Data-Driven Modeling and Simulation in Forestry and Agricultural Product Transportation Management by Small Businesses: A Case Study

Abstract

This article proposes an innovative methodology for data-driven modeling and simulation of transportation management through cross-sectoral collaboration in small businesses. The present research is multidisciplinary and interdisciplinary in nature. We investigate the improvements in logistics management that can be achieved through cross-sector collaboration in agriculture and forestry. A data-driven method, such as symbolic regression, is used to identify the relationships between factors in a modeled system using mathematical expressions. These expressions are directly integrated into the simulation models. Simulation spreads the modeling of transportation processes over a period of time. The system dynamics model is designed to analyze and assess the performance of a system based on its past behavior and is, therefore, deterministic. The discrete-event model enables the simulation of future scenarios and outcomes over time, given random input variables. As new data become available, relationships within the symbolic regression method are discovered more accurately, and simulations are updated accordingly. The tools offered for implementation are supplemented by a multi-user web simulation. The proposed case study is based on a real-life example. The obtained results allow small agricultural companies to use transportation and labor resources more efficiently when organizing the transportation of their agricultural and forestry products. Integrating data-driven models into simulations enables a better interpretation of data across the entire data value chain.

1. Introduction

The challenges of rural transportation services are widely discussed in the literature and require the implementation of innovative approaches, cooperation policies, and the integration of new technologies [1]. The proposed work presents methods and tools for managing the transport activities of individual small enterprises and farms in rural areas. They are based on the integration of data-driven modeling and simulation-based technologies and take into account the possibilities of cross-sector collaboration [2].

Cross-sector collaboration in rural areas has been mainly studied in the fields of public health, employment, and education, with the accessibility of services to communities and the sustainability of rural areas as the focus. In this article, we consider the context of improving transportation management in small businesses, in particular, the transportation of forest and agricultural products.

Transport logistics in the agricultural and forestry sectors are strongly influenced by seasonal demand for transportation. The seasonality of demand for agricultural transportation naturally depends on harvest time, whereas the seasonality of demand for forestry transportation is associated with the greater accessibility of forest roads during cold periods. This seasonal demand presents important economic and social challenges. During busy seasons, large amounts of specialized and expensive resources are required in the short term, and there is usually a shortage of skilled labor. At the same time, during low seasons, the logistics companies involved have idle resources and are forced to pay high wages to unemployed skilled workers in order to retain them in the company for the next season.

Currently, small agricultural transport companies in the Baltic States typically focus only on transporting products from one specific sector (agriculture or forestry). These businesses usually do not consider the possibility of sharing skilled labor and transportation resources in order to improve their economic efficiency. At the same time, individual small businesses, as a rule, have a fairly low level of digitalization and are not sufficiently equipped with modern information and communication technologies. Thus, there is room for improvement through the mutual collaboration of these businesses by recognizing the value of data [3] and leveraging advances in data processing and data-driven modeling technologies [4].

Data-driven modeling involves using historical and other data to create models that identify trends and patterns in the data and represent them in a structural form. The advancement of computational intelligence and machine learning techniques, as well as the wide availability of accumulated data, have enabled a substantial increase in the use of data-driven models in various application areas.

Data-driven simulation is an emerging trend in the development of computer simulation technologies. It is based on the integration of different data models complemented by computational intelligence and machine learning methods. As a consequence, the simulation evolves from a model-based paradigm to a data-driven one [5]. Moreover, recently published scientific papers promote the integration of new technologies (such as big data analytics and deep neural networks) that enable data-driven simulations and expand the scope of their applications. For example, in [6], data-driven industrial control system network simulations were proposed to generate synthetic data that meet the requirements of machine-learning-based intrusion detection systems. In [7], a dual model-data-driven approach was proposed that combined traffic modeling and local big data analysis for public transportation planning. In another study, it was shown that advanced deep neural networks, as a core element of a data-driven framework for traffic modeling, enable more accurate modeling of vehicle behavior by taking into account both vehicle characteristics and environmental factors [8].

In our study, data-driven modeling uses a symbolic regression model that provides data for executing and monitoring a computer simulation throughout its life cycle, starting with defining the structure of a system dynamics model and then the parameters for a stochastic discrete-event simulation model.

An analysis of the organization of transport services and supplies in individual small agricultural, forestry, transport enterprises, and farms was conducted using the example of Latvia [9]. Considering the seasonal demand for transportation in both sectors, it was found that the planning and organization of logistics in such enterprises could certainly be improved by sharing available vehicles and labor to transport products as needed. Such a collaborative organization of transport logistics at the SME level between different industrial sectors must not only be technically and economically justified but must also take into account all current relevant theoretical and technological developments.

