and outbound loading performance.

1 Introduction

Warehouses are crucial for most of the supply-chains (SCs) as they are utilized to meet the growing demand for better service and rapid responses (Roodbergen et al. 2015; De Koster et al. 2017; Kumar et al. 2021). Despite their strategic importance, studies on warehousing activities have predominantly focused on a localized operational level, examining aspects such as cycle time, energy consumption, and investment/operating costs (Staudt et al. 2015), overlooking how they impact on subsequent nodes in the SC (Beamon 1999; Richey et al. 2009; Laosirihongthong et al. 2018).

Nevertheless, with the growing complexity of SC networks, as well as a greater pervasiveness and shareability of data (Ghadge et al. 2020), it is even more relevant and possible to integrate the different goals of the actors (i.e., manufacturing facilities, suppliers, warehouses, retailers, customers etc.) (Wu and Dong 2008; Dominguez et al. 2022) with a broader view of the SC (Cao et al. 2023) in order to improve its resilience (Li et al. 2017) and overall performance (Matopoulos et al. 2007; Mellat-Parast and Spillan 2014).

In this context, logistics hubs play a central role in efficiently coordinating material flows within the SC. Indeed, they are increasingly utilized to serve customers directly or via warehouses across an extensive geographical area (Ghaffari-Nasab et al. 2015).

Logistics hubs serve both multiple customers and other smaller warehouses characterized by minor throughput that usually rely on human operators (Loske 2022) due to the economic convenience compared to automation, particularly in contexts with lower volumes (Richards 2017; Fager et al. 2021), as well as due to the high flexibility demanded by material handling tasks (Vanheusden et al. 2023), which robotic machines struggle to replicate with ease and precision (Winkelhaus et al. 2021). However, in such smaller and manual warehouses the material handling activities are more time-consuming, more prone to human errors or inefficiencies and, therefore, require higher operational costs (Setayesh et al. 2022).

Consequently, logistics hubs are called to provide a cost-effective picking that ensures timely delivery to customers (Gocer and Sener 2022), as well as streamlining deliveries to manual warehouses to support human operators in the receiving and stocking processes. Indeed, optimizing the outbound loading, i.e., the process of loading items onto transportation vehicles, is recognized to reduce the overall costs in the SC (Choy et al. 2014; Díaz-Madroñero et al. 2014; Tadumadze and Emde 2022).

The efficiency of outbound loading depends on the sequence in which items arrive at the outbound loading area, namely the shipping area. Such sequence is, in turn, determined by several factors, including the scheduling of picking operations and the warehouse technology.

Systems with a high degree of parallelization of picking activities, such as the increasingly adopted Shuttle-Based Storage and Retrieval Systems (SBS/RS), are indeed known to require well-structured scheduling of their concurrent activities (Battarra et al. 2022). Indeed, they have a heightened risk of encountering an inefficient sequence of ULs at the outbound loading area, as visible in Fig. 1.

Fig. 1

Front (a) and top view (b) of an SBS/RS with a closed-loop sorting system

To face this issue, fully-automated sortation systems (Boysen et al. 2018) are commonly employed to effectively separate and/or merge items directed towards trucks. These systems may rely on flexible autonomous mobile robots when dealing with a high variety of items and the need to enhance flexibility and scalability in the sorting area (Boysen et al. 2023), or on traditional closed-loop conveyors for the majority of warehousing applications (Boysen et al. 2019a). In Fig. 1, a closed-loop sortation system is used to correctly dispatch ULs retrieved from the SBS/RS to the outbound trucks. However, these systems may not be able to avoid bottlenecks at the shipping area when there is a very large number of ULs to be handled. Furthermore, the implementation of a large sortation system entail a significant capital investment in the loop conveyor infrastructure and require a considerable allocation of physical space (Boysen et al. 2018).

Hence, in contexts characterized by high throughput and diversity of customers, it is necessary to design strategies that balance the need for timely deliveries while maintaining reasonable overall material handling costs (Zhong et al. 2022).

Given the lack of empirical evidence on this topic and with the high complexity of such a system, this study is based on a Digital Twin (DT) developed in a real case study to balance picking and outbound loading efficiency in an SBS/RS.

Despite the majority of SBS/RS studies employ standalone simulation techniques or analytical modeling as research methods (Eder 2019), we opted to leverage on DT technology due to its ability to be updated by the real world thus achieving greater accuracy in replicating complex systems that require ultrafidelity to correctly reflect the state of its physical twin and consequently to better support timely decision-making (Tao et al. 2019). Indeed, potential changes in machine status (e.g., faults), racks accessibility, and order policies make the DT a more advanced and reliable tool compared to simulation alone (Kuhl et al. 2022).

To the best of our knowledge, although this technology is more adopted in other contexts such as manufacturing (Huo and Wang 2022), and despite some recent advancements in employing DT within supply chain (Pereira et al. 2023) and warehouse sections (Braglia et al. 2019), there are still no applications within the SBS/RS.

Therefore, this study is a first attempt to build a DT of the logistics hub of a tire distributor company, whose material handling activities are provided by a multiple-deep SBS/RS.

Specifically, this paper attempts to answer the following research questions (RQs):

(RQ1) How different picking rules and workloads impact on both picking and outbound loading efficiency within an SBS/RS?

(RQ2) How can DT technology support decision making for balancing picking and outbound loading efficiency?

The contribution of this work is twofold. Firstly, we quantitatively measure the impact of different picking rules and workloads on both picking and outbound loading efficiency. Secondly, we provide warehouse managers with a practical tool to properly balance and control these performances.

The findings demonstrate a trade-off relationship between picking and outbound loading efficiency when different picking rules are applied. Moreover, the developed DT shows promising results in supporting operational decisions by managers.

The remainder of this paper is organized as follows: next section describes the background about SBS/RS and outbound loading efficiency, Sect. 3 presents an explanation of the methodology employed, while Sect. 4 offers a detailed description of the case study and the DT. Section 5 provides discussion and managerial implications. Finally, conclusions and future research are presented in Sect. 6.

2 Background

High-throughput warehouses commonly rely on Automated Storage and Retrieval Systems (AS/RS) to efficiently conduct material handling activities (Azadeh et al. 2019). Furthermore, the technological advancement in smart and flexible automation brought by Industry 4.0 gave rise to a new generation of warehouses (Frank et al. 2019). The most representative examples include Vertical Lift Modules (Calzavara et al. 2019b), designed for small items and optimal space utilization, Mobile Robots (Turhanlar et al. 2022) and Automated Vehicle Storage and Retrieval Systems (AVS/RS) (Ekren 2020b) if flexibility and scalability are required.

Particularly, Shuttle-Based Storage and Retrieval Systems (SBS/RS) are an increasingly adopted typology of AVS/RS (Lerher 2016), that operate with a dedicated shuttle carrier for each tier of the warehouse, (see Fig. 1). They can provide very high throughput to the outbound loading area due to the simultaneous usage of multiple shuttles (Zou et al. 2016; Küçükyaşar et al. 2020), outperforming both traditional AS/RS and AVS/RS, which employ fewer shuttles free to move between tiers via lifts.

In this work we adopt DT technology for balancing picking and outbound loading efficiency in an SBS/RS. To the authors' best knowledge, scientific contributions leveraging on DT in SBS/RS are absent, and this is the first instance of investigating the proposed problem.

Thus, the literature is structured as follows. Firstly, an overview of the most relevant studies within the realm of SBS/RS is presented. Subsequently, given the novelty of this topic, we will focus on papers that share similarities with this research, i.e., dealing with automated warehouse with sortation systems and/or addressing shipping operations similar to outbound loading.

2.1 SBS/RS literature

In the last decade, SBS/RS and AVS/RS have garnered significant attention from researchers (Ekren et al. 2023). SBS/RS represents a sub-type of AVS/RS in which every tier has its dedicated shuttle, thus implying higher throughput and investment costs compared to the tier-to-tier solution (Lerher et al. 2015; Küçükyaşar et al. 2020).

The recent reviews of Kosanić et al. (2018) and Li and Li (2022) highlighted that the most debated research stream in SBS/RS literature regards the design, evaluation and optimization of the picking process (Boysen et al. 2019a, b; Cano et al. 2023), i.e., studying the efficiency of automated warehouses in terms of local performance such as cycle time and/or energy consumption (Wang et al. 2022; Lanza et al. 2023). As an example, the combined evaluation of both cycle time and energy performance was proposed by Ekren et al. (2018), which provided a tool for briefly computing such performance by giving input parameters such as number of tiers, shuttle and lifts velocity. Ekren (2020a) presented a simulation-based study for properly designing SBS/RS considering both throughput and energy consumption metrics. We refer to Kosanić et al. (2018) and Li and Li (2022) for more details on energy consumption studies of SBS/RS.

