Supply Chain: A Modeling-Based Approach for Cyber-Physical Systems

Abstract

Within the frame of this chapter, the author focuses on the distribution processes of green supply chain solutions and describes a potential mathematical model, taking environmental aspects into consideration. The first part of the chapter includes a systematic literature review. Based on the identified research gap, a new mathematical model is described, which makes it possible to describe last-mile logistics processes from an environmental point of view. The functional model of the distribution system includes the potential of Industry 4.0 technologies, which makes it possible to gather real-time information from the distribution process and use real-time status information for a sophisticated design and operation. The mathematical model of this approach defines an NP-hard optimization problem; therefore, heuristic optimization algorithm is supposed to solve the design and operation tasks of the green distribution problem. As the computational results show, cyber-physical systems increase the performance of green supply chain solutions and have a great impact on operational cost. As the numerical example shows, the integrated approach resulted in a 5.3% cost reduction in transportation operations.

1. Introduction

In recent years, a rising number of production and service companies work only with suppliers that adhere to environmental standards and regulatory policies, which are drivers for sustainable supply chain operations. These standards and regulatory policies can be classified into nine groups: pollution bans, technology standards, performance standards, emission trading policies, taxes, subsidies, information policies, eco-labels, and sustainable procurement policies [1]. Sustainable supply chain solutions and sustainable distribution solutions are influenced by all of these policies and related fields.

The definitions define that sustainable distribution refers to the macroeconomic allocation of objects (final products). Microeconomic aspects should also be taken into consideration because green distribution is influenced by business decisions, while economic and financial policies are represented by macroeconomics. Green distribution includes a wide range of operations, including transportation, warehousing, loading and unloading, packaging and labeling, custom services, and marketing. This wide range of logistics-related operations must be performed as green as possible. Today, the new technologies of the fourth industrial revolution make it possible to gather information from large complex systems in the form of real-time failure data and status information, and use them for more sophisticated decision-making. Within the frame of this chapter, an optimization-based approach for the optimal design and operation of green distribution is described. The significance of a problem is based on the fact that the application of Industry 4.0 technologies and the transformation of conventional supply chain solutions into a cyber-physical system can increase availability, flexibility, efficiency, sustainability, and transparency. The research question of this work is the validation of the impact of cyber-physical solutions on green supply chains.

This paper is organized as follows: Section 2 presents a systematic literature review, which summarizes the research background of distribution processes in the green supply chain from a descriptive and content analysis point of view. Section 3 describes the model framework of green distribution processes, including both, the functional and the mathematical models. The model is focusing on the sustainability-related aspects, including energy consumption, greenhouse gas emissions, and energy costs. Section 4 discusses the numerical analysis of the defined optimization model and validates the expected impact of cyber-physical solutions on green supply chains. Conclusions, future research directions, limitations, and managerial impacts are discussed in Section 5.

2. Systematic literature review

Within the frame of this systematic literature review, the following questions will be answered: What is the current state of the knowledge in the field of distribution in green supply chain solutions? Which methodologies can be used for the optimization of design and operation of green distribution systems? Which influencing factors are important from the environmental impact point of view? What are the main research gaps and limitations?

2.1 Methodology of systematic literature review

The systematic literature review can be divided into three main parts. The first part is the descriptive analysis, which focuses on the statistical analysis and numerical description of search results in Scopus. The second phase is the content analysis, where based on the results of the descriptive analysis the research topics and the scientific results are described and evaluated. The third part summarizes the results of descriptive and content analysis and focuses on the current state of knowledge, current research results, and research gaps (Figure 1).

Figure 1.

Process of the systematic literature review.

The process of the systematic literature review includes the following main phases: (1) definition of search questions based on the available search fields in Scopus; (2) search process; (3) inclusion and exclusion process, where only journal articles were added from the different types of source types and non-English articles were excluded from the search results; (4) descriptive (statistical and numerical) analysis; (5) content analysis, where the topics and research results are identified; (6) definition of consequences, identification of main research directions, research gaps, and bottlenecks.

2.2 Descriptive analysis

Within the frame of the descriptive and content analysis the following search was used in the Scopus: (TITLE-ABS-KEY (“green supply chain”) AND TITLE-ABS-KEY (distribution) AND TITLE-ABS-KEY (logistics)) AND (LIMIT-TO (DOCTYPE, “ar”)). The following numerical analysis is based on the results of this search. Initially, as a result of this search, 50 articles were identified and analyzed. The search was conducted in March 2022; therefore, new articles may have been published since then.

Figure 2 shows the distribution of published articles based on the search results in Scopus. As Figure 2 shows, more than 50% of the articles were published in the last 5 years, and this fact shows the increased importance of green supply-chain-focused researches.

Figure 2.

Classification of articles by year of publication based on search results in Scopus.

Figure 3 shows the classification of the published articles and research work by the nationality of the authors. As Figure 3 shows, authors from Europe, Asia, and America are working on research topics focusing on green supply chain design and operation. From a global economic perspective, it is an important fact, that this research field is becoming increasingly important not only in developed countries but also in developing countries.

Figure 3.

Classification of articles by the nationality of the authors based on search results in Scopus.

Figure 4 demonstrates the distribution of articles by subject area in Scopus. It can be concluded, that the green distribution-related researches are multidisciplinary researches, where a wide range of science fields is required to solve technological, logistics, human resource management, economic, and ecological problems including business and management, engineering, decision sciences, telecommunication and computer sciences, environmental sciences, social sciences, mathematics and optimization, chemical engineering and materials science. These topics are covered by journals in the following fields: sustainability, operational research, industrial engineering, management research, logistics, manufacturing technologies, mathematics, and transportation business.

Figure 4.

Distribution of articles by Scopus keywords in the field of green distribution-related research.

An internationally accepted measure of the quality of scientific works is the independent citation. Figure 5 shows the ten most cited articles based on the results of the Scopus search and the distribution of the independent citations. The h-index, which is the largest number h of published articles having at least h independent citations is in the case of green distribution research is 20. This h-index seems to be acceptable in the field of technology, engineering, and environmental researches, because in the case of other sciences, such as physics, space sciences, clinical medicine, and genetics, there are more papers, more scientists, and more citations.

Figure 5.

Yearly distribution of independent citation of the ten most cited articles in the field of green supply chain-related research [2, 3, 4, 5, 6, 7, 8, 9, 10, 11].

Figure 6 demonstrates the distribution of green supply chain-related articles by open access types. Gold open access includes journals published only in open access. In the case of hybrid gold open access, the authors can choose the open access publication. In the case of green open access, the published articles are available in different repositories. In the case of bronze open access, the publisher offers temporally or permanently unlimited free access to the articles. 34 of the analyzed 51 articles are available online, which is an acceptable proportion.

Figure 6.

Distribution of green supply chain article from availability (open access) point of view.