Due to the complexity and interdisciplinarity of the presented research, a review of the literature on various aspects of modeling and organizing transport and logistics services in agriculture and forestry is provided. In particular, it focuses on the application of modeling, data collection, and processing, as well as on issues related to collaboration in decision-making and resource sharing in the agricultural and forestry sectors.

In the forestry sector, both analytical and algorithmic models have been studied to improve transport logistics [10,11,12,13,14,15,16], respectively. However, the proposed models often do not take the seasonality of demand into account. The literature suggests many factors that directly and indirectly affect forestry transport businesses and the environment, such as transportation costs, investments in public infrastructure, and financial assessment of the impact on the environment and ecology [14]. The impact on the labor force and its market was assessed in [11]. Multiple studies [14,15,16] have focused not only on the transportation process itself but also on the supply chain management of all products involved. This will allow for the efficient planning and organization of work processes for the benefit of all participants. In particular, transportation models with cost uncertainty are described in [15], and models with shared transportation resources are presented in [17].

The literature on logistics modeling in the agricultural sector mostly carries out process analyses. Priority is given to the transportation of agricultural products from farms to warehouses and further in the logistics chain to processing or transshipment points. Both system dynamics and discrete-event simulation models are used to analyze different transportation processes. Examples of several models based on system dynamics and their comparisons are provided in [18,19]. Examples of discrete-event models for analyzing farm-scale grain transportation systems and modeling grain logistics from farms to ports are described in [20,21]. Furthermore, Petri nets [22] have been widely used to analyze supply and production chains in the agricultural and forestry sectors. For example, hybrid Petri net models have been used to assess the logistic efficiency of forestry production chains [23] and to plan agricultural work processes under conditions of uncertainty [24,25]. The CPN type of Petri net tools has been applied to model and analyze agricultural supply to the European Union [26].

In the literature, much attention has been paid to analytical models to ensure the efficiency of logistics services. A large number of articles, for example [27,28,29], present linear programming models for optimizing the transportation of agricultural products. Although these models are quite effective for solving such optimization problems, they contain many assumptions and simplifications that usually do not take into account the volatility and/or seasonality of demand. The use of complex optimization algorithms to organize efficient logistics has been discussed in [30,31,32,33]; however, these algorithms are always specific to certain transportation factors.

Although the linear programming models mentioned above normally do not take the factor of seasonal demand into account, the fact that demand for agricultural products is highly variable, unstable, and difficult to predict is one of the most important aspects of transport logistics in the agricultural sector mentioned in the literature. There are studies covering both forecasting and modeling the demand for agricultural logistics services [34] and transport models that take into account particularly short periods of high demand for agricultural crops [29].

Various key performance indicators (KPIs) have been identified that need to be analyzed when organizing agricultural transportation. Cost efficiency [27,35,36] is the most frequently selected KPI, followed by energy consumption [28] and supply chain efficiency [35].

Collaborative data collection, analysis, and processing for decision support in the agricultural and forestry industries have been discussed implicitly or explicitly in several research papers [18,37,38]. Although the methods proposed in these studies differ, the common point is that the digitalization of agricultural and forestry transport companies is relevant and important in order to increase the efficiency of these companies and improve their logistics processes. One of the widely recommended methods is the accumulation of process data in order to develop accurate and reliable models for further optimization of business processes.

The possibility of using a resource-sharing approach in transportation has also been studied. In particular, relevant qualitative and quantitative productivity estimates based on an extensive study of the forestry sector are provided in [39]. The impact of such resource sharing on sustainable economic development in the agricultural sector was analyzed in [40]. However, the possibility of sharing resources between agricultural and forestry companies to create a flexible and diversified transport organization in such a case has not yet been widely discussed. Intersectoral cooperation and synergies between agriculture and forestry [41] are analyzed mainly from the perspective of environmental sustainability.

The objective of this work is to develop appropriate data processing, modeling, and simulation methods and tools to ensure the efficient transportation management of agricultural and forestry products by small businesses. This will allow them to expand their business through logistics cross-sector collaboration in forestry and agriculture. They will be able to use their transportation and labor resources more efficiently, obtain better solutions for the organization and planning of ongoing transportation, and support staff training through virtual simulation environments.

The proposed case study is based on a real example and tested under real-life conditions. The obtained results allowed for the organization of a more efficient use of transportation and labor resources in the logistics of agricultural and forestry products by a small agricultural transportation company. Thus, this is an example of how asset sharing among small businesses can improve efficiency. However, most studies in this area analyze asset sharing between individuals and/or large corporations and examine mainly environmental benefits along with economic ones [42]. Our example is set in a different economic environment, namely SMEs, and looks only at the operational and economic benefits of cooperation between them.