In parallel with these advancements, several different configurations of SBS/RS have been explored. The first SBS/RS variant is the double-deep SBS/RS proposed by Lerher (2016), characterized by racks able to store two ULs. Later, Ning et al. (2016) conducted a design study of a multi-elevator SBS/RS, focusing on optimizing both cycle time and throughput. Their research aimed to assist warehouse designers in the choice of the best rack configuration. Another notable design is the aisle changing SBS/RS provided by Lerher (2018) where shuttles can travel both in the horizontal and in the cross-aisle directions, thus achieving a greater shuttle utilization. In this regard, multiple-tier SBS/RS are also used, as their shuttles can serve more than one tier (Lerher et al. 2021). A further extension on shuttle flexibility is provided by Jerman et al. (2021), that presented a performance analysis based on simulation for an SBS/RS in which the shuttle is free to move both among tiers and among bays.

One of the increasingly adopted configurations of SBS/RS, namely multiple-deep, allows the storage of multiple ULs by equipping the shuttle with a satellite. Marolt et al. (2022) and Marolt et al. (2023) provided models and different storage and relocation strategies for calculating and improving throughput in a multiple-deep SBS/RS, while its single- and dual-command time modeling are presented by Kosanić et al. (2023).

Despite the increasing attention in studies on SBS/RS, the literature overlooks warehouse operations related to shipping, such as outbound loading, while keeping focused on picking and stocking.

2.2 Outbound loading problems

In traditional warehouse configurations, outbound loading takes as input the exact sequence in which ULs are retrieved by human or robotic pickers. Thus, the sequencing of operations determines the sequence of outbound loading. In this stream of research, a manual warehouse was studied by Tran et al. (2014) to optimize the sequence pickers retrieve ULs to be loaded onto trucks with the aim of maximizing throughput. The authors consider double cycle of activities and exploit several genetic algorithms to find the best solution. Similarly, Oliveira et al. (2014) present an optimization of the scheduling of warehouse operations in an AS/RS with the objective of completing the tasks in the shortest possible time. The same objective is addressed in Henn (2015), considering both the batching and sequencing problem in a manual warehouse simultaneously. In the work of Boysen et al. (2017) the sequencing of retrieval orders is addressed in a mobile rack automated warehouse with the aim of minimizing the overall cycle time. Kriehn et al. (2018) studied the storage and retrieval requests in an SBS/RS to maximize throughput. They found a possible 12% throughput improvement by properly sequencing the elevators. The study of Dong and Jin (2021) examined how different storage policies and shuttle dispatching rules impact the performance of a SBS/RS. Several factors are taken into consideration, such as the conditions more suitable for single or double cycles, the cost of shuttles and the customer responsiveness. In the paper of Zhong et al. (2022) the planning of picking and packing processes is analyzed in a manual warehouse, and a mathematical model of the whole system is provided to achieve optimal solutions in terms of total order processing time. Similarly, the investigation conducted by (Haouassi et al. 2022) considered jointly the batching, batch scheduling, and picker routing problem with multiple pickers to speed up order picking operations by splitting customer orders among different pickers. In their study, Wang et al. (2023) considered a robotic mobile fulfilment system similar to the one examined in Boysen et al. (2017). In this setting, racks are movable by robots to packing stations. The novel contribution is the simultaneously addressing of order assignment, order sequencing, rack selection and rack sequencing in the proposed mathematical model, with the aim of minimizing the number of rack moves, that is considered as a proxy for distance and time performance. Finally, the work of Cao et al. (2023) focused on four processes: order batching, picker assignment, batch sequencing and picker routing. The authors highlighted the importance of exchanging information among the mentioned activities to schedule them in an integrated way. They proposed a heuristic algorithm based on local search and perturbation strategies to solve the problem effectively and efficiently.

The underlying assumption of the previously mentioned papers regarding the outbound loading process is often not appliable in other complex contexts where the usage of sortation systems is required. In this sense, the work of Bozer et al. (1988) is the first one to deal with a high-volume sortation system, finding different control strategies to maximize its throughput. Later, Gallien and Webe (2010) discussed the risks of congestion (gridlocks) at the sorter and proposed strategies to cope with it while keeping high throughput. An optimization of the sorting slots, i.e., accumulation areas where ULs wait to be loaded onto trucks, is proposed by Jouglet et al. (2016). They created a mathematical model with optimization including trucks departure constraints, with the purpose of maximizing the timespan of orders at the sorting slots to guarantee maximum flexibility. In the paper of Zou et al. (2021), robotic sorting systems are discussed in terms of their performance. Particularly, they compare the performance of two layouts. The first one consists of two vertical tiers: the top dedicated to the movement of automated vehicles and the bottom to complete the sortation of items. The second one is a traditional crossbelt sorter. The authors discussed the operating conditions in which a system provides better performance, such as the throughput capacity threshold below which it is economically more convenient to use the 2-tiers sorting system instead of the crossbelt sorter. Such an innovative sorting system is also examined in the work of Xu et al. (2022), which mathematically modelled the assignment problem of parcels, showing a strategy to balance the throughput of the first-tier with the congestion of the outbound loading. Additionally, we mention the recent study of Boysen et al. (2023) that focused on the throughput of a robotized sorting system, in which picked items are sorted by leveraging mobile robots. The authors supported real-time decision making due to the unpredictability of arrival sequence of picked orders, thus proposing a mathematical model and related heuristics.

Despite incorporating sorting systems, the works of Bozer et al. (1988), Gallien and Webe (2010), Jouglet et al. (2016), Zou et al. (2021), Xu et al. (2022) and (Boysen et al. 2023) do not consider the upstream picking process and only the study of Xu et al. (2022) includes the efficiency of the outbound loading in their study.

Modern warehouse configurations typically include both an automated warehouse and a sortation system. In this context, the paper of de Koster et al. (2012), investigated a manual pick-and-sort system with the aim of minimizing the total cycle time. Differently, Boysen et al. (2018) focused on a specific performance of outbound loading called order spread, thus finding the optimal scheduling for the picking process of an AS/RS with the aim of minimizing the spread of orders at the packing stations of the same warehouse. The authors conducted a case study on a real online shoe retailer, whose packing stations are managed by human operators. They found that minimizing order spread helps reaching both greater productivity and reduced workforce. An automated hub with sorter has been studied by Khir et al. (2021) to determine cost-effective planning of sort operations with time deadlines. The authors conducted a case study in a large parcel express service provider and designed an efficient method to solve the problem. The importance of synchronizing picking and sorting activities is highlighted in the paper of Jiang and Huang (2022). The authors studied a traditional warehouse with manual order picking and robotic sorting, and mathematically formulated the problem of minimizing the overall sum of time and cost of operations. Variable neighborhood search is used to solve the problem efficiently and heuristically. Lastly, we report the paper of Khir et al. (2023) that described the optimization problem of sorting operations for a two-stage sorting system. In their context, ULs arrive in piles at the primary sorter while human worker accomplish the dispatch at the secondary sorters, and the proposed optimal solution minimize the expected sorting time.

However, although the researches of de Koster et al. (2012), Boysen et al. (2018), Khir et al. (2021), and Jiang and Huang (2022) include both a warehouse (or equivalent primary system) and a sortation system, they lack of considerations on the performance of outbound loading and/or of details on the picking (i.e., what, how much, where and when ULs are picked from). Furthermore, their analyses focused on traditional warehouse typologies, specifically manual and AS/RS, thus they may not be directly appliable to modern SBS/RS characterized by a high degree of concurrent operations. In such contexts, the way ULs are retrieved exerts a significant impact on the subsequent material flow at the sorting stage.

In this research we try to fill the existing gap in literature of studies considering the effects of picking operations on outbound loading efficiency in modern warehouses, such in an SBS/RS. More specifically, this is the first work that links the performance of automated warehouses in terms of cycle time and outbound loading efficiency, thus modeling both the automated warehouse operations and their effects on the sorter, which are not considered in studies solely focused on warehouse throughput efficiency. On the other hand, studies on the efficiency of sorting systems overlook what happens in the upstream processes of the automated warehouse, i.e., how the unit loads arrive in the sorter. The same holds true also for Xu et al. (2022), that is the only examined paper addressing both productivity and loading efficiency. Indeed, the referenced robot sorting system represents a second echelon of the sorting process, thus neglecting the antecedent material handling activities. Furthermore, it also exhibits numerous structural differences compared to SBS/RS.

