Optimizing Coffee Logistics via Physical Internet and Multi-Agent PILAR Framework

1. Introduction

The Physical Internet (PI) is a transformative logistics model aimed at improving efficiency, sustainability, and connectivity in transportation networks. It integrates multimodal, intermodal, and co-modal transport systems. Multimodal transport involves at least two transportation modes using various units like containers or vehicles [1], while intermodal transport ensures goods remain in a single unit across modes, reducing handling and delays. Co-modal transport enhances resource efficiency by promoting collaboration among shippers [2]. Synchromodal transport advances these concepts with real-time adaptability via digital technologies. Defined as the flexible, coordinated use of transport modes enabled by data sharing, synchromodality includes key principles such as real-time switching, integrated planning, horizontal collaboration, and mode-free booking [3, 4]. Despite innovations, logistics systems face disruptions, such as unforeseen events that hinder supply chains [5]. These include facility-related and transportation disruptions. Robustness refers to a system’s ability to maintain function during minor issues, while resilience is its capacity to recover from major disruptions like strikes or infrastructure failures [6].

PI is structured around three core elements: π-containers, π-movers, and π-nodes [7]. π-containers are modular, trackable transport units with embedded smart technologies, mirroring data packets in the Digital Internet. They are moved by π-movers; vehicles, carriers, or conveyors, within and between π-nodes. π-hubs, a type of π-node, are essential for routing and optimizing freight flow. Developing this infrastructure is central to scaling PI. Ultimately, PI seeks to establish a modular, standardized logistics network that enhances interoperability, optimizes resource use, and reduces the environmental impact. However, existing literature on the Physical Internet has largely focused on generic freight or industrial goods, with limited attention to agri-food commodities such as coffee, where fragmented production networks, perishability constraints, and reverse logistics of by-products create unique coordination challenges. This research addresses this gap by positioning the coffee supply chain as a critical use case for demonstrating how PI principles can enhance traceability, resource efficiency, and circular recovery.

1.2 Systemic challenges in the coffee supply chain and the role of PI

The global coffee supply chain, from cultivation to retail, faces significant inefficiencies that impact sustainability, cost, and responsiveness. At the farm level, smallholder farmers (responsible for 60% of global production) often lack access to real-time market data and climate-resilient practices, limiting informed decision-making and exacerbating inefficiencies [20]. Fragmented operations hinder yield aggregation, resulting in underutilized transport and higher costs [21]. PI-based digital platforms can address these issues by enabling data sharing and collaborative logistics planning, integrating farmers into a transparent, connected network. In the processing and export stages, manual, paper-based documentation delays customs clearance by 48–72 hours, increasing holding costs [22]. Inconsistent bean quality sorting causes up to 12% processing waste [23]. Implementing digital documentation, AI-driven sorting, and blockchain-backed smart contracts under the PI framework can streamline operations, enhance traceability, and reduce waste and delays.

Transportation inefficiencies further strain the system, with nearly 40% of maritime containers returning empty, adding to fuel consumption and emissions [24]. Static routing fails to account for variables like port congestion and fuel prices. PI’s dynamic routing algorithms and real-time forecasting can optimize container repositioning and route planning, reducing costs and environmental impact.

At the warehousing and retail stage, inventory mismatches and traceability gaps lead to ∼$740 million in annual holding costs, while only 34% of retailers offer sourcing transparency [25]. PI-enabled digital twins and AI inventory systems can improve visibility, reduce overstocking, and support traceability from farm to shelf, enhancing consumer trust and ethical sourcing compliance.

Figure 1 illustrates a PI-modeled coffee logistics flow, where beans move through modular layers (e.g., depots, warehouses, packaging centers) encapsulated in standardized units like π-containers. Each stage applies labeling, routing, and modular handling, reflecting PI principles of modularity, interoperability, and synchronization. Movement between nodes (by road or sea) reflects intermodal transfers governed by PI routing logic based on efficiency and availability, analogous to Internet packet routing. Like digital networks, this system ensures shared infrastructure, real-time visibility, and efficient, scalable distribution.

2. Optimizing recovery and reuse of spent coffee grounds (SCGs) with Physical Internet (PI)

Spent coffee grounds (SCGs) hold significant potential for reuse in biofuel, fertilizers, and bioplastics, yet their recovery is hindered by challenges in collection, transportation, and processing. Applying PI principles offers a structured, data-driven approach to streamline SCGs recovery through automation, interconnectivity, and sustainable logistics.

A key barrier is the fragmented nature of SCG generation, originating from cafés, restaurants, and homes, which makes collection inefficient and costly. Traditional methods lead to inefficient routing, raising operational costs by ∼20% [26], compounded by poor coordination and lack of data visibility, resulting in inconsistent pickups and processing delays.

A PI-enabled solution uses IoT-based smart bins that monitor SCG levels and transmit real-time data to a decentralized network. This enables automated pickup scheduling, reducing idle time by 30% [27]. AI-driven dynamic routing further optimizes logistics by factoring in bin fill levels, traffic, and plant capacity [28]. Establishing decentralized PI processing hubs near urban areas cuts transport distances by 36.8% and reduces emissions [29].