Figure 7 demonstrates the distribution of the keywords mostly used by the authors of green distribution design-related articles. The analysis of keywords shows, that they can be clustered in the following way: environmental aspects (greenhouse gas emission, CO emission, carbon, climate change, sustainability, carbon footprint); optimization (linear programming, decision making, genetic algorithm, fuzzy models, algorithms, knapsack problems, factor analysis, numerical models, dynamic programming, comparative analysis, game theory); and logistics (distribution of goods, facility location problems, coordination management, network design, transportation, vehicles, chain to chain competition).

Figure 7.

Distribution of used keywords of green distribution-related articles based on the results of Scopus search.

The use of keywords e-tailers and e-commerce distribution shows, that the environmental impact is important not for physical distribution but also in the case of e-business and e-commerce solutions, where the design and operation of eco-friendly operation focus on eco-friendly packaging, reusable plastics, purchasing carbon offsets, and reducing shipping distances.

2.3 Content analysis

The importance of the optimization of supply chain processes and the technological and logistics resources is underlined also by the fact, that logistics-induced greenhouse gas emissions caused by economic growth block and obstruct the greening process of supply chain solutions, especially in the field of last-mile logistics [12].

The product development process can be integrated with green purchasing, green manufacturing, green distribution, and green reverse logistics, which are an essential part of the green supply chain. This integration can lead to decreased environmental impact in all stages of the supply chain [13]. The product development environment can be also integrated with the forward and reverse flow of the supply chain in the circular economy including production, distribution, and customers in the forward direction and collection, disassembly, recycling, and disposal in the reverse direction to improve the greening process of supply chain solutions [14]. The products and the behavior of consumers can also influence the performance and environmental impact of distribution processes. From product development and labeling point of view, studies show, that consumers prefer green-labeled products and green distribution labels, especially in the case of tier1, tier 2, and tier 3 consumers [15].

Different models are used to demonstrate the impact of green distribution on the environmental impact of the green supply chain. The path analysis is a useful method to analyze this impact and to justify, that the participants of the green supply chain including suppliers, manufacturers, and service providers must focus on the facilities and operation-related policies to increase the performance of those variables [16].

The Nash and Stackelberg game is also a suitable method to analyze the impact of policies and regulations on the equilibrium strategies from sustainability of competitive forward and reverse supply chains focusing on financial aspects and greening [17]. A survey with 43 items was tested using partial least squares structural equation modeling to identify the most common practices facilitating environmental collaboration. The study shows that internal environmental management, eco-design, and green marketing play an important role in the greening process of supply chains, while no substantial impact was identified between green human resources, green information, and systems technology [18].

Network analysis can be used to perform a wide range of design tasks for green distribution processes including facility location and routing. These design tasks are essential to creating a sustainable and green distribution system, where the optimal location of distribution centers has a great impact on the energy efficiency and greenhouse gas emission of transportation processes [19, 20]. The greening process can be influenced both on the managerial and operational levels [21].

The risk evaluation plays an important role in the operation of green distribution networks because in an uncertain environment the performance of the distribution processes can be influenced by the results of forecasting and super positioning of customers’ demands and other system parameters. This importance of risk evaluation is discussed in the case of agricultural products in a cold chain logistics solution, where the perspective of the ecological economy is taken into consideration [22] and it is shown, that the logistics mechanism of distribution processes can be improved by permanent improvement and supervision of logistics intermodal mechanism. Fuzzy models are also used to solve design and operation problems of green distribution problems in an uncertain environment [23].

The coordinated optimization of the complex system of green distribution networks shows a suitable way to take a wide range of influencing factors into consideration while optimizing the green supply chain because the complex model of the green supply chain defines different layers such as a layer of distributors, producers, and customers, and the coordinated optimization model plays the parameters and influencing factors of these players of the distribution network into consideration [24].

The analysis of action mechanism of cross-border supply chain solutions shows, that in the case of large geographical area the establishment of green supply chain models for green distribution has remarkable importance for the implementation and development of the green supply chain [25].

The design and operation of green distribution systems can be also described as an optimization problem of inventory routing problems, where the bi-objective optimization of both inventory costs and fuel consumption using mixed-integer linear programming can lead to an efficient green distribution [26]. Another approach focuses on a stochastic model, which takes profit, service level, and environmental impact as green criteria into consideration [5]. This is a new way of solving inventory routing problems because in recent decades these problems were focused only on economic performance and service level, shortages, delivery delays, and environmental footprint were not considered.

Investigations focusing on the relationships between proactive environmental strategy, green supply chain solutions, and performances of logistics providers show, that the environmental impact can be positively influenced by eco-efficiency and eco-branding through green distribution, inventory management, and reverse processes [27, 28].

Research results show, that e-tailers, third party service providers, and consumers have a great impact on the greening process of distribution, therefore it is important to involve all of these players in the optimization process of distribution networks and build a close communication between them [29], and strengthen green supply chain coordination system [30].

Cities as major population centers represent supply chain solutions with a high density of distribution operations, therefore in urban regions, the greening of last-mile logistics operations is especially important, especially from the health of residents’ point of view [31]. Another approach to greening distribution processes in the field of urban planning focuses on the assessment of the impact of the urban intelligent transportation system on the success of the green supply chain management system. The study validated the hypothesis that an urban intelligent transportation system, knowledge of manufacturers, and business processes have a great positive impact on the success of green supply chain management (green distribution) in the case of agricultural products [32].

The interconnection and hyperconnection of supply chains represent a special problem for supply chain management because transferring products between the centers of different supply chains can cause waiting queues and high environmental pollution. Research focusing on the design of forward and reverse logistics of hyperconnected supply chains shows, that the integrated optimization of queuing problems and transportation networks can lead to the reduction of environmental impact [3]. Other integrated approaches for the optimization of distribution processes focus on the multi-echelon location routing problem, where genetic algorithm and dynamic island model-based heuristics is used to minimize the energy costs associated with transportation [33]. Using a mixed-integer programming model to solve a large-scale integrated location-routing problem with genetic algorithm and particle swarm heuristics, it is possible to optimize the number and location of cross-docking facilities in green distribution processes [34].

The application of just-in-time philosophy can improve the efficiency of both manufacturing systems and whole supply chains. As research results in the case of return vehicle supply chains show, the just-in-time model can support the greening processes of conventional solutions to improve environmental awareness and reduce environmental impact of distribution processes [35].

The practices of green supply chain management influence not only the environmental effect of distribution processes, but they have a great impact on organizational performance. The study based on the results of questionnaire-related research describes a theoretical model, which explains the analytical relationships between green supply chain processes and organizational performance [36].

Enhancing stock efficiency and environmental sustainability goals in direct distribution logistic networks can be improved using lean management and green management principles within logistics to reduce the environmental impact of distribution processes [37].

The partner selection process is also an important influencing factor for green supply chain solutions, as in the case of the optimization of a reverse logistics network the results of integrated fuzzy-artificial immune optimization heuristics-based solutions show [38].