Table 1 summarizes the characteristics of the relevant discussed papers.

Table 1 Background on related literature

Finally, we mention that despite outbound loading optimization received little attention in warehousing literature, this topic is well-known in other contexts, such as the cross docking platforms (Zachariadis et al. 2022) or rail transport (Ruf et al. 2022), highlighting how much relevant is this process for the downstream nodes in the SC.

3 Methodology

The methodology proposed in this work relies upon the adoption of a DES-based DT due to the complexity and stochastic nature of the real warehouse investigated in this research. Indeed, it can capture non-stationary variations and accurately estimate travel time in concurrent storage/retrieval tasks, which relies on the stochastic order of stocking and picking operations, as well as how they are assigned to the vehicles (Derhami et al. 2020).

As known, DT is not merely a representation of the physical system (Grieves 2014), but it enables bidirectional information exchange. The proposed DT is able to virtually represent warehouse operations, estimate performance, test strategies in acceptable times, and potentially communicate recommended actions to real system actuator while being fed with real data of the system.

Specifically, we leverage on the DT to design and test different picking rules and evaluate their impact on both picking and outbound efficiency with the aim of supporting the warehouse manager on how best to balance these performances when a decision is required.

To this aim, case study was conducted in the SBS/RS of a company's logistics hub. The design and implementation of the DT has gone through the following phases:

• (1) Research setting To properly define the research setting, the first phase involved analyzing the logistics hub context, checking the suitability of the SBS/RS for the research questions, identifying all elements required in the DT, and understanding the unique characteristics of the material handling processes carried out in the warehouse.

• (2) DT building In the second phase, real data related to warehouse geometry, machine kinematics, storage and retrieval process design, and orders were collected to build the DT structure. Stocking and picking processes were modelled, establishing the relationships among customers (i.e., ULs) and servers (e.g., shuttles, lifts, buffers, etc.), and distinguishing between sequential and non-sequential picking orders. More details related to DT building are explained in Sect. 4.2.

• (3) DT validation The DT was validated using real data from the company, ensuring the results produced by the digital model were reliable before proceeding with further experiments. The refinement of the DT was carried out until the gap between simulated and real performance was acceptable, with an average cycle time error of ≤ 5%. More information regarding this phase is available in Sect. 4.3.

• (4) Strategies design The DT was used to define effective picking strategies to dynamically balance picking and outbound loading efficiency. In doing so, different workloads and application easiness were considered, rejecting solutions that would require a significant amount of time to implement.

• (5) Use phase DT was tested in a controlled environment to assess the effectiveness of the selected strategies during the real company operations. Specifically, we fed the DT with the input described in Sect. 4.5 and launched it at the end of every working day to compare the recommended picking rule for the next day with the current one chosen by the company. Additional insights regarding different workloads are also derived to better contextualize the choice of the picking rule.

Feedback was collected through focus group with both staff and managers at every phase to validate the understanding of the outcomes.

4 Case study

This research examines the SBS/RS used in the logistics hub of a leader distributor company in the tire industry. This sector is suitable with respect to the identified RQs since, as explained further in Sect. 4.1, tires may arrive at the sorting area in a unordered sequence, thus affecting outbound loading efficiency. Indeed, to optimize space and volume, tires are frequently stored in stacked configurations and during the picking process, the ULs change their dimensionality from a set of tire stacks to single tires. This company owns also several manual warehouses scattered over the country to efficiently reach its customers. The core business of this distributor is to efficiently receive and store tires from suppliers and dispatch them to customers through direct shipment or via its other warehouses. The SBS/RS located within the logistics hub handles an average of 5000 outbound tires and 5000 inbound tires each day, underscoring its pivotal role for operational costs and profitability of the company.

The whole case study covered a period of 30 days, with 24 days allocated for the validation and 6 days for the use phase.

In the following sections the case-study is extensively described, according to the phases mentioned in Sect. 3.

4.1 Research setting

SBS/RS are utilized to store and retrieve ULs inside a warehouse efficiently and automatically. Their main characteristic is the presence of one shuttle dedicated to each tier (tier-captive). Other components include the rack structure (i.e., the number and the geometries of aisles, tiers and channels), lifts, buffers and inbound/outbound interface points. For this study we consider a variant of the SBS/RS named double-sided multiple-deep SBS/RS, in which each aisle of each tier has two accessible channels, one on the left and the other on the right. Each channel must contain ULs of the same item, and an item can be distributed over one or multiple channels.

Such a configuration results in an increased capacity of the warehouse while maintaining the same number of machines. Moreover, each channel is deep enough to store multiple ULs, accessible through a machine, known as satellite, which every shuttle is equipped with.

The following autonomous machines are responsible for the handling of ULs:

• Lifts There is one lift allocated to each aisle, that vertically transfers items along the various tiers;

• Shuttles There is one shuttle for each pair aisle-tier, which enables horizontal motion throughout the channels;

• Satellites There is one satellite installed onto each shuttle that provides motion within the channel.

The examined SBS/RS has 6 aisles, each one with 6 tiers, each containing up to 45 channels. The overall number of lifts and shuttles is respectively 6 and 36.

Each of the above-mentioned vehicle is used both to store and to retrieve ULs. However, only the lift is able to simultaneously carry both a UL to be stocked and a UL to be retrieved, thanks to its double independent platform.

ULs are also handled by buffers (i.e., small conveyors), inbound and outbound conveyor belts, that connect the SBS/RS to the receiving/shipping zone of the warehouse.

Particularly, inbound ULs (also known as stocking ULs) are handled from the incoming trucks to the SBS/RS, whereas outbound ULs (also known as picking ULs) are handled from the SBS/RS to the outbound trucks.

In this work the UL, both stocking and picking, is defined as a group of tires named train. Each train consists of 1 up to 3 stacks of tires, and each stack can contain up to 5 tires. Consequently, a train can contain from 1 to 15 tires. We will refer to 'train' and 'UL' interchangeably.

Figures 2 and 3 provide an overview respectively of the stocking and picking process carried out in this variant of SBS/RS, where i, j, and k represent the aisle, lift and channel subscript respectively.

Fig. 2

Stocking process in a multiple-deep SBS/RS. a Stocking train entry into the selected aisle. b Lift moving to the selected tier. c Shuttle and satellite stocking operation

Fig. 3

Picking process in a multiple-deep SBS/RS. a Shuttle and satellite picking operation. b Lift moving to the exit tier. c Unstacking of the train and exit onto outbound belt conveyor

4.1.1 Stocking process

The stocking process initiates outside the actual SBS/RS, with inbound trucks that unload tires onto a long conveyor belt. After undergoing quality control operations (i.e., weight, diameter, and height checks), the tires are stacked into piles and logically grouped in the actual UL (i.e., the train). The control system decides for the stocking position of the train, i.e., aisle i, tier j and channel k. Then, the group of tires continues to move along the inbound conveyor belt, as depicted in Fig. 2a, till it reaches the assigned aisle i. There, an independent motor of inbound belt conveyor moves the group of tires onto inbound buffer 1 (IB1).

Every buffer operates as a small conveyor belt and every IB1 is connected to another buffer called inbound buffer 2 (IB2). From IB2, each train is moved onto the corresponding Lift (L). L moves to the inbound buffer 3 (IB3) (Fig. 2b) of the selected tier j of the i-th aisle and moves the train onto it. Afterwards, the shuttle (S) reaches IB3, and the installed satellite loads the whole train onto S. Finally, as S reaches the selected channel k of the j-th tier of the i-th aisle, the satellite grabs one stack at a time from the train, navigates throughout the channel, and places it in the last available position inside the channel, until all the stacks have been placed (Fig. 2c). It is worth noting that in the stocking process, the only logical condition checked to move from one buffer or server to another is the physical occupancy of the next buffer or server.

4.1.2 Picking process

The picking process consists in retrieving a train from its location to the sortation area, where it is loaded onto its corresponding outbound truck. Figure 3 illustrates the picking process in the examined SBS/RS, while Fig. 4 provides the flowchart for the most relevant tasks of the process.

