An Inventory Management Model for City Multifloor Manufacturing Clusters Under Intermodal Supply Chain Uncertainty

Abstract

The development of smart sustainable cities is closely linked to the advancement of city manufacturing, which aims to meet local demand while maintaining economic, social, and environmental balance. This concept is realised in large cities through City Multifloor Manufacturing Clusters (CMFMCs) equipped with City Logistics Nodes (CLNs) that manage intra- and extra-cluster logistics. These flows depend on supplies arriving via Intermodal Logistics Nodes (ILNs) located on city outskirts, where disruptions caused by intermodal supply chain uncertainty can significantly affect production continuity and urban sustainability. This study aims to develop a stochastic inventory management model for city manufacturing clusters operating under intermodal supply chain uncertainty. The model is designed to ensure stable and resilient material supply to city manufacturers by optimising buffer stock (BS) levels, reducing delivery delays, and improving transport and storage efficiency. Based on the Multi-Layer Bayesian Network Method (MLBNM), the model integrates probabilistic reasoning and resilience principles to support decision-making under uncertainty. A simulation-based case study of a representative CMFMC system was used for model verification and validation. The results show that the MLBNM-based approach enhances Sustainable Supply Chain Resilience (SSCR), improves inventory flexibility, and reduces environmental impacts. The study contributes to theory and practice by providing a quantitative framework for ensuring resilient and sustainable inventory management in city manufacturing systems.

1. Introduction

The transformation of city manufacturing and logistics is increasingly driven by Industry 4.0 (I4.0) technologies and the principles of smart sustainable city development [1,2,3]. Limited urban land resources and growing traffic congestion have led to the emergence of City Multifloor Manufacturing Clusters (CMFMCs) located in residential areas. Their activities aim to meet local consumer and business demand through efficient, digitally integrated, and resource-conscious production systems [4,5,6]. A CMFMC represents a group of multi-storey production and residential buildings within a defined city zone, where enterprises of various manufacturing profiles operate under shared logistics and infrastructure frameworks [1,6]. The products and services generated by CMFMCs are distributed both inside and outside the city to meet the needs of citizens and various entities, including industrial companies [7]. The sustainable operation of CMFMCs has become possible through the integration of green and low-waste technologies, socio-cyber-physical systems, big data analytics, cloud computing, artificial intelligence (AI), the Internet of Things (IoT), blockchain, and renewable energy management systems [8,9,10,11]. These technologies support intelligent, adaptive, and sustainable production consistent with the principles of Supply Chain Resilience Theory and Stochastic Optimisation Theory, which provide a theoretical basis for decision-making under uncertainty.

Information and material flows within CMFMCs are coordinated via a platform service supply chain (PSSC) integrating modules for planning, procurement, logistics management, manufacturing execution, inventory management, analytics, collaboration, sustainability, and traceability [12,13].

Material and finished products flow through city logistics nodes (CLNs), serving as logistics facilities for intra-cluster and extra-cluster transport [14]. Typically located near shopping centres, CLNs provide logistics services including sorting, temporary storage, last-mile delivery, e-commerce fulfilment, and crowdshipping [13]. Cargo transportation within CMFMCs is implemented using e-trucks, e-vans, intelligent reconfigurable trolleys (IRTs), and freight elevators in CMFMC buildings (CMFMBs), with the optional use of car-sharing vehicles [13,15]. Intra-cluster deliveries within residential zones are mainly carried out by e-vans [13,16], while external (domestic and international) deliveries to CLNs are handled by e-trucks through Intermodal Logistics Nodes (ILNs) [15]. ILNs function as transhipment and warehouse facilities on the city outskirts, usually in industrial zones, managing long-distance cargo flows transported by sea, rail, or heavy road vehicles with containers and swap bodies [15]. Uncertainty in intermodal supply chains—resulting from organisational inefficiencies, infrastructural constraints, and external factors such as economic crises, extreme weather events, geopolitical tensions, pandemics, or demand fluctuations—directly affects inventory management and the operational reliability of city manufacturing systems [17,18,19,20,21]. Although consolidation and closed-loop logistics strategies can increase efficiency, they also heighten system vulnerability to disruptions due to interdependence between transport modes and nodes [22,23,24]. Consequently, ensuring sustainable supply chain resilience (SSCR) and maintaining effective inventory management are essential for the stable functioning of CMFMCs.

The objective of this study is to develop a stochastic inventory management model for CMFMCs operating under intermodal supply chain uncertainty, aimed at ensuring continuous, resilient, and sustainable supply performance. The model is intended to overcome the limitations of existing deterministic models and simulation frameworks by applying a probabilistic approach that integrates resilience mechanisms and stochastic optimisation. In doing so, it builds on the theoretical foundations of Supply Chain Resilience Theory and Sustainable Supply Chain Management, extending these frameworks to the context of city manufacturing and intermodal logistics. Specifically, the model is designed to:

(1)

Support decision-making on inventory allocation under variable transport conditions;

(2)

Optimise buffer stock (BS) levels to balance cost, reliability, and environmental performance; and

(3)

Enhance the adaptability and efficiency of intermodal supply operations in CMFMCs.

To achieve this, the study addresses the following research questions (RQs):

RQ1: How do disruptions that occur during an intermodal transport preceding intra-urban transfers, i.e., maritime/rail/heavy road transport supplies to ILN, affect delays in deliveries to CMFMBs?

RQ2: In which place(s) along the large city supply chain (ILN, CLN or CMFMBs) should a BS be maintained to ensure a continuous supply of CMFMBs?

RQ3: What should be the optimal quantity of the BS? What factors should be considered when determining this quantity? How often should the BS be verified?

The answers to the questions posed are based on a literature review of the field of SSCR and inventory management in the context of city manufacturing and logistics, and the development of an inventory management model under intermodal supply chain uncertainty to ensure consistent production performance, rational use of transport and storage potential in CMFMCs. The real case study was applied to validate the proposed model and identify managerial implications, gaps, and future research directions. The results demonstrate that the proposed model improves supply chain resilience, inventory flexibility, and environmental performance, providing theoretical advancement in modelling resilient urban supply systems and practical tools for optimising operations in smart and sustainable cities.

The paper is organised as follows: Section 2 presents the literature review on SSCR and inventory management in city logistics. Section 3 describes the materials and methods. Section 4 defines the research problem, notation, and assumptions. Section 5 introduces the proposed inventory management model and the case study. Section 6 discusses the results and managerial implications. Section 7 concludes the paper and suggests future research directions.

2. Literature Review

2.1. Sustainable Supply Chain Resilience in the Context of City Manufacturing

SSCR represents an integrated concept that merges two key paradigms—the Sustainable Supply Chain (SSC) and Supply Chain Resilience (SCR)—to ensure stable, adaptive, and sustainable performance of supply networks under uncertainty [25,26,27]. The SSC paradigm reflects the principles of sustainable development, aiming to minimise environmental and social impacts while maintaining long-term economic efficiency [28]. These three dimensions—environmental and social responsibility, and economic viability—jointly form the sustainability foundation of modern city manufacturing [19,29].

As a core component of the SSC within CMFMCs, environmental responsibility focuses on reducing CO₂ emissions and solid waste [8], increasing the use of renewable energy sources, and promoting the efficient utilisation and recycling of natural resources [11]. It also emphasises deploying energy-efficient vehicles and logistics facilities [13] and eco-friendly packaging across the city manufacturing and logistics network [19]. These practices are supported by Industry 4.0 (I4.0) technologies, which enhance traceability, transparency, and resource efficiency throughout the supply chain, while simultaneously enabling continuous monitoring of environmental impacts and facilitating greener production and distribution processes within CMFMCs [30,31,32,33,34]. Examples include using electric delivery vehicles, consolidated freight flows, and night-time deliveries between ILNs and CLNs to reduce emissions and congestion [15,23,32].

Social responsibility within the SSC framework emphasises fair labour conditions, workplace safety, and ethical business conduct throughout all supply chain stages [19]. The activities of all participants in the supply chain aim to reduce legal, reputational, and operational risks, while building long-term, trusting, and partnership relationships that meet the expectations of all stakeholders [35]. Building socially responsible partnerships throughout the supply chain is based on transparency and effectively monitoring all operational processes and working conditions using I4.0 technology and PSSC [12,19]. The physical and digital collaboration ensures fair competition, reduces reputational and operational risks, and strengthens trust between all actors in the supply network [36].

Economic responsibility addresses maintaining financial viability and competitive advantage without undermining environmental or social performance [19,29]. It defines a strategy for creating sustainable value for all participants in the supply chain, which goes beyond making short-term profits for CMFMC enterprises [15,37]. Long-term profitability and efficiency, as well as just-in-time (JIT) supply planning and implementation, risk and inventory management under supply chain uncertainty and demand changes, are directly relevant to ensuring the competitiveness and economic viability of supply chains for CMFMC enterprises [18,38]. Supply chain economic viability relies on the continuity of the value creation flow and emphasises the operational performance of logistics processes [15,39]. The convergence of these three sustainability dimensions defines the SSC as a system capable of generating long-term value while maintaining equilibrium between efficiency and resilience.