Simulation is widely recognized in the literature and in practice as an effective and flexible approach to designing efficient logistics and supply chain management solutions. It should be noted that this approach can only provide reliable experimental results and estimates if the initial modeling data are reliable and the model is based on a clearly formalized system structure and well-defined processes. The collection and processing of data for small businesses in a target application can be challenging due to the lack of access to many of these data. Additionally, small rural businesses, especially startups, may lack the historical information needed to make the right transportation decisions. In this context, data-driven models, such as artificial intelligence and machine learning methods, make it possible to extract additional information from small amounts of existing data. Thus, the application of data-driven methods to understand and interpret available data and integrate them with simulation technologies appears to be a reasonable option for tackling this problem in the context of this study.

2. Methodology

This study proposes a novel research methodology for data-driven modeling and simulation in transportation management through cross-sector collaboration among small businesses. It is built on a well-known simulation-based approach to logistics and supply chain management [43]. In our study, it is enhanced by integrating data-driven modeling [44] and web-based simulation technologies. In particular, extracting useful information and finding dependencies in datasets, as well as transforming them into modeling formalisms, provide the basis for further simulation experiments. Therefore, the simulation is dependent on and driven by the actual behavior of the system.

The proposed methodology offers a set of applied methods and tools for web data management, data-driven modeling, system dynamics modeling (SDM), stochastic discrete-event simulation, and multi-user web experiments. Although the methods used in this study are well-established in research and have been proven effective when used individually for specific purposes, as described in the literature review, this study aims to integrate them in such a way that they complement and reinforce each other. More specifically, the integration of symbolic regression with system dynamics and discrete-event simulation is innovative. The integrated use of these methods results in more extensive and comprehensive research findings and provides a more in-depth interpretation of the data. Figure 1 shows a flowchart illustrating the relationships between the components of the proposed methodology and specifying their respective outputs. In the figure, the ovals represent the various data modeling methods used, and the rectangles represent their outputs.

An essential data preprocessing component in data analysis, especially in machine learning, involves the cleaning of raw data and the normalization of attribute values to the same units of measurement. Then, a machine learning-based symbolic regression method is used to find dependencies in historical and operational datasets and to represent them in the form of analytical expressions. The obtained analytical models serve as the basis for constructing system dynamics models.

In particular, the operational processes include transportation, loading, unloading, dispatch of vehicles, maintenance, and replacement. The system dynamics model is combined with an economic model to assess the economic viability of potential cooperation scenarios using technical and economic estimates. Additionally, the stochastic discrete-event simulation model provides a virtual simulation of the real processes of transporting agricultural and forest products. This simulation, in turn, takes into account random factors and events that influence the implementation of the developed scenarios, as well as the assessment of corresponding transport solutions using operational efficiency KPIs. The feedback loops between the basic components of the proposed framework make it both flexible and interactive.

The scenario setting plays a key role in this study. Possible options for cooperative transportation scenarios and effective solutions for the use and configuration of transport resources are based on the previous experiences of the involved companies. They take the benefits of cooperation between the two industrial sectors into account. These scenarios may include both existing and potential workflows, as well as available or leased vehicles.

The proposed models and tools were validated during the development process of the case. The purpose was to ensure that at a certain stage in the development, the results of the modeling and simulation were in accordance with the initially defined requirements when using different datasets. For example, in the case of symbolic regression, 80% of the available data were used to train the model, and then 20% were used to test the resulting model. Finally, the results of the experimental scenarios were tested under real-life conditions, allowing them to be compared with practical operational scenarios.

Further validation of the study results is obtained by comparing the past and future KPI performance factor results obtained using different methods. Comparing the results of the combined use of several tools can lead to greater confidence in the final outcome of the study if they support and complement one another.

In the following section, we describe the different methods and tools used in our case study.

Web-based data management. The required data were obtained using a digital web platform for agricultural logistics management [45]. The web platform allows for the collection and storage of business data of individual small businesses and operational data on completed trips. Moreover, it provides data management for the overall control of transportation logistics and improved cost efficiency. An example of statistical data on the transportation of agricultural products obtained from the digital management platform is presented in Figure 2. In particular, the data records in the table include loading and delivery data, total length of the route, types and volumes of transported products, time of contact between the dispatcher and driver, overtime work, data on the driver and vehicle, and fuel consumption.

Data-driven modeling. As already indicated, data-driven modeling is used to create models that identify trends and patterns in historical and other available data. Data-driven models have recently been used more often in various application areas due to a number of factors. The advancement of computational intelligence and machine learning techniques, as well as the wide availability of accumulated data, are the most important factors in this respect.