Fig. 4

Flowchart of the picking process

There are two types of picking ULs in this setting: sequential and non-sequential. They both have a ‘shipment’ identifier, but the first ones have also an additional label that groups together one or more trains of the same shipment (i.e., directed to the same truck). Non sequential ULs have no label. Sequential ULs with the same ‘label-shipment' pair are desired to be loaded onto the truck one after the other. The number of sequential ULs sharing this pair varies from 1 up to 20 or more per label.

The picking process of a non-sequential UL begins with the command to S to reach the channel of the desired train. Then the satellite grabs it, one stack at a time, and loads it onto S. After that, S reaches outbound buffer 3 (OB3) and releases the train onto it (Fig. 3a). From OB3 the train is moved onto L. Then, L reaches the outbound conveyor belt tier (Fig. 3b) and releases the train onto outbound buffer 2 (OB2). Here, each stack of the train goes through the unstacker machine and get unstacked (Fig. 3c). This activity consists in singularizing each tire of the stack, that reaches outbound buffer 1 (OB1). From OB1, each single tire can move onto the outbound conveyor belt in order to reach the sorting system of the warehouse, as depicted in Fig. 5, where the picking process is considered finished.

Fig. 5

Sorting system and shipping area of the logistics hub

For a sequential UL the process is the same except for the peculiar control logic that enables the UL to move from OB3 to L. First, in shipments with two labels or more, all ULs sharing the same label are considered as ‘in progress’ upon the departure of the first sequential UL of that label from OB3. This status persists until the last sequential UL of the same shipment and label reaches a zone of the warehouse named completion point, after which the label is considered as ‘completed’. The completion point is selected by the warehouse manager among the various zones through which each UL must necessarily traverse during the activities that constitute the picking process (see Figs. 3, 4 and 5). A sequential UL is allowed to proceed from OB3 to L if it belongs to the same ‘label-shipment’ pair in progress or if there if there are no ‘in progress’ ULs for that shipment. Afterwards, the UL follows the same activities as described for a non-sequential UL.

In Fig. 5, tires marked with zero are related to non-sequential picking orders, while the other ones to sequential picking orders, with different numbers based on their label. The shipment code, i.e., the reference truck, is represented by a letter. From the sorter, each tire is dispatched to its respective truck in the predefined sequence, at the shipping area.

Sequential orders are typically required by the company's manual warehouses, as they offer an advantage in terms of the time required to perform material handling operations (e.g., forklift travel time during stocking) by operators within such warehouses. Indeed, the outbound loading efficiency of sequential picking is typically higher compared to the non-sequential one. However, also specific big customers can get remarkable advantages in requiring sequential picking orders, as their tire unloading will be simpler, making the sequential picking process a value-added operation.

4.2 DT building

Building a DT is the most crucial aspect of the DT implementation (Uhlemann et al. 2017).

The proposed method follows the object-oriented programming paradigm, which has the advantage of simplifying the building and debugging of the entire DT. This paradigm is indeed employed for modeling complex systems such as warehouses (Braglia et al. 2019).

Thus, the final choice was to adopt MATLAB^® due to its high flexibility and its user-friendly interface. During the initial context evaluation of the real-world SBS/RS, we witnessed that material handling processes are characterized by great complexity, especially in the picking process. This complexity arises from the large number of physical elements involved, the specific rules for sequential picking, and several exceptions that may happen during material flows. Thus, the whole DT code has been opportunely divided into 19 classes, 52 functions and 85 scripts.

The structure of the DT is based on 6 modules, whose functions are presented here following:

• (1) Reading geometrical, kinematical, and service time parameters this module reads general parameters about the physical structure of the warehouse, such as the number of aisles, levels, channels, and their geometries (e.g., width and depth). The characteristics of shuttles, satellites, lifts, buffers, and conveyor belts are also included, such as acceleration, deceleration, maximum speed and other specific times of machines’ activities. We note that the kinematic values may vary depending on the presence of the UL on the vehicle. Manufacturer specifications are used to derive kinematic parameters for vehicles, while time-and-motion study was exploited to get pick-up and set-down times. All the mentioned values reported in Appendix A. In this module, the connection link operates in a one-way manner from the real world to the DT, and it is read and modified every time there is a significant change in the real-world structure. For instance, the WMS provides updated information on the status of shuttles, lifts, and satellites, indicating whether these vehicles are available for material handling activities.

• (2) Build of the warehouse structure geometries read in (1) are used to construct the digital racking system of the warehouse, e.g., the channels inside each aisle and level, as well as the number of ULs that can be stored within them. The outbound belt conveyor is virtually replicated too, with its capacity to accommodate tires. Analogously to the description outlined in (1), if certain areas of the warehouse rack BECOME inaccessible, this information is conveyed to the DT through reading from the WMS. However, no structural modifications of the SBS/RS have been observed during this study.

• (3) Reading tire inventory at the beginning of the day, the WMS communicates the current inventory to the DT by generating a.xls file. This information is used to populate the virtual inventory in the digital model, thus enabling for robust and correct simulation of material handling operations, such as the retrieval of a train. Specifically, the WMS generates a.xls file with the following data related to each stored stack of tires:

• SKU code identifier of the tire typology.

• Quantity of tires number of tires for each stack.

• Shipment name is an alphanumerical code related to the customer order.

• Rack position position in the Storage Rack (SR) in terms of aisle, tier, channel, left/right

• Depth storage position inside the channel, expressed in mm.

• (4) Reading stocking and picking orders information: in this module the orders received by the company are transferred to the WMS that makes a.xls file that is read by the DT to generate the current workload that will be used by its DES engine. An embedded preprocessing module rapidly elaborates such file to provide the DES with a.xlsx file that describes the daily workload in terms of stocking and picking orders as follows:

• Shipment name is an alphanumerical code related to the customer order.

• Label is a number that, if greater than zero, identifies all the tires of the same shipment that are meant to be loaded together onto the outbound truck (i.e., sequential order).

• UL number identifier of the train of stacks of tires.

• Stack number identifier of the stack of tires.

• Quantity of tires number of tires for each stack.

• SKU code identifier of the tire typology.

• Operation binary variable to distinguish stocking and picking operation

• Rack position position in the Storage Rack (SR) in terms of aisle, tier, channel, left/right

• Exit lane only for picking, indicates the exit lane where the outbound truck waits the assigned orders.

• Timestamp start it is an integer that expresses in seconds the time of the day (e.g., 7:00 AM corresponds to 25′200 s).

• (5) Running DT simulation the embedded DES engine of the DT initiates upon the arrival of the first order to the system. If it is a stocking order, the trigger is determined by the arrival of the UL on IB1, otherwise for a picking order it is determined by the order arrival in the WMS. Subsequently, the DES engine proceeds to compute all the events (i.e., advancement status) of each UL, such as the arrival onto the lift. For each motion of vehicles, kinematic parameter values are differentiated considering whether the machine is carrying a load (i.e., a UL) or not, as detailed in Appendix A. For instance, the maximum speed of the shuttle is lower when carrying a load compared when moving without a load. Each of these autonomous vehicles follows a unidirectional motion: vertically along the y-axis for the lift, horizontally along the z-axis for the shuttle, and horizontally along the x-axis for the satellite, as depicted in Figs. 2 and 3. To correctly model their acceleration, constant speed, and deceleration phases, we considered triangular or trapezoidal profile depending on whether the distance to be covered allows to reach the maximum speed, by adapting travel modeling from the methodology outlined in Bortolini et al. (2017).

The simulation stops when all the stocking and picking orders read by the DT for the desired timeframe are completed. For each iteration, both servers and instances are updated and relevant KPIs are computed, thus both emulating the real operations of the warehouse and monitoring them. The DES engine is also exploited to compare the impact of three different picking rules on both picking cycle time and outbound loading efficiency.

• (6) Writing simulation output the DT computes the relevant performance of the SBS/RS such as the cycle time for each order, the outbound sequence of the tires from the warehouse, the distance travelled by shuttles, and other operational performance indicators. These data are used to generate an Excel file that can be read by the manager, while the indication of the recommended picking rule can be encoded in a file to be transmitted to the PLC, thus enabling automatic control based on the required update frequency. In the specific case study, in accordance with the company, the completion point information together with mentioned KPIs are transmitted only to the manager.

Therefore, the developed DT is able to replicate the actual operations of the case-study SBS/RS, with the aim of conducting experiments without interrupting the real-world operationality of the logistics hub.

4.3 DT validation

The validation is a crucial and mandatory phase in the development of a DT that ensures that the outcomes of the DT are aligned and similar with the real-world, thus correcting any discrepancies between the expected and actual behavior of the whole system.

To validate the DT model, we leveraged on stocking and picking event logs.