Using standardized π-containers ensures compatibility across multimodal logistics, while autonomous electric π-movers reduce energy use by 23% [30]. Blockchain-based tracking adds transparency and traceability, while smart contracts automate verification, reducing administrative overhead by 65% [31, 32].

The quantitative impact of these PI methodologies is significant, with AI-driven logistics reducing transportation costs by 30% due to optimized route planning [33]. Enhanced collection mechanisms have been shown to increase SCG recovery rates by 50%, aligning with circular economy principles, while transitioning to PI-enabled intermodal logistics results in a 30% decrease in CO₂ emissions, contributing to global sustainability goals [34]. Given that SCGs contain approximately 5000 kcal/kg of energy, their efficient recovery provides up to 1.5 million MWh of renewable energy (20.92 MJ/kg) annually, further validating the economic and environmental viability of SCG repurposing [35]. Table 1 presents a comparative analysis of the baseline performance and the enhanced outcomes achieved through the integration of predictive intelligence, focusing on cost reductions, environmental benefits, and recovery efficiency using PI models.

The application of PI frameworks in SCG logistics adopts a more sustainable and efficient circular economy. Advanced decision-support systems and real-time predictive analytics can further enhance SCG utilization across global supply chains, ensuring a scalable and impactful transition toward an optimized circular economy for coffee waste management.

3. Technical and functional requirements for PI implementation in the PRISMA context

The implementation of the PI within the PRISMA framework requires integrating real-time analytics with a decentralized logistics architecture. Core components include IoT sensors for SCG tracking, GPS-enabled PI mover monitoring, and AI-driven dynamic routing using techniques like Q-learning and MILP. A unified integration layer enables seamless data exchange across nodes via standardized APIs (e.g., REST/JSON) and secured protocols (TLS/SSL over MQTT).

Figure 2 illustrates a layered architecture aligned with the OSI/TCP-IP model that decomposes logistics into protocol layers. The Application Layer encodes logistics intents, such as shipment scheduling and SCG prioritization, into structured payloads (e.g., JSON/EDI over RESTful APIs). The Network Layer manages intermodal routing and adaptive path optimization using decentralized algorithms. The Data Link Layer addresses π-container communication, MAC-level coordination, and local connectivity via protocols like IEEE 802.15.4 and LoRaWAN. The Physical Layer actuates cyber-physical π-movers using sensor feedback for low-latency control.

Standardized π-movers support multimodal transport and are calibrated with Bayesian updating and Kalman filters to manage demand uncertainty. Stochastic optimization methods and edge computing ensure real-time responsiveness, disruption handling, and deterministic decision-making. API-based integration enables secure interoperability with external systems, reinforced by encryption and access controls. Interconnectivity across stakeholders is established through API-driven data exchange protocols, allowing uninterrupted and secure integration with third-party waste management and energy recovery infrastructures. This architecture ensures scalability, adaptability, and resilience as PI evolves under the PRISMA framework.

4. Framework overview for the PRISMA platform

In this study, a simulation environment is created using an agent-based modeling (ABM) approach in AnyLogic V 8.9.3 to evaluate the OmniLink Nexus PILAR Model’s ability to optimize multimodal coffee supply chains. OmniLink Nexus PILAR (Physical Integration, Intermodal Transport, Logic & Control, Adaptive Service, Responsive Interface) is a hierarchical framework designed to optimize the CSC by integrating digital-physical logistics via a 5-layer Physical Internet (PI) architecture as shown in Figure 3. This virtual setup isolates the Physical Internet’s dynamics from real-world constraints, allowing experimentation with autonomous logistics nodes that mimic the behavior of standardized PI-containers, PI-nodes, and PI-movers within the coffee supply chain. Within this digital “sandbox,” two core elements are modeled. First, the physical logistics networks are represented through PI-nodes (acting as warehouses, terminals, and other facilities) and PI-movers (such as trucks, trains, and barges) that transport PI-containers (coffee containers) across various transport modes. Second, a network of π-clients (digital agents) governs decision-making. These π-clients exchange real-time information, plan routes based on input constraints like time windows and container specifications, and coordinate the flow of goods through different nodes. By setting up initial conditions with actual operational data, the simulation allows us to assess both operating scenarios, where information sharing is limited and fully integrated systems with complete transparency across the network. The flow of coffee containers through the network is determined by these agents’ configurations, decision rules, and the data exchanged among them. Designed to be data-driven, the simulation initializes with pre-defined input parameters, such as geographic locations, transport orders, and mover schedules, which enables us to model various scenarios ranging from conventional practices to a fully integrated, real-time information-sharing environment.