The success of green distribution processes is also based on emission measuring operations and estimation of carbon footprint including capturing, calculation, and management of emissions across the transportation and distribution network [39, 40]. The performance evaluation can be based on logistics performance indicators and environmental performance indicators, and these can be integrated into a green logistics performance indicator [4]. Benchmarking is also a suitable tool to support evaluation and process improvement in green distribution networks [11].

For the solution of green supply-chain-related optimization problems, a wide range of integrated optimization and process improvement methods can be used: game theory [7], spanning-tree based genetic algorithm [9], Lagrangian heuristics [10], path analysis [16], integrated CPU-GPU heuristic inspired on variable neighborhood search [41], fuzzy genetic algorithm [42], simulation [43], analytical hierarchy process [44], decision making trial and evaluation laboratory for the identification of cause-effect chain components of distribution systems [45, 46]. Other heuristic algorithms, such as quantum particle swarm optimization are also suitable for the solution of multi-objective optimization of multi-echelon supply chain and distribution, where a wide range of constraints can be considered including capacity, production cost, transportation and material handling cost, greenhouse gas emissions, and time window [47].

Several scenarios and case studies related to the design and operation of green supply chain and green distribution were assessed and evaluated to compare the effects of technology, logistics, human resources, and policies on the efficiency, reliability, and availability of environmental impact of green supply chain solutions. The most important fields of case studies are from general distribution processes [6, 48], but valuable case studies were published in the field of food industry [2], air conditioner manufacturers [7], third party logistics providers [8], motorcycle industry [17], healthcare [28], direct distribution logistic networks [37], electronic equipment and instruments manufacturing companies [38], distribution of fruits and vegetables [49], automotive industry [50], power networks [51], agri-food supply chain [52] and disrupted supply chain solutions in the pandemic era [53]. The methodological framework and main research directions of green distribution networks, including methods, objective functions, case studies and special conditions, and constraints are shown in Figure 8.

Figure 8.

Methodological framework and main research directions of green distribution networks, including methods, objective functions, case studies, and special conditions and constraints.

2.4 Consequences and identification of research gaps

The consequences based on the above described systematic literature review, including descriptive and content analysis, can be summarized as follows:

• Sustainable distribution is not only influenced by both technological and logistics parameters, but also by product development also has a great impact on the environmental impact of distribution processes.

• Competitive distribution becomes more and more important in the case of disrupted supply chains, where environmental impact plays an important role.

• The risk evaluation has a great impact on the financial and environmental impact of distribution systems, especially in the case of an uncertain environment.

• Consumers influence the environmental impact of distribution networks and their greening process.

• Direct distribution systems can be transformed into multi-echelon distribution networks to decrease the environmental effect and improve cost efficiency.

• Emission measuring operations and estimation of carbon footprint including capturing, calculation, and management of emissions across the transportation and distribution network are key success factors for green distribution.

• Green distribution networks represent NP-hard optimization problems, where integrated heuristic solution algorithms are used to find the solutions to multi-objective problems.

As a research gap, it can be concluded that the analyzed articles are focusing on the analysis and optimization of conventional supply chain and distribution networks and only a few of them discuss the potentials of cyber-physical systems, interconnected and hyperconnected networks.

The increasing number of publications indicates the importance and scientific potential of research on green distribution systems. The articles that addressed the design and operation of green distribution systems are based on conventional supply chain environment, but few of the articles have aimed to research the potentials of Industry 4.0 technologies-based optimization.

Therefore, Industry 4.0 technologies still need more attention and research in the field of integration, cooperation, and globalization of supply chains and distribution networks. Accordingly, the main focus of this research is the modeling and optimization of a cyber-physical distribution network, where not only financial but also environmental aspects are taken into consideration.

The main contribution of this article includes the followings: (1) a systematic literature review with descriptive and content analyses to describe the main research directions and identify research gaps; (2) functional modeling of a cyber-physical distribution network based on Industry 4.0 technologies; (3) mathematical model to find the best parameters for the cyber-physical distribution network from environmental and logistics aspects point of view.

3. Description of a cyber-physical distribution network

Within the frame of this section, the functional and mathematical model of a cyber-physical distribution system is described. The functional model focuses on the transformation of conventional distribution systems into a cyber-physical distribution using Industry 4.0 technologies, while the mathematical model includes “green” objective functions, such as minimization of energy consumption and greenhouse gas emission, and related constraints (time, capacity, and energy).

3.1 Functional model of a cyber-physical distribution network

In conventional distribution systems operating in parallel, the low level of cooperation means that many optimization options are not feasible. This not only reduces the efficiency of distribution systems but also increases their environmental impact. To address this, available Industry 4.0 technologies can be used to transform independent distribution systems operating in parallel into a cyber-physical distribution network, where the integration of individual distribution systems can be achieved, resulting in coordination that can greatly improve system performance and at the same time achieve a much more environmental friendly network operation (Figure 9).

Figure 9.

Transformation of conventional distribution systems into a cyber-physical distribution network using Industry 4.0 technologies including smart sensors, edge computing, digital twinning, discrete event simulation, and real-time data-based decision making.

The transformation of a traditional distribution network into a cyber-physical system may require the use of the following technologies:

• smart sensors: using smart sensors we can gather real-time data from the resources and processes of the distribution network, including real-time failure data and status information;

• edge computing: using this distributed computing paradigm, we can bring computation and data storage operations closer to the sources of data sources, which is important in the case of large geographical areas, such as a distribution network;

• edge node: this layer is the connection between smart sensors of the physical system and the distribution cloud; edge node includes the tasks of IoT management, offline data analysis, and storage;

• digital twin: using different digital twin solutions it is possible to create real-time models of the distribution network; digital twin integrates data from multiple sources, from field sensors to ERPs of the players in the distribution network (manufacturers, distribution centers, and third-party logistics providers);

• discrete event simulation: with a real-time model including real-time failure data and status information more sophisticated forecasting can be made, which is an essential condition for the optimal coordination of technological, logistics, and human resources; the results of real-time discrete event simulation are required for the decision-making process.

3.2 Mathematical models of distribution networks

Within the frame of this section, the mathematical models of a conventional and cyber-physical distribution network are described. The mathematical models are focusing on energy efficiency-related “green” objective functions, including energy consumption and greenhouse gas emission as the most important influencing factors of environmental impact. The mathematical model includes time, capacity, and energy-related constraints.

3.2.1 Mathematical model of a conventional distribution network

The objective function of the optimization problem is either the energy consumption or the real or virtual greenhouse gas emission. The energy consumption as objective function can be defined as follows in the case of conventional distribution:

$${\mathit{EC}}^{\mathit{\text{CONV}}}=\sum _{a=1}^{a_{\mathit{max}}}\underset{a}{\overset{\mathit{MD}}{\mathit{EC}}}+\sum _{a=1}^{a_{\mathit{max}}}{\mathit{EC}}_a^{\mathit{DC}}\to \mathit{min}.$$E1

where ${\mathit{EC}}^{\mathit{\text{CONV}}}$ is the energy consumption of the conventional distribution system, ${\mathit{EC}}_a^{\mathit{MD}}$ is the energy consumption between the manufacturer cluster a and distribution cluster a, ${\mathit{EC}}_a^{\mathit{DC}}$ is the energy consumption between the distribution cluster a and the consumers, $a_{\mathit{max}}$ is the number of independent distribution networks.