Specifically, by exploiting the photoelectric cells positioned in strategic points within the warehouse, we collected over of a period of 24 business days with the aim of verifying the validity of both kinematic models (e.g., shuttle, lift, buffer, and satellite service times) and logical models (e.g., buffer occupancy control of the DT).

The distribution of photocells in the warehouse are reported in Table 2, along with the indication of the related event and service time to be validated.

Table 2 Photocells distribution in the warehouse and tracked events

After removing outliers, which were present in negligible percentage, the outcomes obtained from the DT were juxtaposed against the actual results, specifically with the picking cycle time.

During this phase the digital model has been refined and tuned to minimize differences between the digital and real outputs (e.g., machine service times, waiting times, machine utilization, etc.), with the help of focus group and interviews to the staff to better understand the processes.

Following several adjustments in the DT, a sufficiently accurate model of all operations was achieved, except for the satellite service time, both during stocking and picking operations.

Nevertheless, the satellite service times of the DT did not accurately reflect actual service times, which tended to be significantly longer. Moreover, as the DT was designed to be launched at the end of the working day, measuring the satellite speed in real-time would not have been possible. To address this issue, we collected data on the distribution service time for each satellite both for stocking and picking operations. Then, we inferred statistical distributions over a period of 24 business days. More precisely, such distributions have been collected and stratified according to the depth (step of 1000 mm) of each stocked and picked train and the number of stacks per train. The underlying assumption is that these are the main factors (with the data at disposal) that affect the satellite service time. Other factors such as the channel, the aisle, the tier and the individual weight of ULs are not considered as relevant. Then, we modified and adapted a MATLAB® custom function named fitmethis (Castro 2021) to adjust the satellite service time with its distribution curve, allowing the DES engine to generate a random number based on the distribution to calculate the satellite service time. As an example, if a UL composed of 3 stacks is stocked at a depth of 2700 mm, this corresponds to the time distribution in the range of 2001–3000 mm with 3 stacks. Therefore, a number associated to the satellite service time for that UL is generated from the best fitting distribution (e.g., in the case of a Generalized Extreme Value distribution, parameters μ, σ, and ξ are computed and used to generate a random number). This choice allowed to achieve a faithful approximation of the actual behavior of the satellite, whose data declared by the manufacturer proved to be unreliable in the specific context of the presented SBS/RS.

We also point out that the number and positioning of the photocells used were insufficient to gather precise information on the time service associated with complex movements of UL pick-up and set-down, preventing both an analytical formulation and an observation from the WMS. Therefore, we measured the pick-up and set-down times for ULs through time and motion study techniques. We observed that satellite handles a stack of tires in an average of 37 s from/to the IB3/OB3 buffers. On the other hand, the pick-up and set-down times during the stocking and retrieval operations of the satellite inside the channel are already included in the aforementioned procedure.

Table 6 in Appendix B reports the empirical distributions associated with the satellite travel time. It can be observed that the average values associated with 1 stack of tires in picking are approximately double compared to stocking, while as the number of stacks increases, this ratio decreases. This is because the photocell system records the picking timestamp after the satellite completes both the travels from and to the shuttle. On the other hand, while stocking the photocell records only the first travel time, after the satellite sets the stack of tires down. Therefore, the simulation engine of the DT includes an appropriate function to correctly calculate the shuttle availability after the stocking operation by taking into account the satellite return trip.

The validation phase led to achieve an average cycle time error less than 5% and meeting daily throughput, thus we considered the developed DT a reliable copy of the real-world system.

4.4 Strategies design

In this section we present the picking strategies that have been tested in the DT with the aim of balancing picking and outbound loading efficiency. Accordingly, we firstly introduce the metrics used to measure such performance.

Picking efficiency has been measured through cycle time (CT), that represents the elapsed time to complete the picking process.

To measure outbound loading efficiency, the overlap (OVP) metric is employed, which determines the clutter degree of ULs at the sorting area and constitutes a proxy of how good the loading sequence will be (see Fig. 6).

Fig. 6

Example of two overlaps in an outbound loading sequence

Overlap can be defined as it follows: given a set of labelled ULs and their arrival sequence at the sorting system, an overlap happens when a UL with a different label is located between two ULs with the same label. The following example may clarify the definition: let X and Y be two labels, 4 ULs for X and 2 for Y. An overlap can be found in the sequence X–Y–X–X–X–Y due to the presence of UL ‘Y’ in the middle of two ULs ‘X’. The sequences X–X–X–X–Y–Y and Y–Y–X–X–X–X–X have 0 overlap. The number of overlaps in a sequence is considered summing all the overlaps for all the types of ULs. As an example, the sequence X–Y–X–X–X–Y–Z–Y presents 2 overlaps: one due to UL ‘Y’ between two ULs ‘X’ and the other one due to UL ‘Z’ between two ULs ‘Y’. A representation of the overlap is provided by Fig. 6.

The overlap metric is computed only for sequential picking ULs, by considering the arrival sequence at the sorting area of all tires of each shipment containing at least two labels.

To measure the outbound loading efficiency compared to the overall workload of sequential unit loads ($N{P}_{1}$), we will use the average percentage overlap ($OVP\%$), measured as:

$$OVP\% = \frac{OVP}{{NP_{1} }}$$

(1)

In order to design the most adequate picking strategies, two variables have been considered: (1) percentage of sequential ULs $(SP\%)$; (2) completion point in the picking process. The first one has been chosen as demand for sequential picking may vary from day to day, and it is computed as $SP\%=N{P}_{1}/(N{P}_{0}+N{P}_{1})$, where $N{P}_{0}$ is the number of non-sequential picking orders. Moreover, $SP\%$ is relevant for this study as overlaps are calculated only for sequential picking orders, and it characterizes different demand scenarios (i.e., high- or low-sequential ULs workload). Specifically, $SP\%$ values range from 0 to 100% with a step size of 10, thus there are 11 values.

The completion point has a significant impact for the cycle time of sequential ULs, as it affects their waiting time on OB3 due to the control logic described in Sect. 4.1.2. Consequently, the postponement of the completion point is expected to increase sequential ULs cycle time and decrease overlap. Indeed, their travelled distance before reaching the completion point is greater. On the other hand, the possibility of another UL associated with the same shipment but a different label arriving first on the outbound conveyor belt is lower.

The vice-versa applies as the completion point is upstream in the picking process: the expected cycle time will be lower and the probability of overlap higher.

The three picking strategies correspond to three different completion points that have been chosen in collaboration with the warehouse manager, considering the relevant points of the warehouse:

• (i) Arrival on OB2;

• (ii) Arrival onto the outbound conveyor belt;

• (iii) Arrival at the sorting area.

Indeed, these completion points are representative of the picking process final phase within the SBS/RS, and they effectively map the initial, middle, and final stages of picking activities subsequent the train being served and unloaded by the lift. The warehouse manager confirmed our interpretation and suggested that there is no need for further process segmentation.

Consequently, there are 33 experiments for each day, as each completion point was tested across 11 different scenarios corresponding to different percentages of sequential ULs (i.e., sequential picking ULs over total picking ULs) ranging from 0 to 100 (0, 10, 20, …, 100).

4.5 Use phase

After validating the DT, it was used in a controlled environment to support the daily decision-making process of choosing the most appropriate picking rule, i.e., the completion point, to balance picking and outbound loading efficiency. Particularly, we tested the DT over a 6-day period of July 2020 for a total of 29,607 stocking tires and 26,457 picking tires. The number of article types differs significantly between stocking and picking, respectively 528 and 1650. Data regarding the SBS/RS are presented in Appendix A. We launched the DES engine at the end of every working day with the aim of setting the preferable completion point for the next day. At every run, the DT was fed with the following data: inbound and outbound orders, machine and rack availability, and manager preferences.

Following the warehouse digital twin framework proposed by Kuhl et al. (2022), Fig. 7 schematically illustrates the approach adopted in the utilization of the proposed DT.

Fig. 7

Warehouse digital twin approach in the case-study

Data about the orders is obtained by the ERP. Indeed, at the end of the working day, the demand for next day stocking orders and sequential picking orders is known. Conversely, the demand for non-sequential picking orders derives from a combination of already received orders and forecasts provided by the ERP system.

The WMS communicates to the DT the updated status of machines and rack availability. Particularly, during the use phase there were 2 faulty shuttles out of 36, and a channel was inaccessible due to maintenance.

Furthermore, as the recommendation is about balancing picking cycle time and overlap, to automate the decision on the best completion point the DT has to know the manager preferences.

