Simulation Model as an Element of Sustainable Autonomous Mobile Robot Fleet Management

Abstract

Computer simulations of processes are increasingly used in business practice to improve the results of an enterprise and maximise its value. Designing process models and simulating their behaviour provide the opportunity to analyse economic and operational results before appropriate organisational, location, and investment decisions are made. This article presents the possibilities of using simulation modelling in intralogistics systems. In the presented article, a decision-making support tool based on the DES simulator developed by the authors was proposed. This tool supports the decision-making process based on the analysis of parameters that affect the energy efficiency of the analysed process and its sustainability. The possibilities of the proposed tool were presented by giving an example of the analysis of the implementation of the automation of intralogistics processes. As part of the implementation, the use of Autonomous Mobile Robot (AMR) vehicles was proposed. By conducting experiments of the intralogistics system model and analysing the obtained results also in terms of energy consumption by AMR vehicles, the proposed project can be verified and improvements can be proposed. The results obtained in this research confirmed the possibility of using the proposed tool for supporting the decision-making process for assessing the energy efficiency of the designed intralogistics system. The proposed method is a cost-free element of analysis that helps the management staff of a given enterprise make appropriate decisions.

1. Introduction

Intralogistics, or internal logistics, is a part of logistics that deals with the organisation of the flow of materials and information within an enterprise. It includes areas such as the internal transport of materials, inventory and information flow management, and warehouse management. Intralogistics planning is an extremely precise task that aims to synchronise production and warehouse processes. Therefore, close cooperation is necessary between various departments that influence intralogistics management: supply, marketing, warehouse, production, etc.

The basic task of intralogistics is to organise the flow of products, semi-finished products, and components within a company. Additionally, it includes the flow of information related to it. Internal logistics concerns all activities related to the transport of products in a company, starting from the production line or receipt of goods and ending with their preparation for shipment. It is worth emphasising that intralogistics also includes the traceability of products and their management. Intralogistics is used not only in typical manufacturing companies but also in distribution or warehouse centres. In manufacturing companies, intralogistics focuses on the delivery of components and semi-finished products for production and on the transport of finished products to a specific place in the warehouse, where they are to wait for shipment. Then, the order is completed and sent to the end customer. Distribution centres deal with the receipt of goods from suppliers and the completion of orders together with their shipment to customers. The transport of goods in such places must be carried out quickly and without errors in order to meet customer expectations. Although intralogistics solutions are used only for processes occurring within a company, they are also influenced by external factors such as the supply and demand of goods. The correct sequence of product rotation, quality control, correct order picking, as well as the optimal use of the warehouse are the basis for the proper functioning of the company’s logistics system and contribute to a higher level of customer service, which is the goal of every company. The most important areas of intralogistics are processes related to the internal transport of goods in order to optimally organise production and storage, as well as order picking [1]. Internal transport is an important process that has a great impact on production and storage logistics. Transport logistics is responsible for the correct operation of the flow of materials, both externally and internally. It is responsible for timely deliveries to customers and operational activities taking place inside the plant. The internal transport of goods primarily includes their transfers within the main warehouse. However, this area of intralogistics may also concern transfers taking place between individual production plants and other warehouses belonging to one company. We also deal with internal transport in other areas. In addition to manufacturing companies, distribution centres, or warehouses, internal transport is also used in large-scale stores, where among others, it performs tasks such as replenishing goods on shelves [2]. The process of intralogistics optimisation also requires the use of appropriate intra-warehouse transport. Implementing automation is particularly important for companies that perform many repetitive activities on a daily basis.

The automation of internal product flow is a key element of modern production and storage management systems. Thanks to the use of advanced technologies, such as automated conveyors, robots, and stacker cranes, it is possible to significantly improve internal transport processes [3]. The automation of logistics processes eliminates many manual operations, reducing the risk of errors and increasing efficiency and precision. One of the most important trends in intralogistics are Autonomous Mobile Robots (AMRs) and automated guided vehicles (AGVs) [4,5].

According to a study by Research and Markets, the AGV and AMR market is expected to reach approximately USD 20 billion by 2028, growing by approximately 22% for AGVs and 37% for AMRs [6]. The combined installed base of AGVs and AMRs is expected to exceed 2.7 million by 2028, making mobile robots a common presence in daily operational activities. AMRs are expected to register a compound annual growth rate (CAGR) of approximately 37% between 2023 and 2028, making them a more attractive market segment compared to AGVs by 2028, with increased shipments and share in the total addressable market (TAM) [7].