Symbolic regression [46] is one of the most powerful machine learning methods that allows the direct extraction of key underlying relationships from the data as analytical expressions. This is done without making assumptions about the model structure. Moreover, it can be applied to small datasets. Genetic programming is a widely discussed method for constructing symbolic regressions. It represents evolution using tree-like data structures. This method is applicable in various fields because it allows mathematical relationships to be obtained regardless of the data context. For example, the authors of the article applied it to predict floods and forecast drug demand in [47,48], respectively. In contrast, in [49], the symbolic regression method was used to validate other machine learning models in a specific application.

To construct symbolic regression models for the output variables selected in this study, the HeuristicLab software environment [50] was used.

Finally, the symbolic regression model is deterministic and reflects the past behavior of the system being analyzed using mathematical expressions. When new data are received, these expressions are updated and defined with greater accuracy. The obtained dependencies in the form of analytical expressions were then directly integrated into the system simulation models.

System dynamics modeling. A conceptual system dynamics model is constructed by identifying the causal relationships between the input variables and key performance indicators of the system. In our case, the model assumes that the involved company can use its own trucks and trailers, as well as rented vehicles. The model nodes represent the input, intermediate, and output variables. The input variables define parameters of trips to be performed (e.g., numbers of owned and rented semi-trailers, average transportation distance, loading time, etc.), as well as parameters affecting costs and revenues, such as fuel costs and prices, taxes, and wages. The intermediate variables represent the results of the intermediate calculations of some auxiliary parameters, e.g., time-dependent costs and total travel distance. Finally, the output variables are calculations of the overall final economic and operational performance indicators (KPIs), such as fixed and variable costs, revenue, average vehicle utilization, and driver workload.

The node connection logic and node calculations are based on assumptions derived from the results of symbolic regression analysis as well as from business process analysis. The dependencies and relationships between variables (e.g., the relationship between empty and loaded route distances) that can be derived from data-driven models are substantiated through data analysis. The relationships that could not be identified in this way are determined in the model on the basis of an analysis of the cost and income structure of the analyzed enterprise.

The computational modeling is carried out separately for the transportation of timber and for the transportation of agricultural products. The model itself is deterministic and does not take into account randomness in the behavior of the system and its processes. If the computational model does not have a value for a particular output or if it remains unclear how to calculate it, it can be obtained using a symbolic regression formula derived from the available data. The model is developed using AnyLogic 8.8.0.

Economic feasibility assessment. The SDM model is coupled to an economic feasibility study. In particular, it was developed to assess the economic feasibility of using different types of trailers. It is estimated that transport utilization and cost optimization strategies can determine operating cost variations in the range of approximately 30%. The cost of purchasing equipment and driver comfort requirements, on the other hand, affects the investment amount by approximately 15%. Moreover, the model provides the calculation of the internal rate of return (the margin on the borrowing rate), as well as the calculation of the return on equity under certain conditions. The required calculations are performed in Excel spreadsheets.

Stochastic discrete-event simulation. A stochastic simulation model is developed to generate, simulate, and evaluate transportation decisions for potential vehicle trips according to a given scenario. The model takes into account the inputs and relationships defined in both data-driven models and the SDM and is partly based on their calculations. Specifically, input data include the company’s geographical location, employee wages, transportation costs, depreciation of vehicles (trucks, trailers, and semi-trailers), equipment maintenance and repair costs, fuel consumption, and price.

The model simulates the stochastic nature of random input variables and related process parameters affecting the transportation management of a small agricultural or forestry transport company. For example, the influence of seasonality on the transportation distances of agricultural and forest products is described by empirical probability distributions. In that way, seasonality is taken into account in the model when calculating the distribution of route length and volume of transported orders depending on the month of the year and the product group transported. A preliminary data analysis (see Section 3.1) reveals the rather complex nature of these distributions.

The discrete-event simulation model is built on the well-known event-based mechanism. It ensures the appropriate processing of a discrete sequence of events in time (arrival of transportation orders, assignment of vehicles and drivers, lunch and completion of transportation orders, etc.) and makes appropriate changes to the system state. So, the transportation orders are generated in a specific time period based on the distribution of the obtained empirical data that depend on the number of available assets of each type for the execution of the transportation and the current month. Then, a vehicle is assigned for the dispatch to the sender’s warehouse, and the transportation process is initialized. The duration depends on the distance to the sender’s warehouse. At the end of the transportation process, fuel consumption and driver occupancy are calculated.

Finally, for a given scenario, the model displays the transportation processes and produces values and graphs of economic and operational performance indicators (KPIs) throughout the year.