The energy consumption between the manufacturer cluster a and the distribution cluster a can be defined as follows:

$${\mathit{EC}}_a^{\mathit{MD}}=\sum _{\alpha =1}^{{\alpha }_{\mathit{\text{maxa}}}}{\mathrm{\epsilon }}_{v_{\mathit{\alpha a}}}\left(q_{v_{\mathit{\alpha a}}}\right)\bullet l_{\mathit{\alpha a}}^{\mathit{opt}}\left({\mathrm{\Theta }}_{\mathit{\alpha a}}\right)$$E2

where $v_{\mathit{\alpha a}}$ is the transportation vehicle assigned to route $\alpha$ of distribution system a in Tier1 between manufacturers and distribution centers, ${\alpha }_{\mathit{\text{maxa}}}$ is the number of distribution routes for distribution system a in Tier1 between manufacturers and distribution centers, ${\mathrm{\epsilon }}_{v_{\alpha }}$ is the energy consumption of transportation vehicle $v_{\mathit{\alpha a}}$ assigned to route $\alpha$ of distribution system a in Tier1 between manufacturers and distribution centers, $l_{\mathit{\alpha a}}^{\mathit{opt}}$ is the length of the optimal distribution route $\alpha$ of distribution system a in Tier1 between manufacturers and distribution centers, which is a function of the ${\mathrm{\Theta }}_{\mathit{\alpha a}}$ set of distribution centers assigned to route $\alpha$ of distribution system a in Tier1 between manufacturers and distribution centers, and $q_{v_{\mathit{\alpha a}}}$ is the current capacity of transportation vehicle assigned to route $\alpha$ of distribution system a in Tier1 between manufacturers and distribution centers.

The energy consumption between the distribution cluster a and consumers assigned to distribution center a can be defined as follows:

$${\mathit{EC}}_a^{\mathit{DC}}=\sum _{\beta =1}^{{\beta }_{\mathit{\text{maxa}}}}{\mathrm{\epsilon }}_{v_{\mathit{\beta a}}}\left(q_{v_{\mathit{\beta a}}}\right)\bullet l_{\mathit{\beta a}}^{\mathit{opt}}\left({\mathrm{\Theta }}_{\mathit{\beta a}}\right)$$E3

where $v_{\mathit{\beta a}}$ is transportation vehicle assigned to route $\beta$ of distribution system a in Tier2 between distribution centers and consumers, ${\beta }_{\mathit{\text{maxa}}}$ is the number of distribution routes for distribution system a in Tier2 between distribution centers and consumers, ${\mathrm{\epsilon }}_{v_{\mathit{\beta a}}}$ is the energy consumption of transportation vehicle $v_{\mathit{\beta a}}$ assigned to route $\beta$ of distribution system a in Tier2 between distribution centers and consumers, $l_{\mathit{\beta a}}^{\mathit{opt}}$ is the length of the optimal distribution route $\beta$ of distribution system a in Tier2 distribution centers and consumers, which is a function of the ${\mathrm{\Theta }}_{\mathit{\beta a}}$ set of distribution centers assigned to route $\beta$ of distribution system a in Tier2 between distribution centers and consumers, and $q_{v_{\mathit{\beta a}}}$ is the current capacity of transportation vehicle assigned to route $\beta$ of distribution system a in Tier2 between distribution centers and consumers.

The second objective function is the greenhouse gas emission, which can be defined for the following GHGs: carbon dioxide, methane, nitrous oxide, and fluorinated gases. The GHG emission can be defined in the following way for the different GHGs in the case of conventional distribution:

$${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{\text{CONV}}}=\sum _{a=1}^{a_{\mathit{max}}}{\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{MDa}}+\sum _{a=1}^{a_{\mathit{max}}}{\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{DCa}}\to \mathit{min}.$$E4

where ${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{\text{CONV}}}$ is the $\mathit{GHG}$ emission of the conventional distribution system, ${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{MDa}}$ is the GHG emission of the vehicle assigned to the distribution operations between the manufacturer cluster a and distribution cluster a, ${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{DCa}}$ is the GHG emission of vehicles assigned to distribution operations between the distribution cluster a and the consumers, and $\mathit{\text{MGHG}}=\left[{\mathit{CO}}_2,{\mathit{SO}}_2,\mathit{CO},\mathit{HC},{\mathit{NO}}_x,\mathit{PM}\right]$ is the matrix of greenhouse gases to be taken into consideration.

The emission between the manufacturer cluster a and the distribution cluster a can be defined as follows:

$${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{MDa}}=\sum _{\alpha =1}^{{\alpha }_{\mathit{\text{maxa}}}}{\mathrm{\vartheta }}_{\mathit{\text{MGHG}}}^{\mathit{\text{TIER}}1,v_{\mathit{\alpha a}}}\bullet {\mathrm{\epsilon }}_{v_{\mathit{\alpha a}}}\left(q_{v_{\mathit{\alpha a}}}\right)\bullet l_{\mathit{\alpha a}}^{\mathit{opt}}\left({\mathrm{\Theta }}_{\mathit{\alpha a}}\right)$$E5

where ${\mathrm{\vartheta }}_{\mathit{\text{MGHG}}}^{\mathit{\text{TIER}}1,v_{\mathit{\alpha a}}}$ is the specific GHG emission in the case of transportation vehicle assigned to route $\alpha$ of distribution system a in Tier1 between manufacturers and distribution centers.

The emission between the distribution cluster a and consumers assigned to distribution center a can be defined as follows:

$${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{DCa}}=\sum _{\beta =1}^{{\beta }_{\mathit{\text{maxa}}}}{\mathrm{\vartheta }}_{\mathit{\text{MGHG}}}^{\mathit{\text{TIER}}2,v_{\mathit{\beta a}}}\bullet {\mathrm{\epsilon }}_{v_{\mathit{\beta a}}}\left(q_{v_{\mathit{\beta a}}}\right)\bullet l_{\mathit{\beta a}}^{\mathit{opt}}\left({\mathrm{\Theta }}_{\mathit{\beta a}}\right)$$E6

where ${\mathrm{\vartheta }}_{\mathit{\text{MGHG}}}^{\mathit{\text{TIER}}2,v_{\mathit{\beta a}}}$ is the specific GHG emission in the case of transportation vehicle assigned to route $\beta$ of distribution system a in Tier2 between distribution centers and consumers.

As constraints, we can take the following into consideration: capacity of vehicles, capacity of loading and unloading equipment, capacity of distribution centers, time window for manufacturer, time window for customers, time window for 3PL providers in Tier1, time window for 3PL providers in Tier2, and available energy for electric vehicles.