The automation of intralogistics systems through the implementation of AMR vehicles requires large financial outlays. When choosing an automation system, issues of sustainable development and the efficient use of resources are increasingly taken into account. They are currently becoming increasingly important, which is why energy consumption is one of the key parameters when deciding to purchase new robots, and the effective management of automatic processes can contribute to reducing energy consumption. Total energy consumption is becoming significant, and each kilowatt saved by the company on a yearly basis already yields specific financial savings. AMRs are not only an element of the transport system but also an important element of the energy saving strategy in companies. Therefore, it is justified to conduct simulation studies of the analysed system before its physical implementation in the enterprise, especially since the real environment is usually complex and requires many analyses to ensure that the planned system will operate effectively. The aim of this article is to demonstrate the advisability of using the DES simulator to predict the behaviour of the analysed processes and make decisions, in particular regarding the degree of automation of the analysed process, energy consumption by AMR vehicles, and charging frequency.

The literature review conducted by the authors showed that the works on simulation modelling do not directly concern the issue of supporting the decision-making process based on the results of the energy efficiency of AMR vehicles. Energy efficiency appears in the context of research carried out mainly on physical systems [8,9,10]. Therefore, the authors proposed a tool for supporting the decision-making process based on the analysis of parameters affecting the energy efficiency of the analysed process and its sustainability. In transport systems using AMR vehicles, the issue of task implementation and scheduling depends on the battery capacity and the rate of energy consumption. Therefore, the energy efficiency of such a transport system is another significant challenge for their operational sustainability. Energy efficiency is an important factor in the sustainable operation of many AMR vehicles. Since battery energy consumption is closely related to total mileage, the presented tool focuses on the analysis of tasks performed by individual AMR vehicles, the distance travelled, and the number of battery charges during the tasks performed. Knowledge of all these parameters at the process design stage allows for a company’s management to make the right decisions.

Taking the above into account, the authors formulated the following research question:

Does the proposed decision-making support tool based on the DES simulator enable the assessment of the energy efficiency of the designed intralogistics system?

The structure of this article is as follows. The Introduction presents the characteristics of intralogistics processes and their automation with a particular emphasis on AMRs and AGVs and provides the purpose of the presented research. The Literature Review Section reviews the literature on the use of AMRs in intralogistics and simulation modelling methods applied to AMRs. The second chapter, the Materials and Methods, presents the applied methodology. A modelling and simulation-based methodology for developing a decision-making support tool was proposed for the degree of automation of the analysed process and energy consumption. This method is based on discrete event simulation and a designed module enabling the acquisition of key output parameters and monitoring of environmental conditions and showing correlations between variables in the sets of obtained information. The next chapter, the Results and Discussion, presents a model of the intralogistics system, for which the developed tool was used and its operation was tested. The simulation studies carried out on it allowed for the assessment of the efficiency of the internal transport process. The obtained results were presented and discussed regarding the validity of the proposed solution. The whole article ends with a summary.

2. Literature Review

2.1. The Use of AGVs and AMR Vehicles in Intralogistics

AGVs are used to perform activities requiring a lower degree of autonomy [11]. AMRs, on the other hand, develop in dynamic environments, using autonomous navigation. They create and store maps of facilities, which allows them to adjust routes in the event of obstacles. AMRs are more flexible and easy to implement, requiring minimal adjustments when changes occur in the facility [12,13,14]. This means that the optimisation of intralogistics processes should be viewed comprehensively from the perspective of the entire system. The main direction of intralogistics development in production and warehouse plants assumes minimising human involvement. Autonomous AMRs allow for maintaining process continuity in the event of unpredictable changes in the labour market.

The organisation of a full fleet of robots allows for the comprehensive implementation of intralogistics processes. In order to minimise the need for human involvement and maximise transport automation, autonomous vehicles are adapted to cope with various logistics carriers. The work in [15] presents an example of the use of AMRs to supply assembly lines in the automotive industry. AMRs ensure the security of internal supply chains and the optimisation of transport costs. To achieve maximum transport efficiency, the AMR constantly cooperates with the fleet management system [16,17]. This software, running on a central server, manages the transport orders of robots: it determines collection points, deliveries, and periods and places for stopping and charging batteries. Thanks to the use of artificial intelligence and machine learning algorithms, AMR vehicles are able to quickly respond to changing production conditions and dynamically adjust their trajectories, which is crucial in a rapidly changing work environment [18,19,20,21].

2.2. Overview of Models and Modelling Methods in the Field of Logistics

Effective analysis and planning of internal transport systems require the use of appropriate solutions and tools. Depending on the scale of the problem, as well as the complexity of the system being studied, different classes of methods can be used: analytical methods, identification and optimisation methods based on operational research algorithms, and simulation modelling methods such as discrete event modelling or agent-based modelling. The choice of method should be based on the system being modelled and the modelling goal, although it is often largely dependent on the experience or available toolkit of the modeller.