Thus, when required, the manager compiles a.txt file expressing the relative costs associated with both metrics. In particular, ${w}_{CT}$ is the cost of an additional second in the picking cycle time, and ${w}_{OVP}$ is the cost of an additional overlap.

With this information, the DT launches a simulation and communicates the recommended picking rule to the warehouse PLC.

In the case study the average real $SP\%$ is about 30%, while the already adopted completion point is $C{P}_{1}$, and the manager set ${w}_{CT}={w}_{OVP}$.

However, to verify the adequacy of the current completion point and to strengthen the confidence of the recommendation, different scenarios were recreated for each tested day by varying the percentage of sequential orders. Specifically, during the pre-processing phase in the DT, the labels of picking orders have been increased or decreased to achieve all the scenarios. Similarly, the design of the picking process has been modified to test all the three completion points.

Thus, considering 6 days, 3 completion points and 11 different sequential picking percentages, the DES engine of the DT run for a total of 198 times.

Each simulation took a maximum of two hours on a single thread on a Intel® Xeon® Gold 5120 machine with 32 GB clocking at 2.20 GHz to complete the average workday, and up to eight threads can be used concurrently. However, it took about 10 min to replicate the operations of Saturday, which represents approximately half of the orders of the average day, showing a non-linear dependency between execution time and numbers of operations.

It is worth mentioning that for each UL picked or stored, i.e., for each real order, the satellite service time is generated only once using the procedure described in Sect. 4.3. This ensures unbiased results that could otherwise occur due to the randomness of the procedure. Therefore, the different performance obtained in the various experiments are due only to the different sequential picking workload and completion point.

For every experiment, the DT outputs information such as the completion time for each order and the outbound sequence of the tires from the warehouse. This information is used to calculate cycle time and overlap by applying the definitions given in Sect. 4.4. Moreover, the DT computes other KPIs such as shuttle utilization, waiting times, etc. The most important KPIs were presented to the warehouse manager in a concise format, as detailed in Appendix C.

4.5.1 DT insights

In this section we discuss the application of the DT in the 198 scenarios described in Sect. 4.5. Particularly, we provide an overview of the impact of completion point and sequential picking percentage on both picking and outbound loading efficiency, as well as discuss the results obtained for the specific current scenario of the company. The complete list of the experiment results is reported in Appendix C.

According to the definitions provided in Sect. 4.4, we will use cycle time (CT) to measure picking efficiency and the overlap metrics (OVP and OVP%) to measure outbound loading efficiency.

Figure 8 reports both $CT$ and $OVP\%$ at different percentages of sequential picking and across three distinct completion points, with the term $C{P}_{n}$ that refers to completion point (n). Figure 9 plots $CT$ and $OVP$. The computation of $CT$ entails both sequential and non-sequential picking orders, as they are both of strategic relevance for the economic performance of the company. Indeed, as mentioned in Sect. 4, sequential picking orders are typically required by manual warehouses that are owned by the company, on the other hand non-sequential picking orders are requested by direct customers. The performance of $OVP\%$ is computed based on SP% and $OVP$ on the absolute value of overlaps. Different demand profile across the entire time horizon of the simulation have been considered.

Fig. 8

Plot of CT and OVP% across the three completion points

Fig. 9

Plot of CT and OVP across the three completion points

The plots show that, as the completion point is postponed, there is an upward trend in the average cycle time, and a downward trend in the average overlap. However, the increase of $SP\%$ has a very small effect on $OVP\%$ when $SP\%>30\%$ in all the completion points. Moreover, as $SP\%$ is in the range 0–20% the three completion points exhibit similar performance, with $C{P}_{1}$ that consistently guarantees the lowest cycle time and $C{P}_{3}$ the lowest overlap.

This phenomenon is due to the negligible or absent number sequential picking order, that results in zero or very low $OVP\%$ and a minimal impact on the overall average picking cycle time. With the escalation in the $SP\%$, the selection of the completion point become more relevant. The three distinct completion points, visible in Figs. 3 and 5, implies a different travelled distance of sequential ULs before being completed. Such a distance increases from $C{P}_{1}$ to $C{P}_{3}$, consequently amplifying the waiting time of the other ULs, and thus the overall cycle time. This behavior is notably accentuated with the increase of $SP\%$.

Conversely, it is observable that $OVP\%$ stabilizes for $SP\%>30\%$. This can be explained by the formulation of $OVP\%$: with an increase in $SP\%$, both the numerator and denominator of Eq. (1) increases proportionally.

Hence, it is plausible to correlate each completion point with a characteristic value of $OVP\%$.

On the other hand, Fig. 9 shows that the increase of $SP\%$ implies a bigger number of sequential picking orders, thus a higher overall $OVP$. The vice-versa applies with the postponement of the completion point: the closer it is to the closed-loop sorter, the lower the risk of encountering an incorrect outbound sequence. Therefore, at the same $SP\%$, there is a reduced $OVP$ when moving from $C{P}_{1}$ to $C{P}_{3}$.

To further analyze the impact of each completion point on cycle time and overlap, it is possible to compute both the average increase of $CT$ and $OVP$ for each 10% increase of $SP\%$ as it follows:

$$\Delta CT = \frac{{CT_{N} - CT_{1} }}{N - 1}$$

(2)

$$\Delta OVP = \frac{{OVP_{N} - OVP_{1} }}{N - 1}$$

(3)

where $C{T}_{N}$ is the cycle time at the last $SP\%$ scenario (i.e., N = 11) and $C{T}_{1}$ denotes the cycle time for the $SP\%$ initial value (at $SP\%$ = 0).

Table 3 reports the application of the Eqs. (2) and (3) for all the strategies.

Table 3 Overview of performance evaluation for the three completion point

However, such performance should be converted into costs to allow managers to fairly compare the choice of the completion point. Consequently, it is possible to proceed with a cost/benefits analysis, as it follows.

Given a set of alternatives (i.e., completion points) we define the cost of choosing alternative i instead of j at workload s (i.e., the $SP\%$) as:

$$C_{i,j,s} = w_{CT} \cdot \left( {CT_{i,s} - CT_{j,s} } \right) + w_{OVP} \cdot \left( {OVP_{i,s} - OVP_{j,s} } \right)$$

(4)

where $C{T}_{i,s}$ is the cycle time of completion point i at workload s and $OV{P}_{i,s}$ is the overlap of completion point i at workload s.

Then we search for the i-th alternative that has minimum cost after enumerating and calculating all the possible combinations, with ${C}_{i,j,s}=- {C}_{j,i,s}$.

This procedure can be applied for any value of $SP\%$, as reported in Table 7 of Appendix C.

As an example, with the current company $SP\%$ of $30\%$, the results reported in Appendix C (Tables 8, 9 and 10), show that:

• For $C{P}_{1}$, $CT=$ 260 s and $OVP$ = 32;

• For $C{P}_{2}$, $CT=$ 292 s and $OVP$ = 16;

• For $C{P}_{3}$, $CT=$ 415 s and $OVP$ = 3.

Consequently, we have:

• ${C}_{\text{1,2},30}$ = ${-w}_{CT}\cdot 32+{w}_{OVP}\cdot 16$

• ${C}_{\text{1,3},30}$ = ${-w}_{CT}\cdot 155+ {w}_{OVP}\cdot 29$

• ${C}_{\text{2,1},30}$ = ${w}_{CT}\cdot 32-{w}_{OVP}\cdot 16$

• ${C}_{\text{2,3},30}$ = ${-{w}_{CT}\cdot 123+ w}_{2}\cdot 7$

• ${C}_{\text{3,1},30}$ = ${w}_{CT}\cdot 155-{w}_{OVP}\cdot 29$

• ${C}_{\text{3,2},30}$ = ${w}_{CT}\cdot 123-{w}_{OVP}\cdot 7$

The choice between $C{P}_{1}$, $C{P}_{2}$ and $C{P}_{3}$ depends on the values of ${w}_{1}$ and ${w}_{OVP}$. Specifically, at $SP\%=30\%$, it is preferable $C{P}_{1}$ if $\frac{{w}_{CT}}{{w}_{OVP}}>\frac{16}{32}=\frac{1}{2}$, $C{P}_{2}$ for $\frac{7}{123}<\frac{{w}_{CT}}{{w}_{OVP}}<\frac{1}{2}$ and $C{P}_{3}$ when $\frac{{w}_{CT}}{{w}_{OVP}}<\frac{7}{123}$. With the company manager preferences, ${w}_{CT}={w}_{OVP}$, thus $C{P}_{1}$ is verified to be the best choice. On the other hand, if ${w}_{OVP}=3 {w}_{CT}$, (i.e., 1 additional overlap costs as much as 3 s of delay in cycle time) then it is preferable to set $C{P}_{2}$. Finally, if ${w}_{OVP}=20 {w}_{CT}$, then the most suitable choice is $C{P}_{3}$.