Constraint 1a: We can define the upper limit of the loading capacity of transportation vehicles. It is not allowed to exceed this upper limit of loading capacity while assigning distribution tasks to the routes and scheduling the delivery tasks:

$$\forall \alpha ,a:{\mathrm{C}}_{v_{\mathit{\alpha a}}}\ge \sum _{i=1}^{i_{\mathit{max}}}{\mathrm{q}}_i\in {\mathrm{\Psi }}_{\mathit{\alpha a}}$$E7

where ${\mathrm{C}}_{v_{\mathit{\alpha a}}}$ is the upper limit of loading capacity of the transportation vehicle assigned to route $\alpha$ of distribution system a, $i_{\mathit{max}}$ is the upper limit of customers’ demands, ${\mathrm{q}}_i$ is the volume or weight (capacity unit) of customers’ demand i, ${\mathrm{\Psi }}_{\mathit{\alpha a}}$ is the set of customers’ demands assigned to route $\alpha$ of distribution system a.

Constraint 2a: We can define the upper limit of the material-handling capacity of loading and unloading equipment. It is not allowed to exceed this upper limit of material handling capacity while assigning distribution tasks to the routes and scheduling the delivery tasks:

$$\forall \alpha ,a:{\mathrm{C}}_{z_{\mathit{\alpha a}}}\ge \sum _{i=1}^{i_{\mathit{max}}}{\mathrm{z}}_i\left({\mathrm{q}}_i\in {\mathrm{\Psi }}_{\mathit{\alpha a}}\right)$$E8

where ${\mathrm{C}}_{z_{\mathit{\alpha a}}}$ is the upper limit of the material-handling capacity of the loading and unloading equipment assigned to delivery tasks of route $\alpha$ of distribution system a, ${\mathrm{z}}_i$ is the required material handling capacity of customers demand i.

Constraint 3a: We can define the upper limit of the storage capacity of distribution centers. It is not allowed to exceed this upper limit by assigning manufacturers to distribution centers and distribution centers to customers:

$$\forall a:{\mathrm{CW}}_a\ge \sum _{i=1}^{i_{\mathit{max}}}\sum _{\alpha =1}^{{\alpha }_{\mathit{max}}}{\mathrm{q}}_{\mathit{i\alpha }}\in {\mathrm{\Psi }}_{\mathit{\alpha a}}$$E9

where ${\mathrm{CW}}_a$ is the storage capacity of the distribution center of distribution system a, ${\mathrm{q}}_{\mathit{i\alpha }}$ is the customers’ demand i assigned to route $\alpha$ of distribution system a.

Constraint 4a: We can define a time window for the potential manufacturing process for each demand of customers. It is not allowed to exceed this lower and upper limit while assigning customers’ demands to manufacturers and scheduling them:

$$\forall i,a:{\tau }_{\mathit{ia}}^{\mathit{\text{MINm}}}\le {\tau }_{\mathit{ia}}^m\le {\tau }_{\mathit{ia}}^{\mathit{\text{MAXm}}}$$E10

where ${\tau }_{\mathit{ia}}^{\mathit{\text{MINm}}}$ is the lower limit of the time window for the manufacturing process for customers’ demand i at the manufacturer of the distribution system a, ${\tau }_{\mathit{ia}}^{\mathit{\text{MAXm}}}$ is the upper limit of the time window for the manufacturing process for customers’ demand i at the manufacturer of the distribution system a, ${\tau }_{\mathit{ia}}^m$ is the scheduled manufacturing time for customers’ demand i at the manufacturer of the distribution system a.

Constraint 5a: We can define a time window for the customers’ demands. The manufactured products must be delivered within this predefined time window to the customers and it is not allowed to exceed this time window:

$$\forall i,a:{\tau }_{\mathit{ia}}^{\mathit{\text{MINcd}}}\le {\tau }_{\mathit{ia}}^{\mathit{cd}}\le {\tau }_{\mathit{ia}}^{\mathit{\text{MAXcd}}}$$E11

where ${\tau }_{\mathit{ia}}^{\mathit{\text{MINcd}}}$ is the lower limit of the time window for delivering the manufactured product to customer i in the distribution system a, ${\tau }_{\mathit{ia}}^{\mathit{\text{MAXcd}}}$ is the upper limit of the time window for delivering the manufactured product to customer i in the distribution system a, ${\tau }_{\mathit{ia}}^{\mathit{cd}}$ is the scheduled delivery of manufactured product to customer i in the distribution system a.

Constraint 6a: The material handling operations can be performed by third-party logistics providers in the case of Tier1 and Tier 2. We can define an available time window of these 3PL providers and it is not allowed to exceed this time window while assigning and scheduling material handling tasks performed by the 3PL providers:

$$\forall i,a,\mu :{\tau }_{\mathit{ia\mu }}^{\mathit{MIN}3\mathit{PL}}\le {\tau }_{\mathit{ia\mu }}^{3\mathit{PL}}\le {\tau }_{\mathit{ia\mu }}^{\mathit{MAX}3\mathit{PL}}$$E12

where ${\tau }_{\mathit{ia\mu }}^{\mathit{MIN}3\mathit{PL}}$ is the lower limit of the time window of availability of third-party logistics provider for customers’ demand i in distribution system a in Tier $\mu$, ${\tau }_{\mathit{ia\mu }}^{\mathit{MAX}3\mathit{PL}}$ is the upper limit of the time window of availability of third-party logistics provider for customers’ demand i in distribution system a in Tier $\mu$, ${\tau }_{\mathit{ia\mu }}^{3\mathit{PL}}$ is the scheduled logistics service for customers’ demand i in distribution system a in Tier $\mu$.

Constraint 7a: As a sustainability and energy efficiency-related constraint, we can define the available energy of transportation vehicles and other material handling equipment. For example, in the case of electric vehicles we can define the available capacity of batteries or the required reloading time:

$$\forall a,\alpha :{\mathrm{\epsilon }}_{v_{\mathit{\alpha a}}}\left(q_{v_{\mathit{\alpha a}}}\in {\mathrm{\Psi }}_{\mathit{\alpha a}}\right)\bullet l_{\mathit{\alpha a}}^{\mathit{opt}}\left({\mathrm{\Theta }}_{\mathit{\alpha a}}\right)\le E_{v_{\mathit{\alpha a}}}^{\mathit{max}}$$E13

where $E_{v_{\mathit{\alpha a}}}^{\mathit{max}}$ is the upper limit of available energy (capacity of a battery in the case of electric vehicles).