An example of the use of discrete event simulation (DES) are the articles in [22,23,24,25,26,27,28,29,30,31]. The paper in [22] concerns the examination of the impact of a new solution on the existing internal logistics system in the form of autonomous vehicles, as well as whether new management strategies are needed to meet the throughput levels and general needs of the supply chain. In the paper in [23], the authors conducted simulation studies of a real production line. The authors analysed the current situation and proposed actions to optimise the functioning of the line. The paper in [24] concerns simulation studies to demonstrate the advantage of using a robotic production line in comparison to a manually operated line. The paper in [25] discusses the approach to discrete event simulation, supported by a set of tools that help to build a supply chain model, the purpose of which is to express and assess the risk associated with it, with particular emphasis on the risk associated with orders. Another paper dealing with the subject of discrete event simulation is the paper in [26]. The simulation method was used in the process of designing and analysing an automated sorting system in a warehouse for a company producing bags.

The article in [27] presents the use of discrete event simulations to improve the flow of materials in the process of receiving goods in the warehouse. The work in [28] is also devoted to the simulation of selected activities in the warehouse. As part of the simulation studies, the authors conducted experiments that will allow for the creation of an appropriate operational tool for the analysed enterprise. In the work in [32], the authors used discrete event simulation to model supply logistics problems. The simulations presented by the authors concerned the supply process using the Milk Run system.

In [29], the authors used the DES method in the process of implementing AGVs in the automotive industry. Simulation studies were used, among other things, to estimate the required number of AGVs. An example of the use of simulation studies in the logistics industry is also discussed in [30]. Its aim was to analyse and identify the potential of computer simulation using a hierarchical structure to increase the efficiency of designing logistics systems on a large scale in production, using the example of the automotive industry.

Nowadays, the demand for predicting the behaviour of analysed processes and making decisions in near real time is very common. This has led to the evolution of DES into an integral part of Digital Twins (DTs). Discrete event simulation software takes on the role of the cyber twin, executing simulation software tasks on real-time data generated by IoT devices embedded in the physical twin, i.e., automation, which are then processed, updating the simulation to the next state of the system [33,34,35,36].

The second of the mentioned simulation modelling methods—agent-based modelling (ABM)—is also used in modelling processes in the area of logistics. An example of its use is the work discussed in the following part. The authors of [37] proposed using the ABM method to model and minimise transport costs when collecting logs from several regions and delivering them to the nearest collection point. The work in [38] concerns solving the problem of assigning tasks to a group of automated guided vehicles handling the internal transport of a warehouse or factory. Instead of a central task planner, the authors used an agent-based approach in which agents represent all stakeholders in the transport system. Another example of the use of the ABM method is the work presented in [39]. Its authors used this method to model the problem of designing a closed supply chain network, the aim of which was to integrate customer behaviour with the network. The authors of [40] used the ABM method to analyse the state of a hospital goods delivery system in order to improve internal logistics.

The works discussed above, summarised in

Table 1. Comparison of methods and research areas in the field of logistics and the simulation methods used.

Source	Research Objective	Research Area	Simulation Method
[22]	Research on new management strategies	Internal material flow system using autonomous vehicles	DES
[24,25,30,31,32]	Process optimisation	Production processes	DES
[26]	Business risk measurement	Production processes	DES
[27,28]	Warehouse process optimisation	Warehouse processes	DES
[29]	Selection of the number of means of transport	Automation of internal transport	DES
[37]	Minimising transport costs	Supply chain	ABM
[38]	Assigning tasks	Internal transport system	ABM
[39]	Observing the behaviour of the supply chain network in different conditions	Supply chain	ABM
[40]	Improving internal logistics	Goods delivery system	ABM

, present examples of the use of DES and ABM methods in the area of broadly understood logistics.