Sustainable supply chains depend on the efficient use of resources and their ability to anticipate, absorb, and recover from disruptions. This capability is achieved through effectively managing social and environmental risks and strategically deploying resilience assets across logistics and manufacturing networks [40,41,42]. The SCR paradigm extends the principles of the SSC by focusing on maintaining operational continuity and meeting customer demand under uncertainty [19,43,44]. According to Ivanov [39], SCR can be analysed through two complementary perspectives: the Stability-Based View (SBV) and the Adaptation-Based View (ABV). This dual perspective comprehensively explains short-term restorative responses and long-term adaptive capabilities within supply chains [39,45].

The SBV of SCR focuses on performance stability and the system’s ability to return to its planned state following predictable disruptions. It is based on historical data and accumulated experience, emphasising risk quantification, redundancy, and recovery planning [39,46]. This view addresses known-known and partially known-unknown uncertainties, where sets of probable failures and their corresponding recovery actions are well defined [39,47]. SBV-related mechanisms include risk management, inventory control, and real-time monitoring, increasingly supported by Industry 4.0 (I4.0) technologies such as IoT, predictive analytics, and digital twins [48,49,50,51]. These technologies improve situational awareness and enable data-driven corrective actions responding to disturbances. Among quantitative modelling tools, the Multi-Layer Bayesian Network Method (MLBNM) has gained particular relevance for predicting and analysing the propagation of uncertainties in supply networks [52,53,54,55].

The ABV, in contrast, emphasises proactive adaptation and long-term system viability under known-unknown and unknown-unknown disruptions [56,57]. As Ivanov [58] defines, supply chain viability is the ability “to maintain itself and survive in a changing environment through the redesign of structures and replanning of performance with long-term impacts.” The ABV focuses on structural flexibility, strategic agility, and reconfigurability to ensure performance persistence despite unexpected disturbances [40]. Although distinct in orientation, the SBV and ABV complement one another: SBV ensures short-term operational recovery, while ABV strengthens long-term adaptability and innovation capacity [39].

In the context of city manufacturing, these two perspectives are operationalised through layered logistics and production structures within CMFMCs. SBV mechanisms focus on maintaining stability through buffer stock (BS) management, inventory pooling, and transport reorganisation in CLNs and ILNs [15,39]. ABV mechanisms, in turn, involve adaptive structural network designs—including supplier diversification, dynamic allocation of inventory across ILNs, CLNs, and CMFMBs, and the reconfiguration of production performance and distribution strategies [15,39,59]. Together, these practices ensure operational stability and structural adaptability, forming the foundation of resilience in CMFMCs.

Based on these interrelated perspectives, SSCR can be defined as a supply chain’s ability to balance social responsibility, environmental sustainability, and economic viability while proactively stabilising and adapting to disruptions [19,29,39]. Integrating sustainable and resilient practices into supply chain management helps mitigate negative environmental, social, and economic consequences by anticipating potential risks, adapting to changing conditions, and restoring operational continuity [21,24].

Key indicators commonly used to measure SSCR performance include on-time delivery, fill rate, and time-to-recover [45]. The literature identifies several mechanisms that strengthen SSCR and ensure performance persistence in city manufacturing systems [44]:

• Network diversification and redundancy, achieved through adaptive structural designs integrating suppliers, inventories, and distributed production sites within CMFMCs [60,61,62];
• Collaboration and transparency, enabling strong and trust-based relationships among manufacturers, suppliers, and logistics providers through open communication and shared data platforms [63,64,65];
• Flexibility and agility, supporting rapid responses to demand fluctuations and regulatory or infrastructural changes [66,67].
• Focus on sustainability as a mechanism to integrate environmental, social and governance factors into the supply chain [68,69,70];
• data-driven management, employing analytics, predictive modelling and AI for risk forecasting and process optimisation [71,72];
• Automation and digitalisation, improving system visibility, efficiency, and responsiveness [44,72];
• Stakeholder engagement, including collaboration with customers, communities, and policy-makers to promote shared sustainability and resilience objectives [61,72].

One of the most effective mechanisms for ensuring SSCR is inventory redundancy based on a network approach to BS pooling [39]. Redundancy is a fundamental approach to ensuring performance persistence. Inventory management plays a key role in ensuring the SSCR, as it allows for balancing efficiency, adaptability, and environmental responsibility under uncertainty [49,73]. This mechanism is particularly critical for CMFMCs, where physical space and logistics resources are constrained. In such dense urban production systems, resilience is maintained based on intelligent coordination and dynamic redistribution of inventories distributed across multiple logistics nodes and manufacturing facilities. Within this context, inventory management becomes an operational tool and a strategic enabler of resilience, integrating the principles of the SBV and ABV through networked storage, buffer capacity sharing, and adaptive replenishment practices [38,39,58]. Collectively, these mechanisms position SSCR as a dynamic and adaptive framework that enables CMFMCs to sustain performance and continuity under intermodal supply chain uncertainty. Inventory management is a central operational function within this framework that links resilience theory with practical implementation by regulating material flows, buffer stocks, and recovery capacity across the city manufacturing network.

Accordingly, the following subsection examines the principles and models of inventory management in city manufacturing, emphasising its role in maintaining sustainable and resilient operations and identifying the conceptual and methodological gaps that motivate developing the stochastic modelling approach presented later in this study.

2.2. Inventory Management for City Manufacturing

Inventory management for CMFMC is the process of planning, controlling, and optimising raw materials/materials, components and products stocked in the manufacturing and logistics facilities, and in circulation to ensure their consistent performance with minimal expenses [74,75]. The inventory management problem is maintaining a balance between surplus and shortage. Violation of this balance leads to unnecessary storage costs, product obsolescence, production failures or lost sales [49,74]. Therefore, inventory management aims to the timely provision of materials, semi-finished products, and goods in the required quantities to reduce storage costs, optimise working capital, prevent shortages or surpluses under demand and supply chain uncertainty, product shelf life and other factors [76]. Inventory management in the context of I4.0 takes on new meaning through the integration of key management methods and models, technologies and software such as: just-in-time system, ABC analysis and XYZ analysis, economic order quantity (EOQ) model, big data and analytics, IoT, cloud computing, blockchain technology, AI, machine learning, enterprise resource planning and warehouse nervous system, etc. [77,78,79,80].

One of the fundamental principles of inventory management within CMFMC is the planning and maintenance of BS by manufacturers, considering SBV and ABV, to ensure consistent performance under intermodal supply chain uncertainty [14,39,76]. The BS is an integral part of the reserve stock, and its maintenance policy is based on the use of various models, in particular the EOQ and replenishment model I, Q, [18,76]. In the BSs replenishment model r, Q, its maintenance is fulfilled by ordering Q units when the stock level r is reached [81]. The manufacturer stores the BS in its own or rented warehouse areas within CMFMCs, and in CLNs of a large city [15]. Thus, the manufacturer is the key actor who creates BSs and is responsible for their formation. Lessors of storage facilities represented by CMFMC manufacturers and logistics service providers of CLNs and ILN, in accordance with the service level agreement with the manufacturer (lessee), manage already formed BSs [15]. The amount of BS depends on the delivery time, the probability of on-time delivery, the fill rate and the time-to-recover, which are calculated based on the previous knowledge and experience of the managers [45,58]. The reduction in these indicators’ values and, consequently, the reduction in BSs is facilitated by the proximity of suppliers to the manufacturers within CMFMCs [15]. Typically, the major contributor to the increase in BS is disruptions at suppliers during the intermodal transportation phase outside of a large city [14]. The primary tasks of lessors and logistics service providers include inventory management (often based on vendor-managed inventory), ensuring the rhythmic shipment of orders, and maintaining BS levels in coordination with the customer [15]. The storage capacities of manufacturers within CMFMCs, CLNs and ILN are adaptable structural network designs, which are the basis for implementing SSCR in a large city [58]. One of the SSCR mechanisms within such adaptive structural network designs is the mutual support of manufacturers through mutually beneficial redistribution of their BSs [5,58]. These redistributions of BSs between manufacturers of CMFMCs are carried out continuously using the corresponding PSSC applications.

The literature review and previous studies reflect traditional approaches to inventory management in urban areas, including adjacent industrial zones [82,83,84]. However, with the growing CMFMC market, a new approach to BS management and SSCR has emerged among manufacturers and logistics service providers. That approach is related to the growth in the number of SMEs in CMFMCs and the implementation of additive technologies in the urban environment. As a result, an increase in supply chain volumes can be observed, which are characterised by time-varying quantities related to the JIT logistics formula and a large variety of production materials. For example, CMFMC production based on 3D printing technology is associated with the daily deliveries of various production materials (i.e., filaments, printer resins, powders and accessories) with limited storage possibilities at the production location [7]. Logistics service providers responsible for JIT deliveries ensure consistent CMFMC operations performance under intermodal supply chain uncertainty. That creates new challenges for inventory management, which must be located in urban areas, and their quantity must be adjusted to dynamic disruptions occurring, particularly during long-distance transport preceding intra-urban transfers. Therefore, this study focuses on addressing the identified gaps in inventory management within CMFMCs. Finding meaningful answers to research questions involves developing a new inventory management model for CMFMCs, emphasising disruption forecasting and optimising the BS quantity and allocation in adaptive structural network designs, taking into account delivery delays and time-to-recover.