3.2.2 Mathematical model of a cyber-physical distribution network

In the case of a cyber-physical distribution system, where Industry 4.0 technologies make it possible to integrate the operation of the different distribution system within and between tiers the energy consumption can be computed in the following way:

$${\mathit{EC}}^{\mathit{CYB}}={\mathit{EC}}^{\mathit{MD}}+{\mathit{EC}}^{\mathit{DC}}\to \mathit{min}.$$E14

where ${\mathit{EC}}^{\mathit{CYB}}$ is the energy consumption of the cyber-physical distribution system, which integrates all individual separated distribution systems of the conventional solution, ${\mathit{EC}}^{\mathit{MD}}$ is the energy consumption between manufacturers and distribution clusters, ${\mathit{EC}}^{\mathit{DC}}$ is the energy consumption between the distribution centers and consumers.

The energy consumption between manufacturers and distribution centers in Tier 1 can be defined as follows:

$${\mathit{EC}}^{\mathit{MD}}=\sum _{\alpha =1}^{{\alpha }_{\mathit{max}}}{\mathrm{\epsilon }}_{v_{\alpha }}\left(q_{v_{\alpha }}\right)\bullet l_{\alpha }^{\mathit{opt}}\left({\mathrm{\Theta }}_{\alpha }\right)$$E15

where $v_{\alpha }$ is the transportation vehicle assigned to route $\alpha$ in Tier1 between manufacturers and distribution centers, ${\alpha }_{\mathit{max}}$ is the total number of distribution routes for Tier1 between manufacturers and distribution centers, ${\mathrm{\epsilon }}_{v_{\alpha }}$ is the energy consumption of transportation vehicle $v_{\alpha }$ assigned to route $\alpha$ in Tier1 between manufacturers and distribution centers, $l_{\alpha }^{\mathit{opt}}$ is the length of the optimal distribution route $\alpha$ in Tier1 between manufacturers and distribution centers, which is a function of the ${\mathrm{\Theta }}_{\alpha }$ set of distribution centers assigned to route $\alpha$ in Tier1 between manufacturers and distribution centers, and $q_{v_{\alpha }}$ is the current capacity of transportation vehicles assigned to route $\alpha$ in Tier1 between manufacturers and distribution centers.

The energy consumption between the distribution centers and consumers in Tier2 can be defined as follows:

$${\mathit{EC}}^{\mathit{DC}}=\sum _{\beta =1}^{{\beta }_{\mathit{max}}}{\mathrm{\epsilon }}_{v_{\beta }}\left(q_{v_{\beta }}\right)\bullet l_{\beta }^{\mathit{opt}}\left({\mathrm{\Theta }}_{\beta }\right)$$E16

where $v_{\beta }$ is the transportation vehicle assigned to route $\beta$ in Tier2 between distribution centers and consumers, ${\beta }_{\mathit{max}}$ is the number of distribution routes in Tier2 between distribution centers and consumers, ${\mathrm{\epsilon }}_{v_{\beta }}$ is the energy consumption of transportation vehicle $v_{\beta }$ assigned to route $\beta$ in Tier2 between distribution centers and consumers, $l_{\beta }^{\mathit{opt}}$ is the length of the optimal distribution route $\beta$ in Tier2 between distribution centers and consumers, which is a function of the ${\mathrm{\Theta }}_{\beta }$ set of distribution centers assigned to route $\beta$ in Tier2 between distribution centers and consumers, and $q_{v_{\beta }}$ is the current capacity of transportation vehicles assigned to route $\beta$ in Tier2 between distribution centers and consumers.

The transformation of the conventional distribution system into cyber-physical distribution is suitable from energy consumption point of view, if

$$\sum _{a=1}^{a_{\mathit{max}}}{\mathit{EC}}_a^{\mathit{MD}}+\sum _{a=1}^{a_{\mathit{max}}}{\mathit{EC}}_a^{\mathit{DC}}\gg {\mathit{EC}}^{\mathit{MD}}+{\mathit{EC}}^{\mathit{DC}}$$E17

In the case of a cyber-physical distribution system, the emission of greenhouse gases can be computed in the following way:

$${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{CYB}}={\mathit{EM}}^{\mathit{MD}}+{\mathit{EM}}^{\mathit{DC}}\to \mathit{min}.$$E18

where ${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{CYB}}$ is the GHG emission of the cyber-physical distribution system, which integrates all individual separated distribution systems of the conventional solution, ${\mathit{EM}}^{\mathit{MD}}$ is the GHG emission between manufacturers and distribution clusters, ${\mathit{EM}}^{\mathit{DC}}$ is the GHG emission between the distribution centers and consumers.

The GHG emission between manufacturers and distribution centers in Tier 1 can be defined as follows:

$${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{MD}}=\sum _{\alpha =1}^{{\alpha }_{\mathit{\text{maxa}}}}{\mathrm{\vartheta }}_{\mathit{\text{MGHG}}}^{\mathit{\text{TIER}}1,v_{\alpha }}\bullet {\mathrm{\epsilon }}_{v_{\alpha }}\left(q_{v_{\alpha }}\right)\bullet l_{\alpha }^{\mathit{opt}}\left({\mathrm{\Theta }}_{\alpha }\right)$$E19

where ${\mathrm{\vartheta }}_{\mathit{\text{MGHG}}}^{\mathit{\text{TIER}}1,v_{\alpha }}$ is the specific GHG emission in the case of transportation vehicles assigned to route $\alpha$ in Tier1 between manufacturers and distribution centers.

The emission between the distribution centers and consumers in Tier2 can be defined as follows:

$${\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{DC}}=\sum _{\beta =1}^{{\beta }_{\mathit{\text{maxa}}}}{\mathrm{\vartheta }}_{\mathit{\text{MGHG}}}^{\mathit{\text{TIER}}2,v_{\beta }}\bullet {\mathrm{\epsilon }}_{v_{\beta }}\left(q_{v_{\beta }}\right)\bullet l_{\beta }^{\mathit{opt}}\left({\mathrm{\Theta }}_{\beta }\right)$$E20

where ${\mathrm{\vartheta }}_{\mathit{\text{MGHG}}}^{\mathit{\text{TIER}}2,v_{\beta }}$ is the specific GHG emission in the case of transportation vehicles assigned to route $\beta$ in Tier2 between distribution centers and consumers.

The transformation of the conventional distribution system into cyber-physical distribution is suitable from GHG emission point of view, if

$$\sum _{a=1}^{a_{\mathit{max}}}{\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{MDa}}+\sum _{a=1}^{a_{\mathit{max}}}{\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{DCa}}\gg {\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{MD}}+{\mathit{EM}}_{\mathit{\text{MGHG}}}^{\mathit{DC}}$$E21

As constraints, we can take the following into consideration: capacity of vehicles, capacity of loading and unloading equipment, capacity of distribution centers, time window for manufacturer, time window for customers, time window for 3PL providers in Tier1, time window for 3PL providers for Tier2, available energy for electric vehicles.