The logic of the discrete-event simulation is quite simple. But the specifics of the model’s calculations for each type of product, as well as of the data accounting, is that the number of orders depends heavily on the month of the year and season. For each type of product, there is a queue of orders for transportation and a list of vehicles in the model. Additionally, the model has a training mode designed to train personnel and increase their awareness of the model’s capabilities and applications.

Multi-user Web-based Environment. To make modeling and simulation services widely available to all stakeholders (e.g., managers, planners, drivers, etc.), a multi-user web-based modeling approach is proposed. Web modeling provides multi-user access to models, simulation experiments, their results, and visualizations over the internet.

To enable multiple users to independently conduct experiments online, it was proposed [9] to split the simulation model application into front-end and back-end system components. The front-end component is designed to provide the user with web access to the model, data entry, visualizations, and process diagrams. The back-end component is designed to work with the simulation model, store user data and modeling results, and process the corresponding system behavior. The multi-user approach in the back-end component is organized by storing the model configuration for each user in a separate session. The simulation model updates these sessions in a loop (see Figure 3). The software is developed using the general-purpose PHP 7.4 scripting language for Windows web development.

3. Results

3.1. Case Study

The proposed data-driven and simulation methods and tools were tested on a real-life example (see Figure 4) used to analyze and compare cooperative scenarios for the transportation of agricultural and forestry products by a small agricultural transport company.

As mentioned above, the demand for transportation in the agricultural sector depends largely on seasonal factors. The company has a certain number of trucks and semi-trailers that are used in certain months to transport agricultural products, namely grain. Consequently, the drivers of the vehicles are not fully occupied throughout the year. By renting a special semi-trailer for transporting forest products (Figure 5), it would be possible to expand or partially reorient the business to the transportation of timber. Such a special semi-trailer would allow the agricultural transport company to use its drivers and vehicles more effectively by using them for the transportation of both agricultural and forestry products.

Typically, a small agricultural transport company employs as many drivers as trucks. There is no point in having more vehicles than drivers if there is no one to drive them and vice versa. In the latter case, this may lead to an unjustified downtime for drivers.

There are two main routes for transporting agricultural products, depending on the season. During the harvest season, the route mainly goes from the farm to the elevator. During the rest of the time, it goes from the elevator to the port or processing plant. Crops are grown naturally in the countryside. They are often collected in the field by harvesters. Grain elevators and processing plants are located in the city, and the port is situated on the coast. The routes for transporting timber are also diverse. During the high season (in winter, but not only), the forest roads start from the felling site and go to the intermediate storage area, timber processing plant, or port. For the remainder of the year, the route leads from an intermediate warehouse to a timber processing plant or port.

Based on the analysis of the current situation and recommendations proposed by industry experts, it was assumed that the diversification of product transportation from two sectors—agriculture and forestry—would improve the company’s efficiency. Thus, it is necessary to verify this assumption and assess the efficiency of transportation by combining or distributing available resources between the transportation of products from these sectors. This verification can be performed by modeling the situation in different transportation scenarios.

In summary, the objective of this case study was to conduct a simulation-based analysis of different transportation scenarios for agricultural and/or forestry products by a small agricultural transport company. These scenarios include current and new configurations involving the transportation of both agricultural and forestry products. The analysis aims to identify the best vehicle configurations (e.g., trucks and semi-trailers). As such, the most efficient use of resources (vehicles and drivers) throughout the year can be identified.

3.2. Preliminary Data Analysis

The initial experimental dataset contained data collected from 2021 to 2023. The data originated from 61 forestry companies (approximately 63,000 records) with a wide range of used vehicles from 1 to 29 and 12 small agricultural companies (approximately 6000 records) with fleets ranging from 1 to 8 vehicles. Data on forest product transportation companies were collected using data from the enterprise resource planning system of a large company dispatching forestry products that work with smaller transportation companies in the timber transportation industry. Due to challenges in the data collection in small rural enterprises and the development of data management software, the actual period of collection for the agricultural transportation data was somewhat shorter. In both cases, the collected datasets included historical shipment data, such as delivery date and location, travel distance for empty and loaded trips, type of transported products, weight and volume of transported products, vehicle and driver ID numbers, and supplementary time needed, if any.

A preliminary analysis of the transportation of agricultural products revealed that the demand for transportation in the agricultural sector largely depends on seasonal factors. The probability distributions of the delivery distances of agricultural products are shown in Figure 6. The likelihood of short or nearly identical trips is higher during peak seasons, while the spread of distances is higher during off-peak seasons. This may be due to the more sporadic and irregular nature of these trips. A histogram of the delivery distances for timber transportation in different months is presented in Figure 7.