The Physical Internet (PI) operates through a layered architecture known as the PILAR framework, which ensures seamless integration of physical, digital, and operational components. Table 2 below summarizes the five core layers and their respective functions:

5. Operational framework of an agent-based logistics model in AnyLogic

The block diagram in Figure 4 illustrates a closed-loop supply system, showing the hierarchical flow of coffee products from suppliers and processors to textile plants and customers, and then back through repair, disassembly, cleaning, and remanufacturing centers. It includes reverse logistics for SCGs collected from cafés, hotels, and households to test centers and recycling stations, reflecting real-world recovery flows. The diagram conceptualizes the conversion of post-consumption waste into raw materials, supported by interconnected demand/supply planning modules. It complements the simulation by visually linking reverse logistics nodes with the forward chain, enabling a digitally traceable and physically interoperable circular network.

The model presented in Figure 5 captures the digital twin of a decentralized logistics network mapped onto a GIS-based spatial layer, reflecting real-world infrastructure in the Campania region of Italy, with Naples, Casoria, Afragola, and Torre del Greco as the key logistics nodes. At the core of this simulation is the kanban_logic agent, which encapsulates the behavior and operational control of batch-based inventory movement through PI-containers. This agent is configured to match the logic of decentralized pull-based systems, mimicking PI-containerized flow control using kanban triggers. Each kanban_logic agent is responsible for dispatching, receiving, and matching inventory across distributed nodes based on demand signals, availability, and predefined buffer policies, closely reflecting PI philosophies of modularity, standardization, and self-synchronization.

The GIS environment within the main agent functions as a 3D digital canvas representing a network of geographically anchored PI-nodes (e.g., micro-hubs, warehouses). These nodes are linked via transport arcs, forming a graph-based logistics topology that summaries real-world corridors into digital routing paths. Each PI-node is governed by π-clients, autonomous agents handling localized decision-making, including constraints like batch sizes, inventory limits, lead-time buffers, and service level targets.

Material flow is structured through input/output ports and matched via inventory logic, with connectors (e.g., batchOut → match_inventory) reflecting internal routing triggers. Inventory movement relies on real-time, decentralized decision-making instead of centralized scheduling. Behavior scripts written in Java manage inventory checks, batching, delay mitigation, and service level compliance, allowing adaptive responses to disruptions.

The Order agent, as depicted in Figure 6, simulates π-client transport requests using attributes like product type, arrival time, and quantity, triggering event-based container flows aligned with kanban-controlled logistics. Each order initiates a virtual transport demand, matching autonomous customer nodes within a decentralized network, where π-clients function as decision entities initiating pull signals based on localized consumption or production events. This agent ensures system responsiveness by enabling event-driven generation of PI-container tasks, directly aligned with the PI paradigm of on-demand flow orchestration.

The Producer agent models batch-based production hubs, controlled by a kanban_logic sub-agent that synchronizes material release with demand signals. Processing stages simulate setup, transformation, and dispatch operations. Routing is governed via TMS and TME modules.

The visual logic includes the following:

• Processing_station_1 handles discrete-time production operations, influenced by proc_time_p1 and setup_time_p1 parameters, simulating realistic production lead times.

• Kanban Lot Size (kanban_lotsize_p1) enforces pull-based release thresholds, ensuring no overproduction beyond active downstream demand.

• Packing, seize, unpacking, and release stages simulate transformation, packaging, and final dispatch of materials toward wholesaler or customer nodes, forming a modular PI-container lifecycle.

• TMS (Transport Management System) and TME (Transport Management Entity) blocks serve to model routing and execution logic for dispatch events.

Figure 7 illustrates system output analytics:

• The time-series graph showing demand-driven task fluctuations.

• The bar chart quantifying wrapped batches to evaluate throughput.

Results validate the kanban agent’s role in stabilizing production, avoiding oversupply, and aligning output with actual consumption, effectively demonstrating distributed just-in-time logistics.

Table 3 presents an analysis of how varying the kanbanLotSize affects system performance. By adjusting kanban_lotsize_p1 within the Producer agent, the experiment measured impacts on average inventory, average wait time, and order fulfillment rate. Results indicate that smaller lot sizes (5 units) cause higher inventory levels and longer wait times due to frequent batching and low-capacity utilization. As lot size increases, inventory and delays decrease, while fulfillment rates improve from 92 to 98%, reflecting more efficient pull-based control. The experiment used batch-controlled logic and tracked KPIs via time-series probes and performance counters, confirming that kanban tuning enhances flow responsiveness and system stability.

The Retailer agent, shown in Figure 8, models a last-mile PI-node that handles the receipt, buffering, and final delivery of PI-containers for customer orders. Its operations are governed by an embedded kanban_logic agent, which manages material flow using pull-based triggers aligned with fulfillment cycles.

• source1 is the receiving port for incoming containers.

• sink1 and exitWS simulate dispatch or local unpacking.

• The enterWS to kanban_logic connection enforces a material authorization policy, allowing entry only when demand is confirmed, preventing overstock.

The Retailer functions as a passive but responsive node, driven by kanban signals to enable efficient, demand-aligned container retrieval and delivery.