Constraint 1b: We can define the upper limit of the loading capacity of transportation vehicles. It is not allowed to exceed this upper limit of loading capacity while assigning distribution tasks to the routes and scheduling the delivery tasks. The difference between the constraints 1a and 1b is that, while in the case of a conventional distribution network, customer demand can only be assigned to the transport vehicles within the given distribution network, in the case of a cyber-physical distribution system, any customer demand can be assigned to any transportation vehicle:

$$\forall \alpha :{\mathrm{C}}_{v_{\alpha }}\ge \sum _{i=1}^{i_{\mathit{max}}}{\mathrm{q}}_i\in {\mathrm{\Psi }}_{\alpha }$$E22

where ${\mathrm{\Psi }}_{\alpha }$ is the set of customers’ demands assigned to route $\alpha$ in the cyber-physical distribution network.

Constraint 2b: We can define the upper limit of the material handling capacity of loading and unloading equipment. It is not allowed to exceed this upper limit of material-handling capacity while assigning distribution tasks to the routes and scheduling the delivery tasks. The difference between the constraints 2a and 2b is that, while in the case of a conventional distribution network, customer demand can only be assigned to the transport vehicles and related material handling equipment (loading and unloading equipment, packaging machines, labeling) within the given distribution network, in the case of a cyber-physical distribution system, any customer demand can be assigned to any material handling equipment:

$$\forall \alpha ,a:{\mathrm{C}}_{z_{\alpha }}\ge \sum _{i=1}^{i_{\mathit{max}}}{\mathrm{z}}_i\left({\mathrm{q}}_i\in {\mathrm{\Psi }}_{\alpha }\right)$$E23

Constraint 3b: We can define the upper limit of the storage capacity of distribution centers. The difference between constraints 3a and 3b is that while in the case of the conventional distribution system the capacity of a distribution system depends on only the manufacturers and customers of the same distribution system, in the case of a cyber-physical distribution network all products produced by all manufacturers can be assigned to all distribution centers (warehouses):

$$\forall a:{\mathrm{CW}}_a\ge \sum _{i=1}^{i_{\mathit{max}}}\sum _{\alpha =1}^{{\alpha }_{\mathit{max}}}{\mathrm{q}}_{\mathit{i\alpha }}\in {\mathrm{\Psi }}_{\alpha }$$E24

where ${\mathrm{CW}}_a$ is the storage capacity of the distribution center of distribution system a, ${\mathrm{q}}_{\mathit{i\alpha }}$ is the customers’ demands i assigned to route $\alpha$ of distribution system a.

Constraint 4b: We can define a time window for the potential manufacturing process for each demand of customers. It is not allowed to exceed this lower and upper limit while assigning customers’ demands to manufacturers and scheduling them. In this cyber-physical network, the time windows can be defined for all manufacturers of the whole network, while in the case of conventional distributions networks, the time windows are focusing on the manufacturers of separated distribution systems:

$$\forall i,a:{\tau }_{\mathit{ia}}^{\mathit{\text{MINm}}}\le {\tau }_{\mathit{ia}}^m\le {\tau }_{\mathit{ia}}^{\mathit{\text{MAXm}}}$$E25

where ${\tau }_{\mathit{ia}}^{\mathit{\text{MINm}}}$ is the lower limit of the time window for the manufacturing process for customers’ demand i at the manufacturer of the distribution system a, ${\tau }_{\mathit{ia}}^{\mathit{\text{MAXm}}}$ is the upper limit of the time window for the manufacturing process for customers’ demand i at the manufacturer of the distribution system a, ${\tau }_{\mathit{ia}}^m$ is the scheduled manufacturing time for customers’ demand i at the manufacturer of the distribution system a.

Constraint 5b: We can define a time window for the customers’ demands. The manufactured products must be delivered within this predefined time window to the customers and it is not allowed to exceed this time window. In this cyber-physical network, the time windows can be defined for all customers of the whole network, while in the case of conventional distribution networks, the time windows are focusing on the customers of separated distribution systems:

$$\forall i,a:{\tau }_{\mathit{ia}}^{\mathit{\text{MINcd}}}\le {\tau }_{\mathit{ia}}^{\mathit{cd}}\le {\tau }_{\mathit{ia}}^{\mathit{\text{MAXcd}}}$$E26

where ${\tau }_{\mathit{ia}}^{\mathit{\text{MINcd}}}$ is the lower limit of the time window for delivering the manufactured product to customer i in the distribution system a, ${\tau }_{\mathit{ia}}^{\mathit{\text{MAXcd}}}$ is the upper limit of the time window for delivering the manufactured product to customer i in the distribution system a, ${\tau }_{\mathit{ia}}^{\mathit{cd}}$ is the scheduled delivery of manufactured product to customer i in the distribution system a.

Constraint 6b: The material handling operations can be performed by third-party logistics providers in the case of Tier1 and Tier 2. We can define an available time window of these 3PL providers and it is not allowed to exceed this time window while assigning and scheduling material-handling tasks performed by the 3PL providers. In this case, the 3PL providers can perform all logistics operations in the cyber-physical distribution network, while in the case of conventional distribution systems, the 3PL providers of separated distribution systems can work uncoordinated:

$$\forall i,a,\mu :{\tau }_{\mathit{ia\mu }}^{\mathit{MIN}3\mathit{PL}}\le {\tau }_{\mathit{ia\mu }}^{3\mathit{PL}}\le {\tau }_{\mathit{ia\mu }}^{\mathit{MAX}3\mathit{PL}}$$E27

where ${\tau }_{\mathit{ia\mu }}^{\mathit{MIN}3\mathit{PL}}$ is the lower limit of the time window of availability of third-party logistics provider for customers’ demand i in distribution system a in Tier $\mu$, ${\tau }_{\mathit{ia\mu }}^{\mathit{MAX}3\mathit{PL}}$ is the upper limit of the time window of availability of third-party logistics provider for customers’ demand i in distribution system a in Tier $\mu$, ${\tau }_{\mathit{ia\mu }}^{3\mathit{PL}}$ is the scheduled logistics service for customers’ demand i in distribution system a in Tier $\mu$.

Constraint 7b: As a sustainability and energy efficiency-related constraint, we can define the available energy of transportation vehicles and other material handling equipment. For example, in the case of electric vehicles we can define the available capacity of batteries or the required reloading time:

$$\forall a,\alpha :{\mathrm{\epsilon }}_{v_{\mathit{\alpha a}}}\left(q_{v_{\mathit{\alpha a}}}\in {\mathrm{\Psi }}_{\mathit{\alpha a}}\right)\bullet l_{\mathit{\alpha a}}^{\mathit{opt}}\left({\mathrm{\Theta }}_{\mathit{\alpha a}}\right)\le E_{v_{\mathit{\alpha a}}}^{\mathit{max}}$$E28

where $E_{v_{\mathit{\alpha a}}}^{\mathit{max}}$ is the upper limit of available energy (capacity of a battery in the case of electric vehicles).