In addition, a preliminary analysis of the data shows the complex nature of the empirical distributions of other random variables. For example, a fairly large portion of loaded trips has a length of about 120 km, while the possible distances of the remaining trips are more evenly distributed over the range of possible values (see Figure 8).

3.3. Data-Driven Models’ Generation

The seasonal factors influence the potential order volumes, distances, and deliveries included in the simulation model. At the data-driven modeling stage, various dependencies were obtained using symbolic regression to estimate the trip cost, predict the average volume of transported products in different months, and calculate the empty travel distance for agricultural transport. Data experiments were conducted taking into account all available quantitative factors in the input dataset by analyzing and dividing them into 80% training and 20% testing datasets.

An example of an analytical extract encoded in a tree-like data structure is shown in Figure 9. The leaf nodes of a tree data structure represent specific input variables multiplied by constant coefficients, and the internal nodes represent binary operations on their values or the results of other such operations.

The resulting symbolic regression model for estimating the cost of a trip is presented by the first analytical expression below, which determines the dependence of cost on the travel distance with and without cargo, as well as on the volume of goods transported, which turned out to be the most significant factor, i.e.,:

$$\begin{gathered} C_{trip}\approx 0.85 d_{empty}+1.69 V-14.58{ V}_{veneer}+0.89 d_{load}+ \\ +{\displaystyle \frac{0.89 d_{load}+0.89 d_{empty}}{1.59 V}}+10. \end{gathered}$$

(1)

In this mathematical expression, C_trip stands for the cost of the trip; d_empty and d_load are the distances of travel without and with transported timber, respectively; V is the volume of transported timber; and V_veneer is the total volume of veneer blocks in the transported cargo.

Similarly, mathematical expressions were obtained for various factors and parameters required for further development of the entire simulation model. In particular, it has been found that the only significant factor influencing the distance of empty transportation is the distance of transportation with cargo.

For example, the formulas for calculating the distance of empty transportation for the forestry and agricultural carrier datasets are expressed by mathematical expressions (2) and (3), respectively:

$$d_{empty \left(f\right)}\approx 1.474·{10}^{-3} d_{load}^2+15.898·log\left(7.05·{10}^{-3}·d_{load}\right)+63.413$$

(2)

$$d_{empty \left(agr\right)}\approx {\displaystyle \frac{0.602·d_{load}·\left(0.602 d_{load}+16.54\right)(1.781-0.399·log\left(0.38 d_{load}\right))}{log\left(1.489 d_{load}\right)}}+17.37,$$

(3)

where $d_{empty \left(f\right)}$ and $d_{empty \left(agr\right)}$ represent the distance of empty transportation for the forestry and agricultural carriers, respectively, and $d_{load}$ is the transportation distance with cargo.

In the case of using trucks with specialized semi-trailers for the transportation of timber, the mathematical expression for predicting the “empty” transportation distance $d_{empty \left(s\right)}$ (without cargo) is expressed as follows:

$$\begin{gathered} d_{empty \left(s\right)}\approx -0.311·t_{load}+0.894·t_{doc}+0.368·d_{load}·\mathit{log}\left(V\right)+ \\ +11.933·log\left(d_{load}\right)-19.049 \end{gathered}$$

(4)

where $d_{load}$ is the transportation distance with cargo. $t_{load}$ is loading time in minutes, $t_{doc}$—document processing time, and $V$—order volume in m³.

To support the cost calculation of the specialized semi-trailer in simulation models, based on the analysis of the collected data, the following data models to estimate the provisional unit costs per km and per m³ volume were obtained:

$$\begin{gathered} C_{dist}\approx {\displaystyle \frac{2.092·d_{empty}+\mathit{log}\left(115.2·d_{load}+933.2·d_{empty}\right)\left(0.149·V+0.055·t_{load}\right)}{1.7993·d_{load}}}-{\displaystyle \frac{1}{0.0172 d_{load}^2}} \\ ++{\displaystyle \frac{1}{0.0142 d_{load}^3}}+0.942 \end{gathered}$$

(5)

$$C_{volume}\approx {\displaystyle \frac{0.115·d_{empty}+0.111·t_{load}+0.232·t_{doc}-\frac{1}{0.016·V}+14.941}{1.7993·d_{load}}}-2.39,$$

(6)

where $C_{dist}$ and $C_{volume}$ represent a unit cost in euros per km and per m³ volume, respectively.