The analysis of inventory management approaches in CMFMCs demonstrates that ensuring continuity of operations under intermodal supply chain uncertainty requires efficient logistics coordination and theoretical integration of resilience and sustainability principles. While conventional inventory control models—often deterministic and single-layered—provide valuable baseline insights, they fail to capture the stochastic, multi-causal, and adaptive nature of city manufacturing disruptions. Addressing this limitation calls for a probabilistic and system-oriented modelling approach capable of representing interdependencies among transport modes, CLNs, and manufacturing facilities and the propagation of uncertainty through the supply chain. In response, this study adopts the MLBNM as a theoretically grounded and computationally flexible tool for linking the concepts of supply chain resilience, sustainability, and inventory optimisation [54,55].

The following subsection, therefore, introduces the conceptual and methodological foundations of MLBNM, explaining how this stochastic modelling framework supports quantitative resilience assessment, buffer stock optimisation, and evidence-based decision-making for sustainable CMFMCs.

2.3. The Multi-Layer Bayesian Network Method

The MLBNM provides a robust stochastic modelling framework for analysing interdependencies and uncertainty propagation in complex supply chains [51,52,53]. Rooted in Bayesian inference and stochastic optimisation theory, it enables the quantitative analysis of causal relationships between disruption sources, transport modes, logistics nodes, and inventory states. A Bayesian network represents conditional dependencies among variables and allows the estimation of event likelihoods based on observed data [54,55]. The multi-layer structure of MLBNM extends this concept to multiple operational levels—including intermodal transport, CLNs, and CMFMCs—enabling the analysis of how disruptions propagate across the network. For example, maritime or rail transport delays can be modelled to evaluate their downstream effects on inventory depletion and production continuity.

Unlike deterministic or purely simulation-based models, MLBNM combines diagnostic and predictive reasoning with probabilistic optimisation, offering analytical transparency and prescriptive decision support. It allows continuous updating of conditional probabilities as new data becomes available, reflecting real-time behaviour of the supply chain under uncertainty [54]. In city manufacturing, MLBNM supports decision-making regarding buffer stock allocation, transport planning, and resilience enhancement under intermodal disruptions. Its multi-layer architecture captures local and systemic effects, making it particularly suitable for managing urban supply networks characterised by spatial constraints, shared logistics resources, and high variability [55]. Thus, MLBNM provides a strong theoretical and methodological foundation for developing the stochastic inventory management model proposed in this study.

In summary, prior studies have established valuable insights into sustainable and resilient supply chain management but have not sufficiently addressed the stochastic behaviour of intermodal disruptions and their impact on urban inventory systems. This study develops a stochastic inventory management model for CMFMCs using the MLBNM to fill this research gap. The following section outlines the methodological framework, model design, and validation procedure.

3. Materials and Methods

The inventory management model for CMFMCs is an upgraded version of the decision support model already presented [15]. This new model focuses on intermodal supply chains to CMBFMC using intermodal transport units (containers, swap-bodies, semitrailers). These long-distance deliveries by maritime, railway and road transport are nowadays performed to existing city manufacturing clusters located in European metropolises, i.a. in Berlin (Germany), Amsterdam (Holland), and Lodz (Poland). Figure 1 shows the scheme of a large city with CMFMCs and an accompanying intermodal network. The large city includes residential (1) and industrial (2) areas, ILN (5) operating as an entry point for all external intermodal supplies for CMFMC (4) enterprises. The two possible intermodal options involve sea–land deliveries with the key transhipment point located in a port terminal (6) and land-based deliveries based on the network of intermodal terminals (7) and intermodal train connections supported by heavy goods vehicles (HGVs).

Figure 2 presents a scheme of supply chains for CMFMCs. CLN has a key role in every cluster as it provides logistics services for nearby customers, i.e., SME enterprises in CMFMB.

Each CLN serves several buildings, which corresponds to several dozen manufacturing companies. Services offered by CLN include storage and sorting of IRTs, with the ability to monitor these operations in real time [15]. Within the agglomeration area between the ILN and CLNs, cargo is delivered in IRT units by e-trucks through the two-line internal roads, including the main ring road. Within each CMFMC, cargo transfer between CLNs and CMFMBs is carried out by e-vans using standard city roads [15].

The study follows a structured, multi-stage research process to ensure methodological transparency and reproducibility. The methodological framework integrates theoretical, analytical, and empirical components as follows:

• Conceptual foundation—A comprehensive literature review (Section 2.1 and Section 2.2) establishes the theoretical basis by linking SSCR, city manufacturing, and inventory management principles.
• Model development—The MLBNM (Section 2.3) is applied to formalise causal dependencies and quantify intermodal supply chain uncertainty affecting CMFMCs.
• Model formulation—A stochastic inventory management model is constructed to optimise BSs allocation under uncertainty, integrating sustainability and resilience criteria.
• Simulation and validation—The proposed model is tested through a case-based simulation, using representative data for a typical CMFMC to verify model reliability, sensitivity, and robustness.
• Analysis and implications—Results are interpreted to identify managerial and theoretical implications, highlighting contributions to sustainable city manufacturing and outlining directions for future research.

This stepwise approach ensures methodological coherence between conceptual reasoning, model design, and empirical verification, directly addressing the issue of intermodal supply chain uncertainty and the operational resilience of CMFMCs.

The development of the inventory management model for CMFMCs is based on the Material Flow Analysis and MLBNM [15,54,85]. The MLBNM [54,84] is a key methodological approach used in the inventory management model, as it uses probability theory to determine dynamically changing delays occurring in the supply chain. The MLBNM applied to model supply chain disruptions and BSs located in logistics nodes are new elements concerning the already-presented decision support model [15].

Figure 3 shows the differences between the previously proposed deterministic approach in the CMFMC decision support model [15] and the new stochastic approach based on MLBNM implemented in the CMFMC inventory management model. The new modules include a supply chain disruption generation module based on MLBNM and a BS inventory module to counter supply shortages.

Quantitative assessment of flows, stocks, incoming and outgoing cargoes to/from ILN and CLNs was carried out using Material Flow Analysis [15]. The measures of freight flows are the number of IRTs, the level of freight vehicles loading capacity utilisation, the number of e-truck and e-van transfers and two types of inventories maintained in the supply chain, overnight stock (OS) and BS [15,23]. Based on these parameters, it is possible to make decisions regarding inventory management in the CMFMC supply chain according to the adopted strategy (e.g., ‘zero shortages’ versus ‘acceptable waiting time for supplies’).

The case study verification and validation of the proposed inventory management model for CMFMCs under supply chain uncertainty was made using MATLAB (version 2024a) programming.

4. Problem Definition, Notation, and Assumptions

4.1. Problem Definition

Disruptions in international and intermodal supply chains have become increasingly frequent and complex, exposing the vulnerability of global logistics systems. Since 2008, a series of crises—including the global financial downturn (2008–2009), the COVID-19 pandemic (2020–2022), and the war in Ukraine (since 2022)—have destabilised global trade, disrupted transport networks, and intensified uncertainty in supply lead times. In addition to these global shocks, regional and local events such as extreme weather, port strikes, border restrictions, infrastructure accidents (e.g., the blockage of the Suez Canal by the container ship Ever Given), and security threats have further hindered the reliability of intermodal logistics [86]. Enterprises dependent on intermodal supply chains, particularly those relying on maritime and rail connections, are most affected by such disruptions. SMEs within CMFMCs are especially vulnerable because they often lack the infrastructure and storage capacity to absorb transport delays. Within CMFMCs, production continuity depends heavily on coordinated deliveries through ILNs and CLNs that operate under constrained urban conditions. These disruptions directly undermine the sustainability and resilience of city manufacturing by increasing material shortages, congestion, and emissions from emergency deliveries. Consequently, effective inventory buffering becomes essential to ensure continuity of production while maintaining sustainable resource use. Yet, existing inventory management approaches for CMFMCs lack the ability to determine where and how much BS should be maintained under stochastic intermodal disruptions. Most traditional models are deterministic or descriptive, not incorporating uncertainty propagation between intermodal and intra-urban transport stages.

Figure 4 shows the propagation of intermodal supply chain disruptions and the potential BS locations in the context of CMFMC operations. Events causing delays can originate in long-distance transport before reaching the ILN and during ILN–CLN and CLN–CMFMC transfers. They may also occur at transhipment points and storage facilities, such as ports, terminals, or warehouses. To demonstrate the propagation of intermodal disruptions under different transport conditions, this study analyses three representative product flows: Product A delivered by sea, Product B by rail, and Product C by road (see Figure 4). These scenarios reflect typical intermodal routes serving CMFMCs and capture varying levels of transport uncertainty and lead-time variability. Although the causes of disruptions differ, their most evident consequence is unpredictable delivery delay, ranging from days to months. Since neither timing nor duration can be precisely forecast, historical data must be used to estimate the probability and expected magnitude of delays in each supply segment.

A typical preventive strategy is maintaining BS of production materials and semi-finished goods to ensure operational stability. However, no universal methods exist for optimising the BS quantity or location along the city supply chain. Large enterprises often maintain private storage, but SMEs operating within CMFMCs must rely on shared logistics infrastructure, which limits their flexibility and increases exposure to transport uncertainty.