The decision between agent-based modelling (ABM) and discrete event simulation (DES) is a key choice for any simulation project. Each approach offers distinct advantages that are useful in different situations. Agent-based modelling is useful for modelling complex, adaptive behaviour in a system. This approach works best when individual entities must make autonomous decisions or when interactions between system components significantly affect overall behaviour. In contrast, discrete event simulation is useful in process-driven, sequential operations where time and resource utilisation are paramount. DES is valuable for analysing structured workflows, optimising resource allocation, and identifying bottlenecks in the analysed processes. This method is effective in scenarios where events occur in a relatively predictable order and system states change at specific times. The decision-making tool proposed by the authors is intended for internal transport systems operating in the production hall. The process under consideration is a structured workflow. Vehicles perform sequential operations. Therefore, a decision was made to implement a discrete event simulator into the proposed solution. The conducted analysis of the literature led the authors to the conclusion that the use of simulation methods in intralogistics processes mainly concerns research in the area of optimisation of the analysed production processes focused, among others, on the analysis of bottlenecks or transport processes in terms of the selection of means of transport. No work was found in which simulation methods would be used to analyse automated transport processes based on indicators proving their energy efficiency and thus achieving sustainable development through the optimisation of energy consumption. Therefore, the authors decided to use this gap to develop a tool supporting the decision-making process based on the analysis of parameters affecting the energy efficiency of the analysed process and its sustainability.

3. Materials and Methods

Process simulations are a tool that is increasingly used in business practice. Creating process models and simulating their behaviour enable the analysis of both economic and operational results before appropriate organisational, location, and investment decisions are made. They are activities carried out before the planned reconstruction of processes or organisational structures of the enterprise. The need for modelling and simulation is the result of striving to improve the results of the enterprise and maximise its value [41]. The modelling and simulation of processes in the supply chain results from the need to test various scenarios of actions and variants of organisational solutions such as work organisation, the allocation of production stations, production route scenarios, material flow, internal transport, and co-production processes.

Simulation models are generally classified as descriptive models. Their main goal is to imitate the behaviour of a real system using a created model of its functioning. The results of a simulation model contain two parts: a diagnostic part, which provides information about the dynamics of the system’s operation at subsequent points in time, and an analytical part, which contains aggregate numerical data describing the characteristics of the analysed processes. Simulation models can also be used to optimise the behaviour of a process, and therefore they can also be classified as normative models.

Discrete event simulation (DES) refers to modelling a system in which any changes in the simulation model are represented by events that occur when certain conditions occur. Due to the dynamic nature of discrete event simulation models, the current value of the simulated time must be tracked as the simulation progresses, and a mechanism is required to shift the simulated time from one value to another. This is because time changes in increments depending on the occurrence of discrete events. The variable in the simulation model that provides the current value of the simulated time is called the simulation clock.

The DES method is used in situations where we are dealing with known processes for which uncertainty situations can be defined using probability distributions.

There is no single universal way to build simulation models. Models can be built using a variety of techniques and methods, each of which can meet the goal of the simulation project. Modelling and simulation usually proceed in three successive stages: defining the simulation model; validating the model; and generating simulation results.

In stage 1, the simulation model is defined. The definition process consists of describing the simulation goals, input and output data, assumptions and adopted simplifications of the simulation model being built, and system elements selected for modelling and their mutual relations. Proper implementation of the tasks in stage 1 reduces the costs of building the simulation model and reduces the number of possible corrections. The second stage includes model validation, i.e., building the model in the selected IT tool and its testing and approval. Validation consists of checking whether the model reflects the real system, whether the results from the model are consistent with the real results, and whether the model can be used to make decisions about the real system. The model is usually approved by the staff of the company where the project is carried out. These are usually employees of middle or higher management level. The aim of stage 3 is to conduct simulation experiments and develop various scenarios, depending on the variable parameters of the model. At the stage of the analysis and interpretation of the results, the results of experiments are analysed step-by-step, and the optimal solution is selected in terms of the optimisation criteria adopted in stage 1.

One of the most time-consuming tasks in developing simulation models is the process of collecting and preparing data that are then used to build a computer model. That is why there is an increasing tendency to feed simulation models with data from enterprise IT systems, such as Enterprise Resource Planning (ERP), supply chain management (SCM), Customer Relationship Management (CRM), Manufacturing Execution System (MES), Product Lifecycle Management (PLM), and computer-aided technologies (CAx).

The current production, logistics, or transport processes are complex and often very complicated. The mathematical models built for these processes are based on advanced mathematical apparatus. In such a situation, it is beneficial to use ready-made simulation packages. In such a solution, the mathematical model can be implemented using programming languages or specialist tools designed for modelling and simulation. The use of computer tools for modelling and simulation significantly shortens the time of analysis of the modelled process and thus allows for quick decision-making.

In the case of computer simulation tools, there is no universal software. When choosing software, one should be guided by the purpose of the simulation and the type of process being analysed. The main areas related to the management of economic processes in which computer modelling and simulation are used include production logistics, management of the flow of goods in non-production economic units, supply chain management, manufacturing processes, reorganisation and workflow, and risk analysis.