Table 4 demonstrates that the kanbanLotSize parameter significantly affects both the average dispatch interval and overproduction rate. Smaller lot sizes lead to tighter demand alignment, reducing overproduction and dispatch intervals but may increase operational overhead. In contrast, larger lot sizes enhance throughput but risk exceeding inventory thresholds. Optimizing kanbanLotSize is essential to balance system responsiveness, efficiency, and ensure high service level compliance.

The simulation models’ mobile agents to represent π movers. TruckPR agents handle container transport between producers and retailers, triggered by kanban-based dispatch events. Meanwhile, TruckWS agents move containers between wholesalers and other PI-nodes using dynamic, client-bound task allocation based on real-time system state.

The Wholesaler agent, shown in Figure 7, simulates a midstream PI-node that buffers, processes, and redirects containers between producers and retailers. Governed by kanban_logic, it enforces batch-level flow control, ensuring dispatch only upon validated demand. Containers arriving via TruckWS go through a structured sequence (seize → unpack → pack → release), with resource gating to model handling delays. This models regional consolidation behavior, maintaining flow stability while synchronizing with network-wide kanban signals.

Table 5 presents task-level resource utilization metrics essential to flow efficiency. The RecyclingUnit shows high usage (80%) with a queue peak of 4, indicating near-saturation and queuing delays. The Wholesaler’s unpacking stage operates at 65%, reflecting moderate load and smoother flow, while the Producer’s packing station at 72% suggests stable throughput. These values demonstrate how resourceTaskStart/resourceTaskEnd blocks model processing delays and control flow. High utilization signals congestion risk, whereas balanced usage supports continuous agent movement, validating the model’s focus on agent-based flow control and capacity-aware scheduling.

Figure 9 presents the configuration and results of a genetic algorithm-based optimization experiment aimed at maximizing the utilization of PI-movers within the Physical Internet-enabled supply chain. The model targets the producer-side TruckPR utilization as the objective function, seeking an optimal balance in vehicle deployment under constrained resources. The optimizer was executed over 500 fixed iterations with a memory cap of 512 MB, exploring integer-valued truck allocations within a defined range of 1–5 for both TruckPR (producer-to-retailer movers) and TruckWS (wholesaler-linked movers). The genetic algorithm was configured with a population size of 30, crossover probability of 0.8, mutation rate of 0.05, and elitism of two individuals per generation.

At the point captured, the current evaluated configuration utilizes 2 TruckPR units and 1 TruckWS, while the best-performing solution discovered assigns only 1 truck to each category, demonstrating that a minimal configuration can yield the highest efficiency under existing network dynamics. The plotted fitness trajectories visualize the algorithm’s exploration path, with the red curve representing convergence toward the best solution and the blue indicating ongoing parameter evaluation. This output confirms the system’s ability to identify lean and effective truck deployment strategies that uphold utilization goals while adhering to PI principles of resource efficiency and dynamic scalability.

The genetic algorithm optimized truck allocation by maximizing the truckPR.utilization() fitness function under constrained resources. As shown in Table 6 early iterations with more trucks (e.g., 3 TruckPR) led to lower utilization and suboptimal fitness due to underuse. In contrast, lean configurations (1 TruckPR, 1 TruckWS) achieved higher efficiency and the best fitness score (0.97), confirming that fewer, well-utilized trucks perform better. This supports the model’s methodology, where decentralized kanban control and agent-based mobility prioritize resource efficiency.

Figure 10 illustrates the reverse logistics layer of the coffee supply chain, where waste collection points act as distributed PI-nodes capturing spent coffee grounds from cafés, households, and retail stores. Trucks, modeled as mobile PI-movers, transport the collected waste to a centralized recycling unit, also a PI-node, for processing and reintegration into upstream flows. The setup includes six waste nodes, one recycling facility, and five trucks operating under road-based routing logic. The GIS layer supports distance-sensitive modeling (e.g., fuel use, delays) while maintaining agent-based routing. This reverse flow demonstrates a closed-loop system, aligning with the circular economy principles and highlighting the proposed framework’s adaptability to both forward and reverse logistics.

Figure 11 depicts the internal architecture and performance analysis of the RecyclingUnit agent, a PI-node responsible for receiving, processing, and dispatching spent coffee grounds collected via mobile PI-movers. Operating under capacity constraints, the simulation enforces a truck utilization limit of ≤85%, optimized through a parameter sweep varying numberTrucks from 1 to 5. The system uses truck.utilization() as the objective metric, dynamically adjusting fleet size for balanced efficiency, reflecting decentralized kanban-based flow control triggered by waste accumulation at autonomous collection nodes.

Within the RecyclingUnit, trucks follow a sequenced task flow: enter → packing → seize → travel → unpack → release, governed by resourceTaskStart/resourceTaskEnd blocks and stochastic service times.

Output metrics validate system behavior:

• Top-left graph: High packing resource usage indicates tight alignment with truck arrivals.

• Middle-left bar graph: Queue peaks at 1 container, confirming minimal congestion.

• Top-right sinusoidal graph: Cyclic delay to reach collection points (∼50 time units), reflecting routing/distance variability.