To address these limitations, this study’s stochastic inventory management model focuses on optimising BSs allocation under intermodal supply chain uncertainty. The model assumes that disruptions primarily occur in intermodal transport segments (sea, rail, and heavy-road transport to ILNs) and that the BSs are located at CLNs of CMFMCs. This design reflects the real operating conditions of sustainable city manufacturing, where space, environmental restrictions, and cost efficiency necessitate centralised yet adaptive inventory management.

4.2. Notation

Table 1. List of indexes and parameters.

Indexes		Unit
$a_{md}$	availability of m-type production material in d day $(a_{md}=$ $1—\mathrm{available},a_{md}$ = 0—unavailable)
$d$	day d = 1, 2, 3, … 365
l	$\mathrm{number}\mathrm{of}\mathrm{child}\mathrm{events}\left(\mathrm{triggers}\right)\mathrm{in}\mathrm{the}\mathrm{conditional}\mathrm{probability}P=P\left(Y_j|X_l\right)$l = 1, 2… L
j	$\mathrm{number}\mathrm{of}\mathrm{parent}\mathrm{events}\left(\mathrm{events}\right)\mathrm{in}\mathrm{the}\mathrm{conditional}\mathrm{probability}P=P\left(Y_j|X_l\right)$j = 1, 2 … J
$m$	$\mathrm{type}\mathrm{of}\mathrm{production}\mathrm{material},m=A,B,C,\dots P$
$n$	$\mathrm{number}\mathrm{of}\mathrm{CMFMBs}\mathrm{in}\mathrm{CMFMC},n=\mathrm{1,2},3,\dots$, N
k	$\mathrm{number}\mathrm{of}\mathrm{CMFMCs}\mathrm{and}\mathrm{CLNs}\mathrm{in}\mathrm{a}\mathrm{large}\mathrm{city},k=\mathrm{1,2},3,\dots$, K
Parameters
Independent parameters
$C^{van}$	level of utilisation of e-van loading capacity (last e-van in transfer group)	%, IRT
$t_{truck}$	transit time between ILN and CLN	days
$t_{van}$	transit time between CLN and CMFMB	days
$t_{cargo}^{truck}$	e-truck loading/unloading time	days
$t_{cargo}^{van}$	e-van loading/unloading time	days
$t_{cargo}^{CLN}$	cargo handling time in CLN	days
Dependent parameters
$P_{md}^{CMFMB\left(n\right)}$	demand for d day and m-type production material in non-unitised form ordered by CMFMB	%, tonnes
${D^{\prime }}_{md}^{CLN}$	reduced demand for d day and m-type of production material ordered by CLN	IRT
${D^{\prime }}_{md}^{CMFMB\left(n\right)}$	reduced demand for d day and m-type of production material ordered by CMFMB	IRT
${D^{″}}_{md}^{CMFMB\left(n\right)}$	reduced demand for d day and m-type of production material ordered by CMFMB and calculated in full IRT units	IRT
$S_{md}^{CMFMB\left(n\right)}$	supply of m-type of production material based on the order of CMFMB on d day	IRT
$S_{md}^{CLN}$	supply of m-type of production material based on the order of CLN on d day	IRT
$P_{SC}$	relative probability defined for successive stages of the supply chain
$BS$	total volume of BS	IRT
${BS}_m$	volume of BS of m-type of production material	IRT
BSL	BS level	%
${SD}_m^{CLN}$	cumulative period of shortage of m-type of production material in CLN during one year (365 days)	days
${SD}_m^{CMFMB\left(n\right)}$	cumulative period of shortage of m-type of production material in CMFMB during one year (365 days)	days
${SV}_m^{CLN}$	shortage of m-type of production material in CLN on d day	IRT
${SV}_m^{CMFMB\left(n\right)}$	shortage of m-type of production material in CMFMB on d day	IRT
$Q_{md}^{CLN}$	overnight stock of m-type of production material in CLN after d day	IRT
$Q_{md}^{CMFMB\left(n\right)}$	overnight stock of m-type of production material in CMFMB after d day	tonnes, IRT
$T_{lead}$	supplier lead time	days
$d_{delay}$	delay time related to production materials ordered by CMFMB on d day	days
$t_{delay,m}^{ILN}$	period m-type of production material unavailability in ILN (product not in stock in ILN)	days
$d_{start,m}$	first day on which m-type of production material is not in stock in ILN
$d_{end,m}$	last day on which m-type of production material is not in stock in ILN
$t_{delay,m}^{CLN}$	delay of shipment from CLN to CMFMB resulting from limitations in the use of e-vans.	days
$t_{delay,m}^{CMFMB\left(n\right)}$	number of days in which the materials are not delivered from CLN to CMFMB	days

presents the list of all indexes and parameters applied in the subsequent stages of the analysis. The key parameters related to the model of the CMFMC operational system include: daily demand for production materials ($D_{md}^{CLN}$, $D_{md}^{CMFMB\left(n\right)}$) reported by CLN and CMFMBs, shortage of production materials in CLN and CMFMBs (${SV}_m^{CLN}$, ${SV}_m^{CMFMB\left(n\right)}$), and the BS volume (${\mathrm{B}\mathrm{S}}_m$) kept in CLN and overnight stock volumes ($Q_{md}^{CLN}$, $Q_{md}^{CMFMB\left(n\right)}$) kept in CLN and CMFMBs. The parameters have been classified as independent or dependent in line with the research assumptions adopted.

4.3. Assumptions

For the CMFMC inventory management model-based analyses, assumptions were made for the inventory management model for CMFMCs under supply chain uncertainty based on MLBNM. Figure 5 presents a diagram of disruptions affecting intermodal stages of the supply chain, i.e., preceding delivery to ILN. The diagram nodes represent respective identified events categorised as triggers, events, and consequences, while the edges indicate the assumed conditional probabilities of the events occurring. The probability values (Figure 5) and event assumptions were determined using an expert-based approach, drawing on real delay situations and consultations with experienced logistics operators active in the international intermodal transport market.

Dedicated assumptions for the CMFMC inventory management model, other than those formulated for the CMFMC decision support model [15], include:

(1)

Orders from CMFM enterprises for production materials are processed according to two rules: ‘next-day delivery’, i.e., orders are collected on a given day and delivered the next day, and ‘never less than ordered’, i.e., the volume of transported materials can be increased due to the best use of the vehicle’s cargo capacity. Shortages in supply may occur due to disruptions in intermodal transport prior to the delivery to ILN and may be affected by any of the production materials.

(2)

The demand for production materials ordered by CMFMC enterprises is highly variable because it is related to the volume of next-day planned production generated independently for each CMFMB and to the JIT ordering regime.

(3)

There are two types of IRT storage areas in each CLN, enabling daily shipments to CMFMBs, i.e., the BS area aimed at maintaining a safety stock supplementing the shortages in CLN deliveries, and the overnight stock area aimed at storage of redundant IRTs that were delivered to CLN as a result of optimisation of vehicle capacity utilisation. The total storage area in CLN is always limited by the parameters of the building in which it is located.

(4)

Each CMFMB has a very limited storage area. As a rule, SMEs are located in multi-storey buildings that correspond to urban development. The available space is intended for production, and the pre- and post-storage processes should be limited to the necessary minimum. Additional storage restrictions result from the permissible load of the floor and the freight elevator.

5. Results

5.1. The Inventory Management Model for CMFMCs Under Supply Chain Uncertainty

The model utilises input data on production material demand and vehicle utilisation levels to determine optimal inventory levels and recommend transportation options for IRT loads. The solutions are consistent and deterministic regarding the defined operational assumptions and decision structure.

Based on the model developed by Wiśnicki et al. [15], an extension was introduced to simulate supply chain disruptions. These disruptions are periods during which goods are unavailable at the ILN due to various operational or random factors. This mechanism reflects the broader body of research on the ripple effect in supply networks [44,55].

According to the approach by Hosseini and Ivanov [45,55], the probability of a specific consequence (e.g., “product not in stock”) is modelled using the formula:

$$P_{SC}=P_{SC}\left(X_1,X_2,\dots X_L\right)=\prod _{l=1}^{L}P\left(Y_j\right|X_l)$$

(1)

where

$P_{SC}$—the relative probability defined for successive stages of the supply chain

$X_1,X_2,\dots X_L$—child events, i.e., triggers

$Y_1,Y_2,\dots Y_J$—parent events, i.e., events

$P\left(Y_j\right|X_l)$—the relative probability ($Y_j$ depending on $X_l$), e.g., the probability of an event $Y_j$ given trigger $X_l$ occurs (as in Figure 5).

In the presented model, each event $Y_l$ depending on the trigger$X_l$ leads to a specific consequence in the supply chain. Such a three-layer causal structure allows for accurate modelling of cause-and-effect relationships under CMFMC supply chain uncertainty. A similar conceptual framework was discussed in [30,39].

The partial probabilities of events and their consequences in the CMFMC supply chain are specified in Figure 5. An example of the path trigger-event-sequence is as follows. The probability P of consequence “Product A not in stock in ILN for 7 days” is calculated considering:

(1)

the consequence “Product A not in stock in ILN for 7 days” has a probability factor of 1.00, provided the event Y “Delay in delivery of product A to INL for 7 days” occurs;

(2)

the event Y “Delay in delivery of product A to INL for 7 days” has a probability factor of 0.90, provided the trigger X “Event in maritime transport (long term)” occurs;

(3)

the trigger X “Event in maritime transport (long term)” has a probability factor 0.02.