The software offer is very wide. The most popular simulation packages include Arena, AnyLogic, FlexSim, Simio, Plant Simulation, Enterprise Dynamics, and Simul8. All of the above-mentioned packages are classified as discrete event simulators and can be used to study intralogistics processes. A detailed review of the most popular discrete event simulators is presented in [42]. In the research presented in the article, the Enterprise Dynamics (EDs) programme was used, which is a programme designed to create models for the simulation of processes, including production processes, storage and distribution processes, and transport processes [43,44,45,46].

The research results presented in this paper concern the development of a tool supporting the decision-making process in intralogistics processes based on system parameters influencing the energy efficiency of the proposed solution. A case study analysis was also conducted for an exemplary company. The scheme of the proposed methodology is presented in Figure 1.

The basic element of the proposed methodology is modelling and simulation. The developed DES model takes into account all the elements necessary to analyse the system under study. They create a set of input parameters, which is described by Equation (1).

IP = {Iw, Iv, Id}

(1)

where:

• Iw—information about work stations (number, operation time);
• Iv—information about AMR vehicles (speed, load time, unload time, battery capacity);
• Id—distances between objects defining transport routes for the transport of raw materials and final products.

These parameters were determined based on an interview conducted at a company wishing to implement an automated transport system within the production line and a market study of AMR vehicles, which allowed for the selection of an appropriate hardware solution. During the interview, collection and pickup points were designated and the lengths of the transport routes and the widths of corridors were measured. The location of chargers was also determined (the location of chargers was not subject to optimisation; it resulted directly from the current energy infrastructure). When selecting vehicles, criteria such as technical parameters, price, and capabilities of the fleet management software were taken into account. The defined set of input parameters was imported to the database, which then supplied the developed simulation model with the necessary information. The simulation model was developed in the Enterprise Dynamics tool and takes into account all the elements of the process architecture described by Equation (2).

M = {IP, E, R, P, O}

(2)

where:

• IP—input parameters;
• E—elements (raw materials, energy);
• R—resources (machines, vehicles);
• P—transition paths;
• O—outputs: type of tasks performed by AMRs, distances covered, times of operations performed by vehicles (driving with load, driving for load, waiting for a task, picking up load, putting down load).

Simulation studies conducted on the tested system cause a change in the system state at time t, which is described by Equation (3)

O = f(m, t) where m = (IP, E, R, P, t − 1)

(3)

A script written by the authors in 4DScript was used to record tasks performed by individual AMR vehicles. This script enables real-time recording of output parameters necessary for further analysis of the system evaluation. These include type of task (from what point the raw materials were collected or deposited), transport operation time, driving time, etc. The next stage was to prepare a configuration file allowing for loading output parameters characterising the designed system into the analytical module of the developed tool (for simulation studies lasting 120 h, the file recorded over 25 thousand data records). The developed analytical module is characterised by a universal architecture that allows it to be adapted to various analysed scenarios (e.g., different configuration of the transport system). The module also allows for sorting output data according to the established criteria, e.g., travel between individual points, counting travel times, etc. In order to increase the readability of the analysed data, visualising the results in the form of standard charts (bar, line) and in the form of a heat map is proposed, which is very helpful in the analysis of tasks performed by the vehicle.

Validation was performed for the developed model. Its purpose was to minimise the risk of an incorrect decision being made based on an incorrect model or a model generating incorrect results. Static and dynamic validation was performed. Static validation concerned the conceptual model and the correctness of its mapping to the computer model. In this case, analyses of data flow and syntax and semantics of the model were performed. In the case of dynamic validation, the dynamic behaviour of the model was analysed. Face validity was used among the techniques used.

The capabilities of the developed tool were tested for a case study, which was the intralogistics system in an example enterprise presented in the next section.

4. Model of an Intralogistics System Based on AMR Vehicles

The proposed simulation-based approach was applied to the intralogistics system in the sample company. Due to the high demand for products and the subsequent increase in production efficiency and flexibility, the company decided to improve the intralogistics process by implementing AMRs in the final stage of the production process. It is expected that such a solution will shorten the transportation time and contribute to the increase in process efficiency. In the analysed company, the following intralogistics-related activities were planned to be performed by AMRs:

• The loading of containers with products delivered from the production line and transporting them to the picking station;
• The unloading of containers and transferring them to the picking station;
• The loading of containers and transport to the quality control station;
• The unloading of containers and transferring them to the quality control station;
• The loading of cartons from the packaging station and transferring them to the finished goods warehouse;
• The unloading of cartons in the finished goods warehouse.