• Bottom-right histogram: Unpacking times mostly between 0.2–0.8 units, indicating stochastic task variability.

These results confirm the RecyclingUnit’s accurate simulation of PI-container handling, resource constraints, and agent-based logistics coordination, while maintaining efficient operations under a bounded truck utilization threshold.

Table 7 highlights time-based variances across agents, essential for analyzing synchronization bottlenecks. The Producer’s high average time (4.8 units) reflects the longest processing delays, impacting downstream responsiveness. Retailer and Truck travel times, with the higher standard deviations (0.6 and 0.5), indicate variability in delivery and routing, which may propagate delays across the network. In contrast, the RecyclingUnit shows tight timing control, suggesting efficient resource handling. These differences help identify timing mismatches in the decentralized system that affect overall flow stability.

The RecyclingUnit agent is connected to client-assigned PI-movers, where each truck carries a dynamic client parameter linking it to a specific wasteCollectionLocation. This enables decentralized routing, with pickups triggered by local demand signals rather than central dispatching, supporting bottom-up decision-making and adaptive logistics coordination. Figure 12 illustrates the finite-state logic of wasteCollectionLocation agents, transitioning between normalWork and waitingDetails states via a statechart. When the waste buffer exceeds a threshold, the node shifts to waitingDetails, initiating a pickup request. Once the truck arrives and completes the task, the node returns to normalWork, forming a closed-loop feedback system between node status and PI-mover allocation.

Table 8 demonstrates decentralized control via message-driven coordination. High order trigger messages between π-clients and Retailers (avg 30/day) indicate event-based flow initiation replacing centralized planning. Inventory pull (avg 22) and dispatch messages (avg 18) confirm kanban-based real-time synchronization among Retailers, Producers, and TruckPR agents. Lower waste pickup messages (avg 10) reflect threshold-based activation at waste nodes. These frequencies validate efficient, role-specific communication and autonomous agent interaction.

These layers represent service-level-aware logistics in which mobile agents are contextually aware and behaviorally driven. The model accurately captures truck utilization patterns, local processing delays, and the dynamic coupling between PI-nodes and PI-movers.

6. PILAR architecture and agent-based logistics KPIs

The PILAR framework combines decentralized decision-making with multi-modal logistics to optimize coffee supply chains. Customer agents initiate shipment requests, processed by PILAR-3 (AetherCore), which allocates PI-containers and transport modes using Monte Carlo simulations (10,000 iterations) to account for uncertainty in demand, delays, and fuel prices. PILAR-2 (FluxStream) assigns modes via greedy-epsilon algorithms, balancing congestion, fuel cost, and emissions. Vehicle agents reroute using Q-learning to adapt to disruptions, while hub agents use integer linear programming (ILP) to minimize dwell time. Post-simulation, KPIs (cost, CO₂, latency) feed into a decision-support system (DSS) for Pareto-frontier analysis, enabling multi-objective optimization under stochastic conditions. The integer linear programming (ILP) model minimized total dwell time subject to transport capacity and time-window constraints. Decision variables included container assignment (x_ij) and hub throughput (y_i), with constraints ensuring single allocation and flow conservation.

6.1 Monte Carlo simulations for quantifying uncertainty

Monte Carlo results yield key metrics like delivery time, demand variation, and fuel price fluctuation. Daily order volumes follow a normal distribution (μ = 1001.5, σ = 142.0), confirmed by Q-Q plots (Figure 13) and histograms, with a 95% confidence interval of [706.0, 1294.0]. The distribution’s symmetry and lack of outliers validate the Gaussian assumption, ensuring reliable predictive modeling. This stability reflects the effectiveness of AetherCore’s decentralized logic in managing demand variability and supporting robust inventory control under uncertainty.

Figure 14 analyzes the impact of monthly demand spikes on total transportation costs, modeled as a Poisson process (λ = 3 spikes/month). At low spike frequencies (0–2/month), median costs range from $8 k to $11 k with moderate variability, indicating stable pricing. As spikes increase to 3–5/month, the cost distribution widens, with greater interquartile ranges and outliers, reflecting congestion and capacity-driven volatility. At high spike levels (6–7/month), cost variability narrows, suggesting strategic adaptations such as preemptive capacity scaling or rerouting. Outliers at mid-range levels imply occasional emergency logistics responses. Overall, the analysis highlights the need for dynamic pricing and adaptive logistics planning to maintain cost control and resilience under fluctuating demand conditions.

Simulated via Geometric Brownian Motion (GBM), fuel prices exhibit stochastic trajectories over 30 days (initial price = $3.50/gal, volatility = 20%). The price trajectories exhibit significant randomness, with some simulations showing sharp increases, while others indicate stabilization or downward trends. The spread of possible outcomes is influenced by stochastic drift and volatility parameters, demonstrating the inherent uncertainty in fuel pricing. The log-normal model ensures non-negative prices but highlights forecasting challenges due to high variance as depicted in Figure 15.