The decision variables of this NP-hard optimization problem are the followings:

• assignment of customers’ demands to manufacturers (Tier 1),

• assignment of final products to 3PL providers in manufacturer–distribution center relation (Tier 1),

• assignment of customers’ demands to distribution centers (Tier 2),

• scheduling of manufacturing of customers’ demands (Tier 1),

• scheduling of logistics operations of 3PL provider in manufacturer – distribution center relation (Tier 1),

• assignment of 3PL providers to perform delivery operations from distribution centers to customers (Tier2),

• assignment of vehicles to routes and distribution networks (Tier1 and Tier2),

• scheduling of logistics operations of 3PL provider in distribution center – customer relation (Tier 2).

To solve this integrated assignment, scheduling and routing problem of the green distribution network and heuristic algorithms can be used. In the literature, we can find a wide range of heuristic solutions to integrated assignment, scheduling and routing problems [54, 55, 56].

4. Numerical example

This part of the chapter demonstrates a short numerical example of the application of the above-mentioned methodology from an assignment problems point of view. In our analyzed distribution system there are four suppliers, two distribution centers, and four customers, as Figure 10 shows.

Figure 10.

Locations of suppliers, distribution centers, and suppliers of the scenario analysis (Source: GoogleMaps).

The input data of the scenario are shown in the Appendix, as follows:

• locations of suppliers, distribution centers, and suppliers of the scenario analysis (Table A1 in Appendix A),

• the relative distances among suppliers and distribution centers (Table A2 in Appendix A),

• the relative distances among distribution centers and customers (Table A3 in Appendix A),

• the customers’ demands (Table A4 in Appendix A),

• the specific transportation cost among suppliers and distribution centers (Table A5 in Appendix A). The specific transportation cost between distribution centers and customers is 1 EUR/TEU/km.

In the case of a conventional supply chain solution the optimized material handling (transportation) cost is 54,837 EUR, which can be divided into two main parts: the cost among suppliers and distribution centers is 15,537 EUR and the cost among distribution centers and customers is 39,300 EUR. In the case of a cyber-physical system, where all three levels of the supply chain are integrated through the Internet of Things technologies, the material-handling (transportation cost) is 51,929 EUR, which can be divided into two main parts: the cost among suppliers and distribution centers is 21,557 EUR and the cost among distribution centers and customers is 30,372 EUR. It means, that in the case of this simple scenario the total material handling cost can be decreased by 5.30%.

The optimal assignment of supplier and distribution centers with related material flow intensity is shown in Table 1, while the optimal assignment of distribution centers and customers is shown in Table 2.

	Kecskemét	Cegléd	Szolnok	Karcag
Újszász	30	25	25	0
Kunhegyes	55	65	25	165

Table 1.

The optimal assignment of suppliers and distribution centers with related material flow intensity [TEU/time window].

Distribution center	Customer	Demand 01	Demand 02	Demand 03	Demand 04
Újszász	Hatvan	10	0	15	0
	Jászberény	20	25	10	0
	Polgár	0	0	0	0
	Debrecen	0	0	0	0
Kunhegyes	Hatvan	0	0	0	25
	Jászberény	0	0	0	45
	Polgár	15	45	5	55
	Debrecen	40	20	20	40

Table 2.

The optimal assignment of distribution centers and customers with related material flow intensity in [TEU/time window].

The simplified numerical example shows, that the optimal solution of the integrated system does not lead to decreased costs at all levels of the supply chain, which means that the cyber-physical system focuses on the optimization of the whole system, while in the case of conventional supply chain solutions, the part systems of the supply chain are separately optimized.

5. Discussion and conclusions

The globalization of market processes requires the development of supply chains to meet the increasingly dynamic needs of individual customers with the efficiency of mass production. This means not only increasing the efficiency and flexibility of production processes but also improving related processes such as purchasing and distribution. In addition to increasing efficiency, there is a growing emphasis on the development of “green” systems and “green” solutions to reduce the environmental impact of processes related to meeting market needs.

In this chapter, a systematic literature review is carried out to identify the main lines of research, emphasizing the importance of product development, competitive distribution networks, risk evaluation, application of Industry 4.0 technologies, emission measuring and emission management, and optimization.

Based on the results of this systematic literature review, it is concluded, that using Industry 4.0 technologies, it is possible to transform conventional distribution systems into cyber-physical networks, where smart sensors, edge computing solutions, digital twinning, and discrete event simulation make it possible to coordinate the hyperconnected distribution network based on real-time data and perform a more sophisticated decision-making process. Within the frame of this chapter, a potential approach is described including both the functional model of a cyber-physical distribution network and the mathematical model to optimize the operation from environmental impact point of view.

The described method makes it possible to support managerial decisions, because depending on the results of the optimization different purchasing portfolios can be generated. The described methodology can be used to analyze the potentials of the potential transformation of conventional supply-chain solutions into a cyber-physical supply-chain.

The resources of manufacturing companies and third-party logistics providers are not taken into consideration and the parameters of the distribution network are given as deterministic parameters. These limitations show the directions for further research. In further studies, the model can be extended to a more complex model including resource optimization for manufacturing and logistics services. Second, this study only considered time, capacity, and energy consumption as deterministic parameters. Fuzzy models can be also suitable for the description of a stochastic environment, where capacities and time windows can be taken into consideration as uncertain parameters. This should be also considered in future research.

Conflict of interest

The authors declare no conflict of interest.

	Latitude	Longitude
Suppliers
Kecskemét	46°53′15.9″N	19°40′17.4″E
Cegléd	47°10′15.2″N	19°47′36.7″E
Szolnok	47°09′54.7″N	20°10′32.7″E
Karcag	47°18′35.1″N	20°57′11.8″E
Distribution centers
Újszász	47°16′17.5″N	20°05′33.2″E
Kunhegyes	47°22′01.7″N	20°39′54.6″E
Customers
Hatvan	47°41′48.6″N	19°45′59.9″E
Jászberény	47°28′30.4″N	19°52′02.4″E
Polgár	47°52′33.6″N	21°08′46.5″E
Debrecen	47°32′00.7″N	21°38′54.7″E

Table A1.

Locations of suppliers, distribution centers, and suppliers of the scenario analysis.

	Kecskemét	Cegléd	Szolnok	Karcag
Újszász	62.2	29.4	31.7	82.2
Kunhegyes	102.0	81.5	48.8	31.0

Table A2.

The relative distances among suppliers and distribution centers in [km].

	Hatvan	Jászberény	Polgár	Debrecen
Újszász	80.1	35.0	153.0	183.0
Kunhegyes	108.0	82.4	89.4	96.1

Table A3.

The relative distances among distribution centers and customers in [km].

	Demand 01	Demand 02	Demand 03	Demand 04
Hatvan	10	24	9	25
Jászberény	20	25	10	45
Polgár	15	32	5	27
Debrecen	40	20	20	40

Table A4.

The customers’ demands in [TEU].

	Kecskemét	Cegléd	Szolnok	Karcag
Újszász	1.100	1.085	1.120	1.150
Kunhegyes	1.200	1.160	0.950	1.050

Table A5.

The specific transportation cost among suppliers and distribution centers in [EUR/TEU/km].