The simulation model of the analysed intralogistics system was made in the Enterprise Dynamics 10.6 software. Figure 2a,b show the simulation model and schematic layout of the analysed intralogistics system. In the case under consideration, it was determined that the main goal of this research is to analyse the operation of the AMR vehicle system used to implement the auxiliary process of transporting load between stations. The conducted research focused on the issue of managing the operation of the transport system, task allocation, the degree of use of individual vehicles, as well as energy consumption, which is one of the key parameters influencing decisions on the purchase of new robots. To conduct the intended research, the proposed and developed decision-making support tool was used.

It was assumed that an AMR vehicle would be implemented as part of the automation of the intralogistics system. The company decided to implement an AMR vehicle from Omron Corporation, Kyoto, Japan. The vehicle and its parameters are shown in

Table 2. Autonomous Mobile Robot LD-90 and its technical parameters.

LD-90	Parameters	Values
	Dimensions	500 mm × 699 mm × 383 mm
	Weight (with battery)	52 kg
	Payload	90 kg
	Maximum speed	1.35 m/s
	Battery	Lithium-ion (3.2 V, 72 Ah)

. Technical parameters are from the manufacturer’s specifications.

The work environment in which the AMR will move does not have too many turns, and the transport routes are wide enough to allow two AMR vehicles to pass each other, as well as to manoeuvre independently around obstacles (e.g., a load left behind or a passing employee). The situations listed are a characteristic feature of the behaviour of AMR vehicles that distinguishes them from AGVs. The independent navigation of AMRs is possible thanks to the use of a system of advanced sensors, AI, and advanced algorithms. These factors were included in the developed model. The AMR will load and unload the load independently, and the time needed to perform these operations is 5 s. It was assumed that the vehicles head to the charging station when the battery charge level drops below 25%. Setting the level of 25% after which the vehicle starts the charging process is a standard recommended by the vehicle manufacturer LD-90. Therefore, simulation studies were conducted for this threshold. In the presented tool, it is possible to change this threshold and conduct studies for a different set of input parameters.

The technical analysis carried out showed that a maximum of three AMR vehicles could operate in the analysed environment. Therefore, the designed system also included three charging stations for AMR vehicles and reserved appropriate space for them in the hall.

5. Results and Discussion

Simulation studies were conducted for a period of 120 h. The analysis covered an internal transport system consisting of three AMR vehicles. First, the operation of the fleet management system responsible for assigning tasks to individual vehicles was analysed. Tasks were assigned to AMR vehicles in accordance with the order of their assignment in the fleet management system offered by the manufacturer. According to this rule, the system searches for a free AMR, starting the search from the first vehicle in the fleet management system database. This is one of the available methods of assigning tasks to the AMR vehicles available in the real fleet management system. Therefore, it was implemented in the presented case. The model allows for testing other rules as subsequent scenarios. The queue of transport tasks is handled in accordance with the FIFO rule. AMR vehicles had to perform three different tasks, consisting of driving the AMR for cargo, collecting the cargo, and transporting it to designated positions and depositing the cargo. Within these three tasks, subtasks were specified, consisting of driving the AMR for cargo or collecting the cargo, transporting it to the designated position, and depositing the cargo. Since the AMR could be located in different places in the system at the time of receiving the task from the fleet management system, 12 such subtasks were specified, as shown in Figure 2.

Table 3. Number of tasks completed by individual AMR vehicles.

-	1-2	2-1	2-3	2-5	3-4	4-1	4-3	4-5	5-6	6-1	6-3	6-5
AMR1	1842	966	174	702	941	504	131	306	1435	371	637	427
AMR2	1348	405	428	515	1686	629	455	602	1334	314	802	218
AMR3	1042	172	338	532	1604	568	430	605	1461	302	836	323

presents a numerical summary of tasks assigned and performed by individual AMR vehicles during the 120 h simulation period of their work.

The implementation of individual tasks is closely related to the AMR vehicle covering appropriate distances between the places where the load is picked up and deposited. The graph in Figure 3 shows the distances covered by individual AMR vehicles. As can be seen, the greatest distance of 260.03 km was covered by AMR1. This is the first vehicle assigned to the AMR fleet management system. The second vehicle covered a distance of 239.13 km, while the third covered a distance of 224.65 km. The last vehicle on the AMR fleet management system list covered a shorter distance of 35.38 km compared to the first AMR.

The distance travelled by the AMR vehicles was also presented in relation to the tasks completed by the individual AMR vehicles, and the results are presented in

Table 4. Distance in km covered by AMR vehicles in the implementation of individual tasks.