This method is similar to examining all 11 Pareto frontiers, each corresponding to different percentage of sequential picking. However, due to the limited number of experiments, this approach is more practical. Figure 10 shows an instance of a Pareto frontier at $SP\%=30\%$.

Fig. 10

Pareto frontier for SP% = 30%

4.5.2 Sensitivity analysis

To enhance the generalizability of the findings to other warehouse designers and managers, a short sensitivity analysis was conducted. Conducting a comprehensive sensitivity analysis is unfeasible due to computational time constraints; however, two new kinematic profiles, referred to as ${k}_{2}$ and ${k}_{3}$, were proposed, borrowing SBS/RS parameters by Lerher (2016). In accordance with the literature, in this analysis we assumed kinematic parameters (e.g., shuttle velocity) not to change whether the vehicle is carrying a load or not. Moreover, the same shuttle parameters were used for the satellite (Eder 2022) in both ${k}_{1}$ and ${k}_{2}$. Hence, the same modeling formulas employed for shuttle travel time are also used for satellite travel time. The total distance traveled by the satellite accounts for both its outbound and inbound movements from and to the shuttle, the number of stacks of tires (i.e., the number of travels), the tire diameter, and the overall time of 20 s taken by the satellite to grab and release a stack. This time was obtained via stop and motion study and was confirmed by real data, wherein the satellite carried only one stack for a very short distance.

Table 4 outlines which motion parameters were varied and their values relative to the kinematic profile of the case study, denoted as ${k}_{1}$. All the other parameters presented in the case study have been fixed during the sensitivity analysis (e.g., number of aisles). We refer to Appendix A for parameters notation. Therefore, we conducted a total of 396 additional simulations, 198 for each new profile tested. The results obtained, detailed in Appendix D, demonstrate that indeed, as kinematic parameters increase, cycle time decreases and overlap increases. Importantly, these results confirm that the change in completion point is the most impactful factor, among those tested, on both performance metrics, thus augmenting the generalizability of the proposed approach.

Table 4 Kinematic scenarios of the SBS/RS

5 Discussion and managerial implications

5.1 Theoretical contribution

Modern SBS/RS are increasingly used for their high throughput that supports timely delivery to customers, but present unique challenges and require novel solutions (Battarra et al. 2022; Eder 2022) to effectively manage their operations. In this regard, DT provides one of the technologies that will make a significant impact toward advancing smart warehouses (Kuhl et al. 2022). In this paper, we leveraged on a DES-based DT to support warehouse managers in balancing picking and outbound loading efficiency with the aim of facilitating the material handling activities of subsequent nodes in the SC while shipping on time. In line with prior literature, we used cycle time as a proxy for picking efficiency, and overlap for outbound loading efficiency, a metric similar to the order spread used by (Boysen et al. 2018) in a sorting system. Furthermore, applying the DT allowed to assess the impact of three proposed picking strategies on both cycle time and overlap, while also considering various workload scenarios.

Consistently with past research that highlighted the relevance of integrated planning of multiple activities to avoid local optima in other warehouse contexts (Jiang and Huang 2022; Zhong et al. 2022; Cao et al. 2023), this study underscores the significance of material handling activities within a logistics hub for the subsequent nodes in the SC.

More specifically, the application of DT in a real-world SBS/RS showed that, given a certain workload and managerial preferences, a balance between picking and outbound loading efficiency can be attained by selecting the picking strategy recommended by the DT.

The theoretical contribution of this research addresses the formulated RQs (see Sect. 1) as follows:

(RQ1) How different picking rules and workloads impact on both picking and outbound loading efficiency within an SBS/RS?

In this study the developed DT is employed to define and assess the effects of three picking rules on both picking and outbound loading efficiency across various workloads. Specifically, these picking rules were defined based on the choice of the completion point and the workloads were defined by the number of sequential picking orders.

The experiments conducted on the DT allowed us to observe that as the number of sequential ULs increases, both cycle time and overlap also increase due to the more complex scheduling of picking orders. However, how much they increase varies depending on the choice of the completion point. When dealing with a low number of sequential of ULs (0–10% of the total picking demand), both cycle time and overlap are low, regardless of the completion point. Then, as sequential ULs increases, from 20% of the total picking demand, cycle time and overlaps grow differently according to their completion point: the earlier it is, the lower is the cycle time and the higher is the overlap, and vice-versa. For higher percentage of sequential ULs, the impact of completion point on cycle time and overlap becomes even more pronounced. The utilization of the developed DT enabled a performance evaluation, which is detailed in Table 3 (see Sect. 4.5.1).

(RQ2) How can DT technology support decision making for balancing picking and outbound loading efficiency?

In this paper we leveraged on DT to define three picking strategies, i.e., completion points, which influence both the efficiency of picking and outbound loading. This approach allowed to dynamically support the choice of completion point for the sequential picking process within an SBS/RS. During the case study, at the end of the working day we fed the developed DT with WMS stocking and picking order, information on machine and rack availability and manager preferences on picking and outbound loading. The inputted data may change according to several variables, such as machine faults, diverse workload and different manager preferences, which may vary according to the requirements of downstream nodes. For instance, if the next node is a direct customer, it is likely that the cost associated with an increased picking cycle time will be higher than the cost associated with an increased overlap. The vice-versa may apply if the next node is an own minor warehouse with human operators, as described in Sect. 4.

By knowing in near to real-time this information, the DT computes the recommended picking strategy in a maximum of two hours and communicates it directly to the warehouse PLC that eventually changes the current one. Therefore, the DT can support the balancing in the picking and outbound loading efficiency at an operational level.

This is one of the first studies addressing both picking cycle time and outbound loading efficiency within an SBS/RS. Furthermore, we mention that these findings may be applicable to other warehouses, highlighting the potential generalizability of the contribution.

Indeed, while the present study is tailored to the mentioned company, such problem holds relevance for other distribution companies leveraging on large and highly parallelized AS/RS to retrieve ULs, adopting different picking process policies and employing a closed-loop sorting system for accurate dispatching. This includes systems such as SBS/RS with conveyor belts.

The suitability of the presented approach increases with the number of concurrent executions of operations and with the diversity of customers served. For instance, big e-commerce companies dealing with small and varied items (e.g., online pharmacies, fashion retailer, etc.) may benefit from this study due to their large volumes and diversity of customers. Indeed, to effectively consolidate their picking orders, they require rapid and efficient UL retrievals, necessitating an optimized sequence of ULs at the sorting area (Boysen et al. 2018). This not only ensures high warehouse productivity but also enhances the efficiency of the receiving and stocking processes at subsequent nodes in the SC, such as any subsidiary warehouses owned, or to optimize courier delivery (Pollaris et al. 2015). Other sectors that could benefit from this study include food and beverage as well as paper tissue industries. Indeed, in such sectors a UL may be retrieved as a stack, pallet, or batch and then singularized before reaching the sorting system. This is because ULs should have a low center of gravity compared to the size of the supporting area to avoid tipping over during curves or braking when transported (Kasahara and Mori 2015). Thus, in case the UL changes its dimensionality during the picking process, the risk of having suboptimal sequence at the sorting area increases.

Lastly, this research responds to the need for more empirical studies on the use of DT in warehousing (Agalianos et al. 2020) and contributes to the ongoing call for further investigations of shipping operations for improved SC performance (Kumar et al. 2021).

5.2 Managerial and practical implications

The findings of this research provide insights into potential management and practical applications. First, by using the DT, warehouse managers are assisted in their operational decisions, i.e., in choosing the picking rule such as to achieve the desired balance between cycle time and outbound loading efficiency at a certain workload.

Particularly, the DT replicates the operations conducted in the SBS/RS and applies Eq. (4) (Sect. 4.5.1) to compare and communicate the most suitable completion point to the warehouse PLC according to the inputted preferences of cycle time and overlap, thus allowing a near to real-time control of the two conflicting performances. As an example, in the real case-study, the SBS/RS presented SP% = 30%, with ${w}_{CT}={w}_{OVP}$. In this case, the choice of $C{P}_{1}$, has been verified to be the best choice for balancing cycle time and overlap.