After calculating the probability of the “product not in stock” consequence, the model generates a random set of days when a given product is unavailable. Based on this output, a product availability matrix for the ILN is constructed and used as input for the subsequent decision-making steps. Based on the calculated probabilities, product failures are generated as days when a given item is unavailable. In this simplified probabilistic model, the causes of these shortages are not analysed; only their consequences are considered.

Moreover, the decision support model presented in [15] is modified or upgraded, as follows:

(i)

Overnight stock in CLN and CMFMB is calculated as follows:

$$Q_{md}^{CLN}=S_{md}^{CLN}-\sum _{n=1}^N{\displaystyle \frac{P_{md}^{CMFMB\left(n\right)}}{S{F}_m}}$$

(2)

$$Q_{md}^{CMFMB\left(n\right)}={\displaystyle \frac{P_{md}^{CMFMB\left(n\right)}}{S{F}_m}}-{D^{\prime }}_{md}^{CMFMB\left(n\right)}$$

(3)

$${maxQ}_m^{CMFMB\left(n\right)}=\underset{d}{\max }\left\{Q_{md}^{CMFMB\left(n\right)}\right\}$$

(4)

$${avgQ}_m^{CMFMB\left(n\right)}={\displaystyle \frac{\sum _{d=1}^{365}{Q}_{md}^{CMFMB\left(n\right)}}{n}}$$

(5)

(ii)

Upgraded suppliers’ lead time of agglomeration transfers, i.e., on the ILN-CLN-CMFMB section, is calculated as follows:

$$T_{lead}=t_{truck}+t_{van}+{2\cdot t}_{cargo}^{truck}+{2\cdot t}_{cargo}^{van}+t_{cargo}^{CLN}+t_{delay}+t_{storage}$$

(6)

where

$$t_{delay}=F\left(d,n,t_{delay,m}^{ILN},t_{delay,m}^{CLN}\right)$$

(7)

The value $t_{delay}$ is the delivery delay time of m-type of production material to CMFMB. It depends on many factors, including: the date the order was made by CMFMB, the type of production material ordered, the location of the CMFMB that placed the order, and the delay time $t_{delay,m}^{ILN}$ of delivery to ILN (Equation (8)), and the delay time $t_{delay,m}^{CLN}$ of shipment from CLN to CMFMB resulting from the assumed utilisation of e-van loading capacity.

$$t_{delay,m}^{ILN}=\left\{\begin{array}{c}{d}_{delay,m}\in {\mathbb{N}}_0:d_{delay,m}=d_{end,m}-d_{start,m}+1:\\ a_{m{d}_{start}}=a_{m\left(d_{start}+1\right)}=\cdots =a_{m{d}_{end}}=0\end{array}\right\}$$

(8)

where $d_{start,m}$ and $d_{end,m}$ are the numbers of the first and the last day on which m-type of production material is not in stock in ILN.

(iii)

volume of BS in CLN is calculated as follows:

Taking into account shortages in the supply chain, the sequence ($a_{d_{start},m}=a_{\left(d_{start}+1\right),m}=\cdots =a_{d_{end},m}=0$) imposes the necessity of holding BS. The presented model assumes only one BS located in CLN. The BS volume depends on the number of days during which the product was unavailable, i.e., between $a_{start,m}$ and $a_{end,m}$. Hence, the maximum BS volume in CLN is given by the formula:

$$max{BS}_m^{CLN}=max\sum _{d=d_{start}}^{d_{end}}{D^{\prime }}_{md}^{CLN}+N\cdot \left(C^{van}-1\right)$$

(9)

In the CMFMC supply chain, there is a need to increase the amount of BS in order to supplement the number of IRTs shipped to the assumed level of utilisation of vehicles’ loading capacity. This situation occurs in the case of BS located in CLN when there is a long-term shortage of a given production material and overnight stock volumes are insufficient. The number of additional IRTs is calculated by multiplying the N number of CMFMBs served by one CLN and the corrected $\left(C^{van}-1\right)$ level of utilisation of e-van loading capacity (measured in IRT), e.g., each last e-van in the transfer group is directed to each CMFMB.

Depending on the CLN storage policy, the volume level of the ${BS}_m^{CLN}$ can be reduced using the BSL parameter expressed by the formula:

$${BS}_m^{CLN}=BSL\cdot max{BS}_m^{CLN}$$

Reducing the volume of ${BS}_m^{CLN}$ may generate a shortage of m-type of production material, which is expressed by the formula:

(i)

in CLN

$${SD}_m^{CLN}=\max \left\{\mathsf{\chi }:\sum _{n=1}^N{S}_{{md}_{start+\mathsf{\chi }}^{CLN}}^{CMFMB\left(n\right)}=\sum _{n=1}^N{S}_{m{d}_{start+\mathsf{\chi }-1}^{CLN}}^{CMFMB\left(n\right)}=\cdots =\sum _{n=1}^N{S}_{m{d}_{start}^{CLN}}^{CMFMB\left(n\right)}=0\right\}$$

(10)

$$max{SV}_m^{CLN}=\max \left\{0,\sum _{n=1}^N{D″}_m^{CMFMB\left(n\right)}-\left(Q_m^{CLN}+B{S}_m\right)\right\}$$

(11)

where χ =$t_{delay,m}^{ILN}$.

(ii)

in CMFMB

$${\mathrm{S}\mathrm{D}}_{\mathrm{m}}^{\mathrm{C}\mathrm{M}\mathrm{F}\mathrm{M}\mathrm{B}\left(\mathrm{n}\right)}=\max \left\{\mathsf{\lambda }:{\mathrm{S}}_{{\mathrm{m}\mathrm{d}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}+\mathsf{\lambda }}^{\left(\mathrm{n}\right)}}^{\mathrm{C}\mathrm{M}\mathrm{F}\mathrm{M}\mathrm{B}\left(\mathrm{n}\right)}={\mathrm{S}}_{{\mathrm{m}\mathrm{d}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}+\mathsf{\lambda }-1}^{\left(\mathrm{n}\right)}}^{\mathrm{C}\mathrm{M}\mathrm{F}\mathrm{M}\mathrm{B}\left(\mathrm{n}\right)}=\cdots ={\mathrm{S}}_{{\mathrm{m}\mathrm{d}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}^{\left(\mathrm{n}\right)}}^{\mathrm{C}\mathrm{M}\mathrm{F}\mathrm{M}\mathrm{B}\left(\mathrm{n}\right)}=0\right\}$$

(12)

$$\mathrm{m}\mathrm{a}\mathrm{x}{\mathrm{S}\mathrm{V}}_{\mathrm{m}}^{\mathrm{C}\mathrm{M}\mathrm{F}\mathrm{M}\mathrm{B}\left(\mathrm{n}\right)}=\max \left\{0,\sum _{\mathrm{d}={\mathrm{d}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}^{\left(\mathrm{n}\right)}}^{{\mathrm{d}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}+{\mathrm{r}}_{\mathrm{n}}}^{\left(\mathrm{n}\right)}}{\mathrm{S}}_{\mathrm{m}{\mathrm{d}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}^{\left(\mathrm{n}\right)}}^{\mathrm{C}\mathrm{M}\mathrm{F}\mathrm{M}\mathrm{B}\left(\mathrm{n}\right)}-{\mathrm{Q}}_{\mathrm{m}\mathrm{d}}^{\mathrm{C}\mathrm{M}\mathrm{F}\mathrm{M}\mathrm{B}\left(\mathrm{n}\right)}\right\}$$

(13)

where λ =$t_{delay,m}^{\mathrm{C}\mathrm{M}\mathrm{F}\mathrm{M}\mathrm{B}\left(\mathrm{n}\right)}$.

The model was implemented in MATLAB. The computational complexity of the simulation algorithm is proportional to the product of the number of buildings and product types $\left(O\right(M·N\left)\right).$ The maximum execution time recorded for the scenarios presented in Section 5.2, with daily discretisation, was 1.8915 s.

5.2. A Case Study

5.2.1. Model Inputs

The CMFMC inventory management model was tested using input data determined by the expert method. The data are characteristic of commonly known transport and logistics processes, including intermodal transport, urban transport, short- and long-term storage, and city manufacturing. The authors verified this data during research on the previous version of the model, i.e., the CMFMC decision support model. Importantly, it is impossible to observe these processes in their entirety in a single location; hence, integrating data relating to the individual stages of the supply chain under study is necessary.

The authors only intended to extend the data used to test the CMFMC decision support model [15]. The changes in test data include:

(1)

The standard level of cargo capacity utilisation is 83% for e-trucks (minimum 20 of 24 IRTs) and 50% for e-vans (minimum 3 of 6 IRTs).

(2)

Every CLN within the area of its CMFMC supplies four CMFMBs.

(3)

Demand ordered by each of four CMFMBs is generated randomly for each day and each production material, and its maximum value for one material is 3 tons/day, i.e., the daily demand may be 0% to 100% of the maximum value (

Table 2. Demand for production material ordered by four CMFMBs within one CLN.