In symbolic regression, validation metrics are critical for assessing how well a model generalizes to unseen data. In our study, key validation metrics commonly used in symbolic regression were analyzed, in particular, error-based and goodness-of-fit metrics. To assess the fitness of the obtained symbolic regression models, a cross-validation method was employed by splitting the data into training (80%) and testing (20%) subsets. Accordingly, numerical accuracy metric scores were estimated for each subset.

For example, a dataset whose data model is expressed by Equation (1) for the months of January and February was collected from 46 vehicles, 26 carriers, 93 unique delivery points, and 194 unique loading points. It contained 2495 data records, which were then split into training and testing subsets. The following estimates were obtained: normalized root mean square error of 0.03 and 0.02, respectively, and Pearson coefficients (R²) of 0.973 and 0.977, respectively. Since similar results were obtained for the other data models described above, these models can be considered reliable.

Finally, economic and logistics experts were consulted to assess the relevance of these data models in the context of the application.

3.4. Conceptual System Dynamics Model

The resulting conceptual system dynamics model, which determines the cause-and-effect relationships between the input variables and key performance indicators of the company, includes more than 20 nodes. The model nodes, node connection logic, and node calculations are described in the methodology section. An overview of the model is shown in Figure 10.

In this model, it is assumed that both owned and rented vehicles can be used for transportation. Tractors with semi-trailers are used for transporting agricultural products, which are usually loaded directly from an elevator or agricultural machinery. For transporting timber, specialized semi-trailers equipped with a hydraulic loader (see Figure 5) can be used. By renting such a semi-trailer, it is possible to ensure the loading and transportation of timber using only the available capacity and drivers, who are often idle during the off-season. To assess the economic feasibility of using different trailer types and determine the expected return on investment, the SDM is also linked to the feasibility study model. The SDM has been validated by experts in engineering economics.

Similarly, a cause-and-effect diagram was created to set workforce parameters, such as the number of drivers, and to determine the impact on the resource utilization of both vehicles and drivers.

3.5. Simulation-Based Comparison of Cooperative Scenarios

3.5.1. Setting Up New Transportation Scenarios

A scenario in which a given company owns three trucks for transporting agricultural products and employs three drivers is considered the baseline scenario. Key costs are estimated, taking transportation, labor, and equipment maintenance into account.

This scenario is compared with several new collaboration scenarios. In the first new scenario (called ‘Scenario 1’), this small agricultural transportation company primarily transports grain and has one specialized semi-trailer that could also be used to haul wood. This scenario was introduced to simulate the synergies of transporting products from the two industrial sectors (i.e., grain and timber) and to assess the impact on its performance.

In further new scenarios (all brought together under the name ‘Scenario 2’), this small agricultural transport company is still primarily engaged in transporting grain. However, it can use or share a certain number of semi-trailers (more than one), either owned or rented, for the transportation of forestry products. The priority is the transportation of grain, but if the drivers are free and the specialized semi-trailers are idle, they are used to transport timber. In these situations, different configurations of the company’s vehicles and workforce can be analyzed, taking into account the benefits of diversifying transportation by transporting both agricultural and forestry products.

3.5.2. Experimental Results

The results of the monthly stochastic simulation for the baseline and cooperative scenarios for the agricultural company are presented in Figure 11. In particular, the figure presents the results for the cases with one and three drivers (and trucks, respectively) and different configurations of agricultural and forestry semi-trailers simulated over the year. Figure 11a shows the results of the simulation experiments for the case of one driver, one truck, one agricultural trailer, and one forestry trailer. Figure 11b shows the results for three drivers, three trucks, three agricultural trailers, and one forestry trailer. In Figure 11a,b, the dark green line represents the utilization rate of agricultural trailers, the light blue line represents the utilization rate of forestry trailers, and the brown line represents the utilization rate of trucks (and drivers). Note that in the baseline scenario, where the company is only engaged in the transportation of agricultural products and does not have a specialized semi-trailer for transporting timber, the loading of trucks and drivers will correspond to the dark green lines. Thus, the difference between the brown and dark green lines illustrates the possibility of transporting timber cargo in the off-season and its impact on increasing the resource utilization rate.

Finally, the results of the simulation experiments comparing the transportation scenarios over the year are presented in

Table 1. Results of the simulation experiments comparing cooperative scenarios.

Number of Semi-Trailers		Trips per Year		Total Distance in Thousands Km per Year		Average Vehicle Utilization Rate
Agriculture	Forestry	Agriculture	Forestry	Agriculture	Forestry	Trucks	Agriculture Semi-Trailers	Forestry Semi-Trailers
Baseline Scenario
3	0	173	0	28.7	0	0.23	0.23	0.00
				Scenario 1
3	1	173	176	28.7	30.2	0.47	0.23	0.72
Scenario 2
3	2	173	348	28.7	60	0.70	0.23	0.71
3	3	173	439	28.7	75.7	0.83	0.23	0.60
2	3	115	485	19.1	83.9	0.81	0.23	0.66

.