-	1-2	2-1	2-3	2-5	3-4	4-1	4-3	4-5	5-6	6-1	6-3	6-5
AMR1	58.944	30.912	0.696	16.146	12.233	24.696	1.703	1.836	40.180	30.793	29.939	11.956
AMR2	43.136	12.960	1.712	11.845	21.918	30.821	5.915	3.612	37.352	26.062	37.694	6.104
AMR3	33.344	5.504	1.352	12.236	20.852	27.832	5.590	3.630	40.908	25.066	39.292	9.044

.

As part of the simulation studies, it was also possible to analyse the states of the AMR vehicles: taking the load, putting the load down, driving with the load, driving for the load, waiting for the task, and charging. Detailed data on the individual AMR vehicles are presented in Figure 4. The first vehicle devoted 61.44% of the simulation time to performing the assigned tasks, and 10.77% of the simulation time was waiting for the task to be assigned. On the other hand, it spent 27.79% of the simulation time in the charging station. In the analysed period, the AMR1 vehicle performed the charging operation eight times. The second AMR vehicle devoted 57.91% of the simulation time to performing the assigned tasks, and 14.25% of the simulation time was waiting for the task to be assigned; on the other hand, it spent 27.84% of the simulation time in the charging station, performing eight charging operations, just like the first vehicle. In the case of the third AMR vehicle, it performed its tasks for 54.91% of the simulation time, waited for the next task for 20.73% of the simulation time, and spent 24.36% of the simulation time charging the battery; it performed seven charging operations.

Based on the results obtained, the average charging time of AMR vehicles can be determined, which was approximately 4 h 9 min 46 s to 4 h 10 min 14 s with a 95 percent confidence interval. The results obtained are consistent with the information provided by the manufacturer.

As part of the simulation studies, we also decided to analyse one work cycle of individual AMR vehicles and determine the battery discharge curve for individual AMR vehicles. This graph is presented in Figure 5. A cycle from the middle of the simulation period was selected to analyse the battery discharge curve for the steady state of the analysed system. For the first vehicle, the work cycle was 9 h and 23 min, for the second vehicle it was 10 h and 44 min, and for the third vehicle it was 12 h and 23 min. It should be noted that the work cycle in this case also includes the vehicle waiting for the next task. In this state, the vehicles did not consume energy in the simulation studies. In real operating conditions of the transportation system, task waiting operations involve minimal energy consumption.

For one cycle of work of AMR vehicles, data were also presented that allowed for the analysis of the states in which the vehicles were. These data are presented in Figure 6. Within one cycle of work, the AMR1 vehicle spent 7 h and 59 min on the implementation of assigned tasks, which is 85% of the duration of a single cycle of work for the AMR1 vehicle. The AMR2 vehicle spent 8 h and 10 min on the implementation of assigned tasks, which is 76% of the duration of a single cycle of work for the AMR2 vehicle. In turn, the AMR3 vehicle spent 8 h and 8 min on the implementation of assigned tasks, which is 66% of the duration of a single cycle of work for the AMR3 vehicle.

Table 5. Number of tasks completed by individual AMR vehicles during one work cycle.

-	1-2	2-1	2-3	2-5	3-4	4-1	4-3	4-5	5-6	6-1	6-3	6-5
AMR1	205	100	15	90	110	75	11	23	156	30	83	43
AMR2	161	49	48	64	217	85	59	72	159	26	110	23
AMR3	127	13	55	59	214	63	54	96	191	51	104	36

and

Table 6. Distance in km covered by AMR vehicles as part of the implementation of individual tasks during one work cycle.

-	1-2	2-1	2-3	2-5	3-4	4-1	4-3	4-5	5-6	6-1	6-3	6-5
AMR1	6.560	3.200	0.060	2.070	1.430	3.675	0.143	0.138	4.368	2.490	3.901	1.204
AMR2	5.152	1.568	0.192	1.472	2.821	4.165	0.767	0.432	4.452	2.158	5.170	0.644
AMR3	4.064	0.416	0.220	1.357	2.782	3.087	0.702	0.576	5.348	4.233	4.888	1.008

present the number of tasks completed by individual AMR vehicles during one work cycle and the distance travelled over the course of completing individual tasks.

The results presented in Table 3, Table 4, Table 5 and Table 6 were developed using heat maps. These maps are analytical tools that allow for a graphical representation of the most important information related to the behaviour of AMR vehicles. Warmer colours—such as red and orange—indicate the most frequently performed tasks and the longest distances travelled. On the other hand, cooler colours—such as green—suggest areas with lower AMR activity within the performed tasks and shorter distances travelled.