Day	1	2	3	4	5	6	7	…	365
$P_{Ad}^{CMFMB\left(1\right)}$ [%]	87%	20%	12%	83%	9%	12%	63%	…	69%
$P_{Bd}^{CMFMB\left(1\right)}$ [%]	94%	41%	33%	64%	72%	86%	86%	…	58%
$P_{Cd}^{CMFMB\left(1\right)}$ [%]	19%	46%	49%	79%	95%	32%	1%	…	56%
$P_{Ad}^{CMFMB\left(1\right)}$ [t]	2.61	0.60	0.36	2.48	0.28	0.36	1.88	…	2.07
$P_{Bd}^{CMFMB\left(1\right)}$ [t]	2.83	1.24	0.98	1.93	2.15	2.58	2.58	…	1.73
$P_{Cd}^{CMFMB\left(1\right)}$ [t]	0.56	1.38	1.47	2.37	2.85	0.95	0.03	…	1.67
$P_{Ad}^{CMFMB\left(2\right)}$ [%]	21%	31%	84%	80%	1%	24%	95%	…	75%
$P_{Bd}^{CMFMB\left(2\right)}$ [%]	22%	22%	58%	92%	96%	99%	66%	…	35%
$P_{Cd}^{CMFMB\left(2\right)}$ [%]	37%	66%	24%	71%	98%	45%	35%	…	92%
$P_{Ad}^{CMFMB\left(2\right)}$ [t]	0.62	0.92	2.52	2.40	0.03	0.72	2.85	…	2.24
$P_{Bd}^{CMFMB\left(2\right)}$ [t]	0.65	0.65	1.73	2.75	2.88	2.97	1.97	…	1.04
$P_{Cd}^{CMFMB\left(2\right)}$ [t]	1.10	1.97	0.73	2.13	2.95	1.35	1.06	…	2.77
$P_{Ad}^{CMFMB\left(3\right)}$ [%]	5%	76%	30%	30%	20%	0%	84%	…	90%
$P_{Bd}^{CMFMB\left(3\right)}$ [%]	92%	98%	24%	31%	51%	40%	41%	…	91%
$P_{Cd}^{CMFMB\left(3\right)}$ [%]	3%	29%	91%	40%	52%	34%	50%	…	34%
$P_{Ad}^{CMFMB\left(3\right)}$ [t]	0.15	2.27	0.90	0.89	0.60	0.01	2.51	…	2.71
$P_{Bd}^{CMFMB\left(3\right)}$ [t]	2.76	2.95	0.73	0.92	1.54	1.19	1.23	…	2.74
$P_{Cd}^{CMFMB\left(3\right)}$ [t]	0.10	0.88	2.74	1.21	1.57	1.02	1.51	…	1.02
$P_{Ad}^{CMFMB\left(4\right)}$ [%]	33%	23%	91%	63%	96%	87%	35%	…	43%
$P_{Bd}^{CMFMB\left(4\right)}$ [%]	11%	38%	76%	88%	11%	37%	84%	…	45%
$P_{Cd}^{CMFMB\left(4\right)}$ [%]	63%	73%	66%	44%	53%	70%	73%	…	36%
$P_{Ad}^{CMFMB\left(4\right)}$ [t]	1.00	0.68	2.72	1.88	2.89	2.60	1.04	…	1.29
$P_{Bd}^{CMFMB\left(4\right)}$ [t]	0.32	1.14	2.28	2.65	0.33	1.10	2.51	…	1.34
$P_{Cd}^{CMFMB\left(4\right)}$ [t]	1.89	2.18	1.98	1.33	1.60	2.11	2.19	…	1.09

).

(4)

Production materials are transported to ILN by different transport modes, in compliance with the principle that the largest share in the supply of production material A is provided by maritime transport, production material B by rail transport and production material C by heavy road transport (Figure 3).

(5)

The partial probabilities of transport disruptions identified for each engaged transport mode and supply chain stages are shown in Figure 4.

(6)

Parameters that determine supplier lead time:

$d_{truck}$ = 30 km, $d_{van}$ = 5 km

$v_{truck}$ = 40 km/h, $v_{van}$ = 20 km/h

$t_{cargo}^{CLN}$ = 0.20 h

$t_{cargo}^{truck}$ = 0.20 h, $t_{cargo}^{van}$ = 0.15 h

$t_{storage}$ = 0.00 h ÷ 11.00 h

$DW$ = 8.00 h (day window for e-vans transit from 10:00 to 15:00 and from 19:00 to 22:00)

$NW$ = 8.00 h (night window for e-truck transit from 22:00 to 06:00)

$L_{truck}$ = 3 roundtrips, $L_{van}$ = 6 roundtrips

5.2.2. Model Verification and Validation

Table 3. Matrix of model outputs related to overnight stocks in CLN and CMFMBs.

	BSL					MEDIAN (0% ÷ 100%)
	0%	30%	50%	70%	100%
$\max Q_A^{CLN}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	9	9	8	9	9	9
$\max Q_B^{CLN}$ [IRT]	13	12	10	15	15	13
$\max Q_C^{CLN}$ [IRT]	19	17	17	17	17	17
$\mathrm{avg}{Q}_A^{CLN}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	1.68	1.26	1.19	1.19	1.11	1.19
$\mathrm{avg}{Q}_B^{CLN}$ [IRT]	3.58	2.90	2.83	2.92	2.84	2.90
$\mathrm{avg}{Q}_C^{CLN}$ [IRT]	3.33	3.14	3.12	3.21	3.15	3.15
$\max Q_A^{CMFMB\left(1\right)}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	2.00	2.00	1.98	2.00	2.00	2.00
$\max Q_B^{CMFMB\left(1\right)}$ [IRT]	1.98	1.98	1.98	1.98	1.98	1.98
$\max Q_C^{CMFMB\left(1\right)}$ [IRT]	0.95	0.95	0.95	0.95	0.95	0.95
$\max Q_A^{CMFMB\left(2\right)}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	1.92	2.00	2.00	2.00	2.00	2.00
$\max Q_B^{CMFMB\left(2\right)}$ [IRT]	1.98	1.98	1.98	1.98	1.98	1.98
$\max Q_C^{CMFMB\left(2\right)}$ [IRT]	0.95	0.95	0.95	0.95	0.95	0.95
$\max Q_A^{CMFMB\left(3\right)}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	1.96	1.98	1.98	1.98	1.98	1.98
$\max Q_B^{CMFMB\left(3\right)}$ [IRT]	1.98	1.98	1.98	1.98	1.98	1.98
$\max Q_C^{CMFMB\left(3\right)}$ [IRT]	0.95	0.95	0.95	0.95	0.95	0.95
$\max Q_A^{CMFMB\left(4\right)}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	1.96	1.98	1.94	1.98	1.98	1.98
$\max Q_B^{CMFMB\left(4\right)}$ [IRT]	1.98	1.95	1.98	1.98	1.98	1.98
$\max Q_C^{CMFMB\left(4\right)}$ [IRT]	1.00	1.00	1.00	1.00	1.00	1.00
$\mathrm{avg}{Q}_A^{CMFMB\left(1\right)}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	0.39	0.74	0.76	0.83	0.84	0.76
$\mathrm{avg}{Q}_B^{CMFMB\left(1\right)}$ [IRT]	0.48	0.65	0.62	0.66	0.67	0.65
$\mathrm{avg}{Q}_C^{CMFMB\left(1\right)}$ [IRT]	0.45	0.48	0.48	0.49	0.49	0.48
$\mathrm{avg}{Q}_A^{CMFMB\left(2\right)}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	0.36	0.71	0.78	0.79	0.80	0.78
$\mathrm{avg}{Q}_B^{CMFMB\left(2\right)}$ [IRT]	0.49	0.65	0.66	0.65	0.67	0.65
$\mathrm{avg}{Q}_C^{CMFMB\left(2\right)}$ [IRT]	0.46	0.47	0.47	0.47	0.48	0.47
$\mathrm{avg}{Q}_A^{CMFMB\left(3\right)}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	0.33	0.69	0.73	0.75	0.76	0.73
$\mathrm{avg}{Q}_B^{CMFMB\left(3\right)}$ [IRT]	0.50	0.61	0.63	0.64	0.65	0.63
$\mathrm{avg}{Q}_C^{CMFMB\left(3\right)}$ [IRT]	0.41	0.42	0.43	0.43	0.43	0.43
$\mathrm{avg}{Q}_A^{CMFMB\left(4\right)}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	0.35	0.67	0.74	0.77	0.79	0.74
$\mathrm{avg}{Q}_B^{CMFMB\left(4\right)}$ [IRT]	0.44	0.58	0.60	0.62	0.62	0.60
$\mathrm{avg}{Q}_C^{CMFMB\left(4\right)}$ [IRT]	0.44	0.45	0.47	0.48	0.48	0.47

shows the model outputs related to overnight stock in CLN and CMFMBs for the assumed different BSL scaling from 0% to 100%. The maximum overnight stock level accumulated in the CLN range from 8 to 19 IRT, and average overnight stock levels range from 1.11 to 3.58 IRT, depending on the production material and BSL value. Significantly smaller overnight stocks are maintained in CMFMBs as their maximum volumes range from 0.95 to 2.00 IRT and average volumes range from 0.35 to 0.84 IRT, depending on the production material, CMFMB and BSL value.

Table 4. Matrix of model outputs related to production material shortages in CLN and CMFMBs.