Accordingly, the presented DT approach can be used by managers of large SBS/RS (e.g., logistics hub) to design tailored strategies based on specific orders. In the case study, sequential ULs are directed towards minor manual warehouses of the same company. Therefore, a correct sequence in the loading of trucks from the large SBS/RS is expected to entail improved productivity in the receiving and stocking processes of minor manual warehouses, with positive effects on operational management costs.

Other downstream nodes in the SC include medium/large retailers, that may require both timely delivery and pre-sorted goods within the truck, and small direct customers. These nodes deal with a limited number of items per delivery, prioritizing order punctuality over overlap. Therefore, the logistics hub manager can increase the preference for cycle time and let the DT suggest the completion point for these customers.

Moreover, assessing the performance of the analyzed SBS/RS under different workloads provides valuable insights also for technology suppliers. By understanding the expected cycle time and overlap, suppliers can optimize warehouse design to meet the throughput and outbound loading efficiency demands of their customers more effectively.

Additionally, as reported in Appendix C, it is possible to observe how stocking cycle time deteriorates with the postponement of the completion point. Despite picking cycle time is usually one of the most important key performance indicator in warehousing, stocking process efficiency may have also an impact on the overall material handling costs and performance (Staudt et al. 2015; Raghuram and Arjunan 2022).

Lastly, we mention that the number of overlaps approximates the workload at the sorting area and shipping location. This helps the design stage of the sorting system, particularly to size the capacity of the sorter and to optimize its layout. On the other hand, knowing the expected overlap can also be used to manage the workload of truck operators. Indeed, due to increasingly tight delivery times, workers can suffer from the augmented workload (Calzavara et al. 2019a), i.e., higher overlaps, with the risk of increased errors and augmented stress (Grosse et al. 2015). Again, by knowing the available workforce at the shipping area, it is possible to use the DT to tune the picking process in real-time and facilitate human operators.

6 Conclusions and future research

Although warehouses have a relevant impact on SCs performance, existing research on warehousing operations mainly focused on local performance such as cycle time and energy consumption, overlooking their impact on subsequent nodes. Accordingly, this paper introduced a novel approach using DT to support managers in the balancing of picking and outbound loading efficiency in an SBS/RS. The proposed methodology is applied to a real case-study of a logistics hub, whose picking process differs according to the next node typology. The DT was used to define and assess the impact of three picking strategies, i.e., picking completion point, on picking and outbound loading efficiency, that have been measured respectively by cycle time and overlap.

In the case study, at the end of the working day the DT was fed with real data from WMS, ERP and PLC to evaluate the recommended completion point for the next day. Moreover, several workload scenarios have been evaluated to better contextualize such a decision.

The application of the DT confirmed the adequacy of the current picking strategy of the company at its current workload, but also provided valuable insights. Particularly, we observed both overlap and cycle time increase with the number of sequenced picking ULs, but the choice of the completion point has different impact on their derivatives. Opting for an earlier completion point leads to faster cycle times but higher overlaps, and vice versa. By quantifying this impact, the research offers valuable managerial insights and practical guidance based on the workload of the warehouse and manager preferences in terms of cycle time and overlap.

This study comes along with some limitations. Firstly, it relied on a limited dataset, thus overlooking potential seasonal effects. Additionally, data related to subsequent nodes in the SC, particularly regarding their receiving and storage operations, were not present. Furthermore, we point out that despite its increasingly interest in warehousing applications, implementing a DT in practice still presents some important barriers, such as lack of specialists and expertise and lack of integration between IT systems (Perno et al. 2020).

While acknowledging these weaknesses, this research offers a unique outlook on the SBS/RS performance analysis and opens up new avenues for further exploration of this topic.

The limitations of this work highlight potential directions for future research, which may reinforce our preliminary evidence. The first one is to use the developed DT for an extended period and including different demand loads. Moreover, the DT should be updated and used at increased frequency, i.e., multiple times throughout the day (e.g., at the end of the morning for the afternoon). This would allow to dynamically change the picking rules according to the specific demand throughout the workday. Similarly, the DT can be employed for tailoring picking rules based on specific customer orders. Accordingly, its execution time should be verified to be aligned with the response time required by the system.

Additionally, the receiving and stocking operations of subsequent nodes in the SC should be also considered, as they would more precisely quantify the benefits of this study in terms of downstream node performance and consequently the cost-savings.

Lastly, we call for further studies in different contexts, both to confirm the validity of the DT as a supporting tool for balancing cycle time and overlap and to characterize the relationship between picking and outbound loading efficiency in SBS/RS, thus encouraging further analyses about the influence of picking rules and other design factors on those performances.

Appendices

Appendix A

SBS/RS parameters and assumptions

Table 5 reports the values of the main parameters used to create the DT of the multiple-deep SBS/RS and to conduct the experiments are presented.

Table 5 Parameters used in the digital twin

The DES engine incorporated into the DT is based on the following assumptions:

• The warehouse consists of SR on both sides (left and right).

• The inbound and outbound belt conveyors are positioned at the 5th and 4th tiers of the SR, respectively.

• The dwell position following a picking operation is in front of IB3/OB3 buffers, while after a stocking position, it is in front of the storage channel.

• Lifts and shuttles operate simultaneously. On the other hand, the satellite can operate only when its shuttle is stationary.

• The real sequence of stocking and picking orders is considered. Thus, vehicles can work on both single command and double command modes.

• Trapezoidal and triangular kinematic profiles of shuttle and lifts are considered to model their travel times. Their kinematic parameters can change depending on whether the vehicle is carrying a load or not, as reported in Table 5.

• Constant velocity profile has been considered for inbound and outbound belt conveyors, and for IB1, IB2, OB1, and OB2.

• The modeling of satellite travel time is based on the generation of a random number following the empirical distribution curve of its service time, which is determined by the depth and the number of stacks characterizing the UL. Different distribution curves are considered for stocking and picking operations.

• Service times associated with IB3 and OB3 have been measured through the time and motion study technique. Specifically, the satellite takes an average of 37 s to move a stack of tires to/from the IB3/OB3 buffers.

• The service time of the unstacker machine is 5 s per tire.

• The storage and retrieval positions of ULs used in the simulation precisely adhere to the information derived from the real-world WMS.

Appendix B

Empirical distributions of satellite travel time

Table 6 reports the basic statistical metrics associated with the various empirically obtained distributions over 24 working days (not related to the conducted experiments).

A concise legend accompanies the table: N_obs denotes the number of observations, Avg indicates the average value in seconds and Std the standard deviation in seconds.

If no observation is available for a certain configuration, the asterisk is used.

In case the number of observations is insufficient to derive a statistical distribution, observations from the closest depth ranges with same number of stacks are used.

Table 6 Empirical distributions of satellite travel time

Appendix C

Experiment results

The average number of inbound orders NS resulted 851.

On the other hand, the average picking workload at different values of SP% is reported in Table 7.

Table 7 Workload conditions

In Tables 8, 9, 10, the performance for $C{P}_{1}$, $C{P}_{2}$, and $C{P}_{3}$ are respectively reported at different values of SP%.

Table 8 Performance for $C{P}_{1}$

Table 9 Performance for $C{P}_{2}$

Table 10 Performance for $C{P}_{3}$

Appendix D

Sensitivity analysis results

Below is a summary of the results obtained from the sensitivity analysis of the ${k}_{2}$ and ${k}_{3}$ kinematic profiles described in Sect. 4.5.2.

See Figs. 11, 12, 13, 14 and Tables 11, 12, 13, 14, 15, 16, 17.

Fig. 11

Plot of CT and OVP% across the three completion points for ${k}_{2}$ profile

Fig. 12

Plot of CT and OVP across the three completion points for ${k}_{2}$ profile

Fig. 13

Plot of CT and OVP% across the three completion points for ${k}_{3}$ profile

Fig. 14

Plot of CT and OVP across the three completion points for ${k}_{3}$ profile

Table 11 Overview of performance evaluation for the three experiments in the sensitivity analysis

Table 12 Performance for $C{P}_{1}$ for ${k}_{2}$

Table 13 Performance for $C{P}_{2}$ for ${k}_{2}$

Table 14 Performance for $C{P}_{3}$ for ${k}_{2}$

Table 15 Performance for $C{P}_{1}$ for ${k}_{3}$

Table 16 Performance for $C{P}_{2}$ for ${k}_{3}$

Table 17 Performance for $C{P}_{3}$ for ${k}_{3}$