Delivery times (Figure 16) exhibit a right-skewed lognormal distribution (mean = 76.1 hrs, median = 72.2 hrs), indicating that while delays are generally infrequent, they can be significant when they do occur. The skewness reflects outlier disruptions, such as mechanical failures, extreme weather, and port strikes. These outliers are partially mitigated by the use of integer linear programming (ILP)-based hub sorting, which optimizes sorting and reduces dwell times. The 4-hour mean-median gap, compared to a typical lognormal distribution, illustrates this improvement. Additionally, a moderate Pearson correlation (r = 0.57) between delays and delivery times highlights the nonlinear impact that multimodal disruptions have on end-to-end performance.

6.2 Agent decision-making: Algorithms and learning curves

Figure 17 shows the agent learning curve using the Greedy-ε strategy, where container agents iteratively improve routing and mode selection across ∼1000 simulation episodes where agents decide between road, rail, or air transport under stochastic conditions. The Y-axis depicts the total reward, which is consistently negative since the objective is to minimize costs and penalties, represented by the function as:

R=−α·congestion delay+β·fuel cost+γ·carbon intensityE1

The Q-learning algorithm employed a learning rate (α) of 0.1, a discount factor (γ) of 0.95, and an exploration rate (ε) decaying from 0.9 to 0.1 across 1000 simulation episodes. The Greedy-ε policy ensured balanced exploration and exploitation under stochastic network conditions.

Rewards range from −1600 to −600, reflecting cost variability due to disruptions like demand surges and fuel volatility. Agents apply Q-learning, updating decisions via the Bellman equation, with α (learning rate) and γ (discount factor) guiding adaptation. Early episodes involve exploration (high ε), shifting toward exploitation as ε decays, achieving logarithmic regret bounds O (log T) under stochastic bandit assumptions. Despite environmental noise, performance trends toward convergence, suggesting an approximate Nash equilibrium. Vehicle agents reroute dynamically to avoid congestion, optimizing for latency. Fluctuations in reward curves reveal sensitivity to real-time disruptions, confirming the adaptive potential of reinforcement learning in PI-enabled coffee logistics.

The tradeoff between CO₂ emissions and delivery time in multimodal transport is depicted in Figure 18. The X-axis shows emissions (700–1300 kg), and the Y-axis represents delivery time (50–200 hours). Road transport yields faster delivery but higher emissions, while rail offers lower emissions with longer transit times. The red Pareto frontier marks optimal tradeoff points, where improving one metric worsens the other. A highlighted solution at 900 kg CO₂ /70 hours represents an “Optimal Rail–Air Hybrid,” balancing sustainability and speed. Deviations from the frontier reflect disruptions (e.g., rail congestion), with Q-learning agents dynamically adjusting routes to maintain near-optimal performance. The graph highlights the efficiency-sustainability tension and the value of hybrid strategies in dynamic supply chain networks.

Hub Agents (ILP) reduce dwell time skewness via throughput-optimized sorting, critical for mitigating lognormal delivery time tails. In addition, agent decisions directly shape logistics KPIs, analyzed below.

6.3 Transport mode analysis: Delays, costs, and reliability

Transport delay distributions for Road, Rail, and Port modes on a logarithmic scale, revealing mode-specific efficiency profiles (Figure 19). Road transport shows the highest reliability, with a median delay of 1.5–2.5 hours, IQR of 1–5 hours, and a maximum delay near 10 hours. Rail delays are moderately variable, with a median of 3–4 hours, IQR of 2–6 hours, and outliers exceeding 20 hours. Port transport is the most unpredictable, with a median delay of 5–6 hours, IQR of 4–12 hours, and extreme cases over 100 hours, reflecting congestion and procedural inefficiencies. These distributions emphasize that road is optimal for time-sensitive shipments, rail suits bulk cargo with moderate delays, and port transport requires risk mitigation due to high delay variability.

The cumulative delay distribution across transport modes reveals differences in reliability (Figure 20). Road transport displays a steep curve, with 80% of delays under 15 hours, indicating sensitivity to real-time disruptions. In contrast, rail and port exhibit flatter curves, reflecting higher variability due to scheduling constraints and infrastructure inefficiencies. These patterns support the use of Q-learning by vehicle agents for dynamic rerouting, particularly effective in road networks, whereas rail and port delays are less responsive to real-time adjustments.

The interquartile range (IQR) analysis (Figure 21) of transport mode costs highlights efficiency trade-offs. Rail transport is the most cost-effective, with a median cost of $289 and IQR of $266–$314, indicating low variability and stable pricing. Road transport offers more flexibility but at a higher median cost of $381 and IQR of $363–$398, reflecting moderate variation. Air transport is the most expensive (median $949, IQR $933–$969) but shows the least variability, making it suitable for time-sensitive, high-value shipments. The analysis emphasizes modal trade-offs such as rail is optimal for bulk/long-haul (68% of iterations, Nash equilibrium), road serves as a flexible mid-cost option, and air remains a premium choice. These insights inform cost-efficient mode selection in logistics optimization.