	BSL
	0%	30%	50%	70%	100%
max${SV}_A^{CLN}$ [IRT]	162	113	79	47	0
$\max {SV}_B^{CLN}$ [IRT]	21	10	9	3	0
$\max {SV}_C^{CLN}$ [IRT]	45	26	15	5	0
${SD}_A^{CLN}$ [days]	167	38	15	4	0
${SD}_B^{CLN}$ [days]	19	11	6	1	0
${SD}_C^{CLN}$ [days]	10	10	4	1	0
$\max {SV}_A^{CMFMB\left(1\right)}\left[\mathrm{I}\mathrm{R}\mathrm{T}\right]$	46.28	29.28	20.28	10.46	0.00
$\max {SV}_B^{CMFMB\left(1\right)}$ [IRT]	5.78	3.60	2.00	0.00	0.00
$\max {SV}_C^{CMFMB\left(1\right)}$ [IRT]	12.00	8.05	4.05	0.60	0.00
$\max {SV}_A^{CMFMB\left(2\right)}$ [IRT]	29.22	22.22	18.82	8.82	0.00
$\max {SV}_B^{CMFMB\left(2\right)}$ [IRT]	8.75	4.75	3.75	0.75	0.00
$\max {SV}_C^{CMFMB\left(2\right)}$ [IRT]	12.10	6.25	3.30	0.30	0.00
$\max {SV}_A^{CMFMB\left(3\right)}$ [IRT]	36.98	23.10	15.2	9.44	0.00
$\max {SV}_B^{CMFMB\left(3\right)}$ [IRT]	6.57	4.13	3.90	1.90	0.00
$\max {SV}_C^{CMFMB\left(3\right)}$ [IRT]	11.40	7.40	4.40	1.40	0.00
$\max {SV}_A^{CMFMB\left(4\right)}$ [IRT]	47.98	35.58	22.58	16.58	0.00
$\max {SV}_B^{CMFMB\left(4\right)}$ [IRT]	6.43	3.45	0.45	0.00	0.00
$\max {SV}_C^{CMFMB\left(4\right)}$ [IRT]	12.70	8.70	4.70	0.85	0.00
${SD}_A^{CMFMB\left(1\right)}$ [days]	175	38	15	3	0
${SD}_B^{CMFMB\left(1\right)}$ [days]	40	9	7	0	0
${SD}_C^{CMFMB\left(1\right)}$ [days]	17	9	4	1	0
${SD}_A^{CMFMB\left(2\right)}$ [days]	164	36	13	4	0
${SD}_B^{CMFMB\left(2\right)}$ [days]	46	12	8	1	0
${SD}_C^{CMFMB\left(2\right)}$ [days]	14	6	2	1	0
${SD}_A^{CMFMB\left(3\right)}$ [days]	181	37	11	4	0
${SD}_B^{CMFMB\left(3\right)}$ [days]	46	12	6	1	0
${SD}_C^{CMFMB\left(3\right)}$ [days]	15	7	2	1	0
${SD}_A^{CMFMB\left(4\right)}$ [days]	177	36	14	4	0
${SD}_B^{CMFMB\left(4\right)}$ [days]	48	15	2	0	0
${SD}_C^{CMFMB\left(4\right)}$ [days]	19	7	3	1	0

presents model outputs related to production material shortages in CLN and CMFMBs for the assumed different BSL scaling from 0% to 100%. The tabular breakdown includes: cumulative time of shortage of deliveries to CLN ${SD}_m^{CLN}$ and to individual CMFMB ${SD}_m^{CMFMB\left(n\right)}$, the maximum shortage volume in CLN max${SV}_m^{CLN}$, and in each CMFMB max${SV}_A^{CMFMB\left(n\right)}$. Based on the shortage volumes in CLN, BS values corresponding to different BSL were calculated in accordance with Formula (9) and are presented in

Table 5. Volumes of BS in CLN.

	BSL
	0%	30%	50%	70%	100%
${BS}_A^{CLN}$ [IRT]	0	51	85	119	170
${BS}_B^{CLN}$ [IRT]	0	9	15	21	29
${BS}_C^{CLN}$ [IRT]	0	16	27	38	53

, as well as shown in Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10.

Moreover, supplier lead time is calculated for any IRT transported from the ILN to CMFMBs, as follows:

$$\begin{array}{ll}{\mathrm{T}}_{\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{d}}={\displaystyle \frac{d_{truck}}{v_{truck}}}+{\displaystyle \frac{d_{van}}{v_{van}}}& +{2\cdot \mathrm{t}}_{\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{o}}^{\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{c}\mathrm{k}}+{2\cdot \mathrm{t}}_{\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{o}}^{van}+{\mathrm{t}}_{\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{o}}^{CLN}+t_{delay}+t_{storage}\\ & ={\displaystyle \frac{30}{40}}+{\displaystyle \frac{5}{20}}+0.40+0.30+0.20+t_{delay}+t_{storage}=1.90\mathrm{h}+t_{delay}+t_{storage}\end{array}$$

The minimum delivery time of production materials from ILN to CMFMBs is 1.90 h. To this time, you should add the delay time$t_{delay}$, which includes the delay time due to disruptions in intermodal transport prior to delivery to the ILN and the storage time required to wait for e-vans. The maximum delay time is 15 days and occurs when BS is not maintained (see production material A shortage period between day 136 and day 150 in Figure 6). The storage time depends on the time difference between e-truck arrival at the CLN and e-van departure from the CLN, which may range from 0.00 h up to 11.00 h.

The obtained results of the analysis based on the CMFMC inventory management model allowed the following conclusions (Table 4 and Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10):

(1)

Transport disruptions cause the cumulative time of the shortage of deliveries ${SD}_m^{CLN}$ to CLN from 166 days per year for material A, 19 days per year for material B and 10 days per year for material B. Differences result from different probabilities of disruptions and their negative effects assigned to other transport modes involved in intermodal transport. Thus, in maritime transport, which carries out the main part of the carriage of production material A, events that trigger delivery delays to ILN for up to 7 days are assigned. In the case of long-distance rail and heavy road transport, which are responsible for transporting production materials B and C, the maximum delivery delay to ILN can be 1 day.

(2)

Disruptions in intermodal transportation result in the inability to deliver materials ordered for production according to the ‘next-day delivery’ rule. The shortage of production materials in CLN accumulates with increasing delay time. The largest deficit max${SV}_m^{CLN}$is observed in the case of production material A, where the most significant volume of missing material was 165 IRT, corresponding to a mass of 82.5 tons. For production materials B and C, the maximum volumes of shortage are much lower, i.e., 23 IRT (9.2 tons) and 48 IRT (9.6 tons), respectively.

(3)

Shortages in deliveries to CLN translate into shortages in deliveries to individual production enterprises in CMFMBs. Considering the dynamically changing orders, different for each CMFMB, the maximum shortages max${SV}_A^{CMFMB\left(n\right)}$ and the cumulative time of production materials shortage ${SD}_m^{CMFMB\left(n\right)}$in each CMFMB, there are differences. For the four CMFMBs operated by one CLN, the longest waiting time and shortage volume were for production material A, namely CMFMB(1) had to wait 160 days for this material, and CMFMB(4) had a material A shortage as much as 47.4 IRT (23.7 tons). The distribution of production material shortages between individual buildings is uneven and, on average, annually ranges from 19% to 30% for one CMFMB concerning the entire volume of production material needed in a given cluster.

(4)

There is no clear correlation between volumes of overnight stock maintained in CLN or CMFMBs and BSL variants. A significant correlation has been identified between maximum and average overnight stock values in CMFMBs and CLN concerning different types of production materials. This results from the adopted priority rule in loading production materials into e-vans while maintaining their minimum 83% capacity utilisation level. Surplus IRTs are selected so that IRTs with material A are sent from CLN to CMFMBs first, followed by B and then C. Hence, in CLN, the maximum and average O overnight stocks are smallest for production material A and largest for production material C, as shown by the median $med\left(max{Q}_m^{CLN)}\right)$ i $med\left(avg{Q}_m^{CLN)}\right)$. The opposite relationship occurs in CMFMBs, where surplus materials are stored upon arrival from CLN. The overnight stocks are largest for production material A and smallest for material C, as shown by the medians $med\left(max{Q}_m^{CMFMB\left(n\right)}\right)$ i $med\left(avg{Q}_m^{CMFMB\left(n\right)}\right)$.

(5)

Maintaining BS in the CLN allows for the complete or partial elimination of delays resulting from disruptions in intermodal transport. To eliminate delays, it is necessary to maintain BS at a constant volume level equal to 100% of the most significant deficiency recorded (BSL = 100%, Figure 9), i.e., 165 IRT of product ion material A, 23 IRT of production material B and 48 IRT of production material C. In the case of lower BSL levels, a smaller volume and shorter duration material shortage is formed. Each time, the highest and longest shortage applies to production material A. For example, for this material and BSL increasing from 30% up to 70%, the maximum shortage decreases from 113 IRT to 49 IRT, with the cumulative shortage duration per year decreasing from 40 days to 4 days, respectively. Different BSL and related levels of material shortages in CLN translate into adequate shortages in deliveries to individual production enterprises in CMFMBs.

(6)

Figure 7, Figure 8, Figure 9 and Figure 10 show characteristic variable BS values for different BSL variants. Significant decreases in the number of IRTs maintained in BS are related directly to disruptions in the supply chain, and relatively small fluctuations of 1–2 IRTs are caused by the need to preserve e-vans’ minimum capacity utilisation level. The latter quantitative changes occur when there is a shortage of the appropriate production materials stored as OS. Due to the adopted rule of surplus IRTs priorities in the e-vans loading process, the greatest BS fluctuations concern material A, followed by B, and to the least extent material C.