In Scenario 1, the average utilization rates of trucks and specialized semi-trailers for timber transportation increased significantly compared to the baseline scenario, reaching values of 0.47 (up from 0.23) and 0.72 (up from 0.00), respectively. Thus, assuming that the company can operate in accordance with the demand model obtained from the analyzed data, the provision of timber transportation with just one semi-trailer will significantly improve the use of the company’s resources. The highest average utilization rate was achieved with a configuration of six semi-trailers. This will provide the greatest diversification of deliveries. However, it will also be the most expensive configuration in terms of both fixed and operating costs.

Furthermore, maximum resource utilization throughout the year can be achieved by having diversified access to both agricultural and forestry transport (as described in the different possibilities of Scenario 2).

This means that if a transport company is primarily engaged in the transportation of agricultural products, diversifying the types of goods transported with forestry products will provide the existing and shared transportation resources (and the corresponding drivers) with additional work, even outside the harvest season. Indeed, the average vehicle transportation load for trucks and forestry semi-trucks increased in the simulation model for each of the different sub-scenarios investigated, working with a different number of semi-trucks used for transporting agricultural and forestry products. However, assessing the cost-effectiveness of using additional vehicles requires a complete examination of the model’s input data for individual item costs, as well as clarification of both fixed and variable costs for different trailer categories.

4. Discussion

Modern digital platforms and computing techniques are helping to assess radical transformation options in the business models of small and medium-sized businesses that will change their relationships. One new opportunity that can be considered is intersectoral cooperation.

Modern digital technologies provide opportunities for the accumulation and processing of large volumes of data. The available data can be further used to extract useful information in the analyzed applications and gain a better understanding of the cause-and-effect relationships in the behavior of the real system. This enables the implementation of data-driven approaches to support decision-making in different fields of application, such as transportation management.

This paper proposes methods and tools for data-driven modeling and simulation in small business transportation management through cross-sectoral cooperation. It was developed based on a real case of synergy in the transportation of products in two sectors: agriculture and forestry. The case study is based on a real-life example of a small agricultural transport company that owns a fleet of vehicles and thus has its starting point in the industries that have a need for transportation and are creatively looking for cross-sectoral synergies. However, the advantages of such intersectoral synergy may also be explored by small and medium-sized companies starting in the transportation industry itself or by third-party logistics companies that provide transportation of a wide range of goods.

Data-driven modeling and simulation that integrate different data science models may significantly improve the model-based simulation paradigm in practice. Extracting useful information from data, finding dependencies in datasets, and transforming them into analytical modeling formalisms provide the basis for their direct integration into simulation models.

5. Conclusions

The methods used in this study, such as symbolic regression, STM, and stochastic discrete-event simulation, are well-known in research, especially in transportation management applications. They have been proven effective when used separately for specific purposes, as described above.

In this case study, they were used in such a way that they complemented and reinforced each other. Finally, the integrated use of these methods results in more extensive and comprehensive research findings and provides a deeper interpretation of data across the entire data development value chain, from data acquisition to the stochastic simulation of future transportation scenarios over time. Symbolic regression identifies relationships between various inputs and outputs using mathematical expressions that are directly integrated into simulations. Additionally, symbolic regression can incorporate new data that become available. As such relationships are discovered more accurately, the simulation is updated accordingly. Thus, simulations provide a flexible, iterative model for experimentation over time, incorporating changes in the available data.

The proposed work is based on a real example and is tested under real-life conditions. It pertains to the logistics of agricultural and forestry products carried out by a small agricultural transportation company. The results obtained allowed the organization to benefit from a more efficient use of transportation and labor resources. As such, it is an example of how sharing assets between economic actors, whether individuals or small businesses, can improve economic outcomes. This example is also specific in the sense that cooperation between SMEs in different economic sectors that experience seasonal differences is investigated. However, from a more general perspective, this case study should incite SMEs to more actively consider the economic benefits of such a novel approach, in particular when assets are too expensive for one SME alone and can be used with some or no adaptation costs (e.g., due to different types of products or services provided or due to seasonal variations in usage) by other SMEs.

Furthermore, a cost-benefit analysis of cross-sector collaboration instruments is planned. This analysis is needed to gain further insight into the scalability of the results for microenterprises. This will enhance the real-world relevance of the present study.

Future research is planned to increase the level of technology integration and automation in this study. In this way, the simulation becomes even more dependent on and controlled by the actual behavior of the system being analyzed.