The strong positive correlation (R² = 0.78) between fuel price volatility and delivery costs (Figure 22) highlights the economic sensitivity of the supply chain. Delivery costs surge disproportionately during fuel price spikes, reflecting the greedy-epsilon algorithms’ prioritization of cost efficiency over alternative objectives (e.g., emissions reduction) under the volatile conditions. The scatterplot’s dispersion at higher simulation iterations (>6000) captures emergent trade-offs between fuel-driven cost escalations and carbon constraints, emphasizing the need for Pareto-optimal routing strategies in the DSS to balance competing objectives during demand spikes.

After running 10,000 simulations with n_sims = 10,000 and n_steps = 30 it is observed that a 20% daily volatility leads to a ± 85% annualized volatility, which represents real-world energy markets as given in Table 9.

Statistic	Day 1	Day 30
Mean Price ($)	3.50	3.72
Standard Deviation	0.00	0.85
Minimum Price ($)	3.50	1.90
Maximum Price ($)	3.50	6.10

Table 9.

Descriptive statistics of fuel price simulation over a month and observed price range.

Price spikes force agents to prioritize cost over sustainability, escalating emissions (e.g., air freight substitutions). The aggregated results of these findings are given in Table 10. These tradeoffs are quantified in environmental-economic analyses.

KPI	Mean	Std Dev	95% CI
Delivery Time (hrs)	72.3	±18.2	[68.1, 76.5]
Cost per Container ($)	420.50	±85.30	[398.20, 442.80]
CO2 Emissions (kg)	1250	±320	[1160, 1340]
Asset Utilization (%)	82.4	±6.7	[80.1, 84.7]

Table 10.

Statistical summary of logistics performance indicators (KPIs).

To improve transparency result, Table 11 provides a comparative summary between the baseline (conventional logistics) and the PI-enabled scenario simulated under the PILAR framework. Each value represents the mean outcome from 10,000 Monte Carlo runs, with corresponding standard deviation (SD) and 95% confidence interval (CI). Percentage improvements (e.g., 30% cost reduction, 50% recovery efficiency increase) were calculated as relative differences between baseline and scenario means. These figures quantify the performance gains attributable to the PI-based coordination, confirming the statistical robustness of the reported trends.

KPI	Baseline (mean ± SD)	PI-enabled scenario (mean ± SD)	95% CI (scenario)	Improvement (%)
Transportation Cost ($/year)	2.00 × 106 ± 0.18 × 106	1.40 × 106 ± 0.15 × 106	[1.38 × 106, 1.42 × 106]	−30%
SCG Recovery Efficiency	0.28 ± 0.05	0.42 ± 0.06	[0.40, 0.44]	+50%
CO₂ Emissions (tons/year)	1000 ± 120	750 ± 110	[730, 770]	−25%
Asset Utilization (%)	63.0 ± 7.5	82.4 ± 6.7	[80.1, 84.7]	+31%

Table 11.

Comparative analysis of baseline versus PI-enabled scenario across key logistics KPIs.

The scatter plot in Figure 23 illustrates the relationship between total cost and CO₂ emissions in a simulated logistics environment. It displays a total cost (x-axis: ∼$4000–$20,000) vs. CO₂ emissions (y-axis: ∼1.5–4.5 metric tons), revealing a positive correlation, higher-cost shipments often produce higher emissions. This reflects modal tradeoffs as air freight is fast but carbon and cost-intensive; road offers moderate costs with variable emissions; rail is the most sustainable but slower. Variability arises from disruptions (e.g., delays, demand surges, fuel prices), affecting both cost and emissions. For instance, a 10% modal shift from road to rail reduces emissions by 18% but increases delivery time by 12%. The Monte Carlo simulation (10,000 iterations) captures these uncertainties, highlighting the core logistics challenge: balancing cost efficiency and sustainability under dynamic, multi-objective constraints.

Each figure collectively validates the PILAR framework’s ability to integrate agent-based decision-making, real-time adaptation, and multi-objective optimization, providing empirical evidence of its robustness in balancing cost, sustainability, and reliability in coffee supply chains. The PILAR framework bridges theoretical architecture with empirical validation, proving adaptive resilience through hybrid strategies (e.g., rail-air) and probabilistic modeling. Future work will focus on refining regret bounds and expanding state-action spaces for complex disruptions.

7. Analysis of technological and infrastructural barriers for PILAR model application

Implementing PILAR models in real-world supply chains faces key technological and infrastructural barriers. A major challenge is the lack of standardized modular π-containers, which hampers interoperability across legacy systems due to differences in geometry, RFID, and sensor interfaces. Adopting standards like ISO 668 and IoT protocols is essential for seamless tracking and integration. The data exchange layer requires secure communication protocols (e.g., MQTT, OPC-UA) with TLS/SSL encryption, aligned with ISO/IEC 27001 to mitigate cybersecurity risks in decentralized networks.