(7)

It should be remembered that the costs related to BS, i.e., the operating costs of storage space, are appropriate for the number of IRTs stored. For different BSL scenarios, the necessary space must correspond to the sum of ${BS}_A^{CLN}$+${BS}_B^{CLN}+{BS}_c^{CLN}$, and amount to 76 IRT (BSL = 70%) or 127 IRT (BSL = 50%) or 178 IRT (BSL = 70%) or 252 IRT (BSL = 100%).

The divergence intervals between the upper and lower trajectories correspond to the periods in which the difference between the fully available and limited availability (BSL < 100%) resource flows increases, reflecting the system’s deviation from its optimal state. These differences can also be observed indirectly from the trends presented in Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10.

6. Discussion

Based on analyses performed using the CMFMC inventory management model, the previously asked research questions can be answered as follows.

(1)

Ad RQ1. Disruptions that occur during intermodal transport preceding intra-urban transfers, i.e., maritime/rail/heavy road transport supplies to ILN, heavily affect the delivery delays to CMFMBs. Considering that the production materials orders differ for each CMFMB, the maximum shortage per building is almost 50 IRT per type of production material. The longest waiting time for missing production material can be as long as 15 days, and the cumulative time of production material shortages in one year can reach 160 days.

(2)

Ad RQ2. The model proved the effectiveness of localisation of BS in each CLN of CMFMCs. In addition, it is about halfway between the ILN and the final consignees in CMFMBs. An alternative to CLN is the ILN and CMFMBs locations. The following arguments speak for the location of BS in CLN instead of these two alternative places. Firstly, the CMFMB infrastructure is very limited, and storage in this location is a last resort due to the principle of holding only overnight stock. Secondly, ILN is the largest of the logistics centres under consideration and serves almost all intermodal supply chains focused on customers within the agglomeration. Any disruptive event in ILN will delay delivery to all clients in all CMFMBs. A rational solution is accumulating production material stocks in ILN, but in a form not yet unitised in IRT. Storing larger cargo units (containers, replacement bodies, big bags) will allow for a reduction in demand for storage area and a more efficient operational link between the intermodal supply chain and intra-agglomerate transport.

(3)

Ad RQ3. To determine the volume of BS, you need to calculate expected supply chain shortages based on past data. The key input data required for calculations are partial probabilities of disturbances characteristic of the engaged mode of transport, including transhipment hubs. These model inputs should be based on statistical data on the reliability of widely understood global supply chains. The presented inventory management model allows calculating the BS volume in option BSL = 100%, eliminating interruptions in deliveries and in any options (0% < BSL < 100%), reducing the BS volume and the delivery delay time.

The presented model is aimed at standardising and planning BS to ensure the consistent performance of CMFMC enterprises under intermodal supply chain uncertainty. The model allows for determining the size of BS for each type of production material based on an accepted stochastic approach, considering previous disruptions in intermodal supply chains [44,45,55]. Even during supply chain disruptions, the BS and overnight stock enable just-in-time and capacity-efficient deliveries to CMFMC enterprises. Hence, the model addresses the stochastic behaviour of intermodal disruptions and their impact on city inventory systems, filling an identified gap in the literature.

Theoretical implications are related to the advancement of the SSCR framework through its integration with stochastic and data-driven modelling principles. The application of the MLBNM extends existing resilience theories—particularly the SBV and ABV [38,39,56]—by introducing a probabilistic mechanism that models interdependencies and uncertainty propagation across intermodal supply chains. This integration bridges conceptual resilience theory with quantitative inventory management, enabling resilience to be understood as a qualitative capability and a measurable system property within CMFMCs. Thus, this study reinforces the theoretical foundation of SSCR and establishes a basis for future research on resilient, data-driven, and smart sustainable CMFMCs [44,52,53,54,55].

Practical implications for CMFMC enterprises involve developing a common inventory management strategy in the supply chain. That is necessary to optimise the costs of maintaining BS and overnight stock. The key decision is to adopt an acceptable BSL for BS maintained in CLN within a single cluster. Adopting a rational BSL value of less than 100% means accepting short-term interruptions in deliveries, which translates into a few days’ wait for the finished product to be delivered to the end customer, e.g., with BSL = 70%, this waiting time does not exceed 4 days.

Importantly for CMFMC enterprises, regardless of the implemented BSL, the maximum volumes of shortages in CLN and CMFMBs apply to production material A imported by sea transport, which is associated with the risk of the most prolonged disruptions in the supply chain (Figure 5). Hence, there is an indication that alternative locations should be secured to source production materials so that supply chains can be redirected in the event of significant disruptions. Diversifying the sources from which production materials are purchased and transported allows for a change in means of transport and transport routes and reduces the risk of long-term supply disruptions.

CMFMB supply chains should be managed by logistics service providers with the support of effective IT systems using PSSC, IoT, blockchain, and AI [15,51,79]. BS levels should be updated routinely in conditions of variability of intermodal supply chains and relatively short disruptions. Any change in the priorities of CMFMC activities in the procurement of materials and uninterrupted supplies should enable a quick change in previously set BS parameters.

The preferences of CMFMC enterprises for specific trademarks of purchased materials should be automatically recorded by PSSC, indicating their degree of importance based on an analysis of order points and frequency. Materials with a short shelf life and high storage cost require a special buffering approach [76]. When forming BSs in CLNs, delivery time, demand variability, shelf life, strategic importance, and financial capabilities should also be considered. SMEs from CMFMC with limited working capital can set BS based on financial capabilities to avoid unnecessary expenses [15,76].

Continuous real-time monitoring of supply chains and BS levels for CMFMCs using I4.0 technologies, primarily IoT, blockchain, and PSSC, as well as the data collection and analysis on logistics processes and operations through a cloud computing network and AI, enable the rapid provision of input data for the proposed model, transparency of ongoing processes, predictive analytics and disruption forecasting, and inventory management [15,28,38]. The combination of the proposed inventory management model for CMFMCs, I4.0 technologies, and PSSC capabilities allows for the timely activation of disruption mitigation mechanisms, adjustment of BSs, including reduction in liquidity or material surpluses, and improvement of the level of service for all stakeholders [15,39].

7. Conclusions

The transport system analysed is characteristic of large cities and agglomerations, where production for the needs of city residents and entities is organised using additive technologies. Production is organised based on cluster networks and multifloor city buildings with appropriate infrastructure, i.e., CMFMC. The subject of the analysis is the CMFMC supply system using intermodal transport, in continental and sea–land relations, including global chains. The challenge is the disruptions in these supply chains, the frequency and intensity of which have recently increased significantly. The inventory management model tailored to the characteristics of the cargo flows handled by CMFMC has been proposed, which allows for the diagnosis of disruptions in deliveries and the implementation of effective measures to ensure continuity and stability of production. The tool guaranteeing the reliability of deliveries is the inventory system, including so-called buffer stocks and overnight stocks, which should be created and maintained in appropriate quantities at key nodes along the delivery route in the agglomeration area. Inventory management includes the selection of the location and size of buffer stocks and the organisation of transport using zero-emission vehicles, i.e., e-trucks and e-vans.

Theoretically, the study advances the SSCR framework by operationalising its principles through a stochastic modelling approach [19,29,39]. The application of MLBNM introduces a probabilistic interpretation of resilience, allowing the identification and quantification of causal dependencies between intermodal nodes (ILN–CLN–CMFMB) and their effects on inventory dynamics [52,53,54,55]. This links conceptual resilience theory [38,44] and practical inventory management in city manufacturing contexts [14,48].

The practical contribution of this research lies in offering a quantitative tool for decision-makers to evaluate disruption risks, define acceptable buffer stock levels, and improve inventory reliability under uncertainty. The model supports sustainable urban logistics by promoting reduced transport emissions, resource-efficient stock management, and adaptive planning of urban supply chains within smart city frameworks [7,15,23,71].

The limitations of the proposed CMFMC inventory management model are related to the assumptions made in Section 4. The model allows for analysis in intermodal transport preceding delivery to the ILN without considering disruptions in urban transport using e-trucks and e-vans and possible delays during handling and storage at hubs, including ILN, CLN and CMFMB. In addition, the model analyses only one BS location in CLN, without considering alternative locations in ILN and CMFMBs. Greater flexibility of internal connections with CLN1-CLN2 and CMFMB(n)-CMFMB(n + 1) transfer options is also not considered. Furthermore, no alternative transport modes to road-only transport were considered within the agglomeration area, i.e., urban rail, waterways, cable, or underground transport systems. However, these limitations do not reduce the value of the proposed model.

The further development of this research will focus on expanding the model’s functionality and scope. Future work will include integrating multiple BS locations (ILNs, CLNs, and CMFMBs), considering multimodal intra-urban transport systems, and adding economic and environmental performance indicators [18,58,76]. Furthermore, extending the model to include reverse logistics, waste recovery, and circular economy processes will enhance its applicability to green manufacturing ecosystems [32,33,71,72]. These developments will strengthen both the theoretical relevance and the practical usability of the model in supporting sustainable and resilient city manufacturing.