The conducted studies have shown, similarly to the works of [22,25,47,48], that the use of discrete simulation allows for the evaluation of complex systems and testing of operational strategies before implementation. In addition, simulation models allow for a better understanding of the characteristics and requirements of the systems. The proposed decision support tool emphasises the analysis of parameters that help achieve sustainable development through energy consumption optimisation. Energy consumption optimisation is possible by reducing energy consumption thanks to energy-efficient drives and reducing greenhouse gas emissions through effective automation and promoting sustainable practices, contributing to a more ecological industry. Therefore, the proposed decision support tool is very helpful in the process of designing an automated intralogistics system because it helps to make decisions that affect effective automation and enables the introduction of sustainable practices in the organisation. Thanks to the possibility of using simulation modelling and the proposed analytical module, it is possible to make the right decisions regarding the selection of the system. The proposed tool, thanks to the use of the DES tool, enables quick adaptation of the analysed system to another selected configuration (layout, number and type of means of transport). On the other hand, thanks to the universality of the developed analytical module, it is possible to quickly obtain output parameters, the assessment of which is crucial at the process design stage.

The simulation studies conducted do not take into account all factors from the real process, e.g., energy consumption in the vehicle waiting mode, floor friction, battery degradation, or ambient temperature. Therefore, they are an element supporting the design process and should be verified by a team of specialists responsible for the implementation of the system. Simulations allow the designer to assess the quality of the project and control the proposed solutions in terms of meeting the assumed priorities. In subsequent works, the authors plan to improve the proposed tool by taking into account the limitations that were identified during the research. Nevertheless, the obtained results of simulation studies regarding primarily battery discharge cycles and their charging times were confirmed in interviews with the manufacturer.

In the next stages, the authors plan to conduct experimental studies on the real system in the field of energy consumption and measurement of parameters indicating the energy efficiency of the analysed system and verify them with the results obtained for the virtual system. As part of future research, the authors also plan to implement deep reinforcement learning (DRL) in their simulator. The possibilities of implementing the DRL method in the DES simulator were presented in [49]. DRL is currently becoming an effective method for solving intralogistics problems, including issues related to electric vehicle control, scheduling, and energy management of electric vehicles. This approach can be found in the works of [50,51,52,53]. For this purpose, the simulation model served as an environment that the DRL agent will use for interaction, learning, and verification. In the case of energy management research, the aforementioned environmental factors are important, such as the energy consumption in vehicle standby mode, floor friction, battery degradation, or ambient temperature. In the case of decision problems concerning multi-vehicle cooperation based on deep reinforcement learning (DRL), the interactions between vehicles should be represented. Transformer learning algorithms presented in [54,55] can be very helpful in such cases. The authors also consider implementing these algorithms in their future research.

6. Conclusions

Automated and robotic intralogistics solutions bring many benefits to companies. The key element for the proper functioning of such systems is the integration of industrial automation systems with IT systems. Implementing devices appropriate for a given company allows for reducing operating costs and increasing efficiency. The use of robots increases precision in processes and relieves employees. Companies that effectively implement automation in intralogistics processes gain competitiveness, better manage resources, minimise errors, and increase customer satisfaction. Since the automation of logistics processes is associated with costs, this article indicates the benefits of using simulation modelling to analyse systems planned for implementation; in this case, these are intralogistics systems using AMR. Conducting previous analyses in a virtual environment allows for analysing the system’s operation and making the right decisions before physically implementing it in the company. The main parameters analysed were the types and number of tasks performed by individual vehicles, the degree of use of individual vehicles, the distance covered, the length of a single AMR vehicle work cycle, and the battery charging time. Knowledge of these parameters allows for appropriate management of the work of AMR vehicles, taking into account the issues of sustainable development and efficient use of resources. In this case, the aim is to use the vehicles as efficiently as possible and minimise their energy consumption. The conducted research for the considered case confirmed the research question. Verification of the obtained results confirmed the effectiveness of using a decision-making support tool based on the DES simulator in the matter of assessing the energy efficiency of the designed intralogistics system. The results obtained from the simulation tests, especially those concerning the energy efficiency of the AMR vehicle, were confirmed on the basis of information obtained from the manufacturer.

As part of the simulation studies, we are able to determine transport tasks consisting of transporting load and driving the AMR vehicle to pickup load. An AMR vehicle moving with a load consumes more energy than when driving without a load. Therefore, knowledge of the number and type of tasks performed, as well as the distances covered in their implementation, allows for the estimation of energy consumption and the length of a single AMR vehicle work cycle. Another important piece of information is the time needed to charge the AMR vehicle battery. In such a case, the vehicle is out of service and the tasks are carried out by the remaining AMR vehicles.

Carrying out simulation studies from this perspective means that AMR can not only be an element of the transport system but can also be an important element of the energy saving strategy in enterprises.