On the infrastructure side, retrofitting hubs with sensors, edge devices, and real-time analytics demand significant investment, typically managed through microservices (e.g., Kubernetes) and distributed engines (e.g., Apache Spark). These setups depend on high-bandwidth, low-latency networks to enable real-time digital twins, posing challenges in low-connectivity regions (e.g., PRISMA project). Integrating robust MILP and reinforcement learning into legacy systems also requires extensive recalibration. Regulatory fragmentation and lack of harmonized global standards hinder adoption, calling for collaboration among industry consortia and regulatory bodies. Table 12 summarizes these challenges, emphasizing the need for standardization, secure data exchange, scalable computing, and regulatory alignment to support PI adoption at scale.

8. Impact assessment of PRISMA model on stakeholders, enterprises, and local communities and strategic recommendations for PI implementation

The PRISMA model introduces a transformative framework for supply chain optimization by applying PI principles and advanced digital technologies. As supply chains transition to smart, resilient systems, the model’s technological, economic, and social impacts must be assessed across stakeholders, enterprises, and communities. Integrating intermodal infrastructure, DLT, and IoT-enabled tracking creates a complex yet high-impact logistics paradigm.

8.1 Stakeholder implications

PRISMA implementation demands structural changes in logistics networks, requiring stakeholders, including policymakers, LSPs, and regulators, to align with the international standards like ISO 668 (container specs), IEC 61499 (automation), and GS1 EPCIS (event tracking). Ensuring π-container interoperability also necessitates cross-border regulatory harmonization and cybersecurity compliance via ISO/IEC 27001 and NIST frameworks. Smart contracts on blockchain enforce governance, real-time visibility, and automated auditing. Figure 24 presents a stakeholder impact matrix, mapping actors by influence and interest in PRISMA deployment, guiding engagement and policy strategies.

8.3 Socioeconomic and environmental considerations

The PRISMA model has notable implications for local communities, particularly due to AI-driven automation and autonomous vehicles (AVs), which may lead to workforce displacement. To address this, reskilling programs aligned with Industry 4.0 standards are essential. Environmentally, PRISMA reduces carbon emissions through V2X communication, dynamic AI routing, and modular energy-efficient hubs. Strategic urban planning and adoption of ISO 14064-1 enable accurate carbon tracking and congestion reduction. Technologies like Vehicle-to-Grid (V2G) and fleet electrification support circular economy goals and sustainability mandates. Figure 25 shows an inverse relationship between job displacement and new job creation, suggesting that while AI/AV adoption may displace some roles, it also drives employment growth in emerging sectors.

8.4 Economic viability and scalability challenges

The PRISMA model offers long-term cost reductions through Just-in-Time (JIT) logistics and resilient supply chain configurations, but high initial investment remains a barrier, especially for SMEs. While blockchain-based smart contracts and DeFi enable flexible financing, their adoption is limited by regulatory uncertainty. To support real-time, autonomous decision-making, PRISMA requires 5G-enabled Multi-Access Edge Computing (MEC) for low-latency operations across distributed logistics networks. To manage cross-border complexity, integrating standardized e-Bill of Lading (eBL) and smart contract-based trade finance ensures compliance with UN/CEFACT and WCO SAFE frameworks. Figure 26 shows that although SME investment costs are high initially, they decline over time, while JIT-related savings increase, ultimately surpassing the investment and demonstrating long-term financial viability.

While PRISMA offers clear benefits in efficiency, sustainability, and resilience, its success depends on addressing key barriers, including regulatory harmonization, economic feasibility, and workforce adaptation. Ensuring long-term scalability requires AI-driven optimization, strong cybersecurity frameworks, and sustainable urban integration strategies.

9. Conclusion

The PRISMA model, grounded in PI principles, presents a transformative approach to modernizing supply chains through modularity, decentralization, and digital intelligence. By integrating agent-based modeling, kanban-controlled flows, and multi-layered PILAR architecture, the framework enables real-time, autonomous logistics coordination across both forward and reverse chains exemplified by spent coffee ground recovery. Simulation results highlight how Q-learning, Monte Carlo methods, and stochastic optimization enhance adaptability, cost-efficiency, and environmental performance under uncertainty. However, successful implementation depends on overcoming challenges such as standardization gaps, high initial costs, cybersecurity risks, and regulatory fragmentation. Strategic investments in IoT, edge computing, blockchain, and reskilling programs are essential to achieving scalable, sustainable, and inclusive adoption. Overall, PRISMA demonstrates strong potential for enabling resilient, low-carbon, and digitally intelligent logistics networks aligned with global sustainability and circular economy goals.

Acknowledgments

We acknowledge financial support under the National Recovery and Resilience Plan (NRRP), Mission 4, Component 2, Investment 1.1, Call for tender No. 104 published on February 2, 2022 by the Italian Ministry of University and Research (MUR), funded by the European Union – NextGenerationEU – Project Title PRISMA Platform (Physical internet RegeneratIve Sustainable MAterials) – CUP I53D23001660006 – Grant Assignment Decree No. 961 adopted on 30/June/2023 by the Italian Ministry of Ministry of University and Research (MUR).