In the case study, smart display units originated at electronics manufacturing centers in Oragadam and Sriperumbudur and were assigned to freight depots in Kanchipuram and Vellore. Deliveries could use either an automated electric truck or an automated electric van over one of two designated routes for each source–destination pairing. The model selected shipment quantities from the available combinations; it did not generate new road routes, determine sequences of stops or simulate driving behavior.

Its scope was therefore a mathematical allocation model for a specified network, not a field trial of automated vehicles. Two competing objectives were minimized simultaneously. The first combined direct transportation expenses, automation costs and energy-related costs.

The second sought to reduce total transportation time. The researchers represented the tradeoff by treating the cost and time objectives as parties in a cooperative bargaining calculation, with a deviation term favoring proximity to ideal outcomes and a satisfaction term favoring plans that perform well across both objectives. In the payoff calculation, the cost-only optimum was ₹147,480 with a transportation-time value of 13,076.1 hours, while the time-only optimum was ₹169,615.76 with 10,159.20 hours.

The distinct optima showed that minimizing one measure did not produce the same allocation as minimizing the other. Uncertain inputs were represented with triangular Fermatean fuzzy numbers, a framework designed to accommodate both membership and non-membership information under the constraint that the cubes of the two degrees do not exceed one. This permits assessments that would be excluded by intuitionistic or Pythagorean fuzzy frameworks in some cases.

The study modeled transportation costs, unit time and energy-consumption costs as fuzzy because market fluctuations, congestion, road conditions and weather can make such values difficult to specify precisely. Route distances, battery capacities, vehicle payloads, supply quantities and destination demands were treated as exact values. The case used two vehicle categories, each with defined capacity and battery limits, and a small set of designated routes rather than a comprehensive road network.

Because directly solving a bi-objective model with fuzzy coefficients would be computationally complex, the researchers first applied a score function to transform each triangular Fermatean fuzzy number into a deterministic equivalent. They then solved the cost and time objectives separately to identify their ideal and anti-ideal values. The hybrid Fermatean fuzzy game-theoretic method normalized each objective against its corresponding ideal and anti-ideal values, making deviations dimensionless despite the objectives having different units.

It then combined these normalized disagreements with Fermatean fuzzy satisfaction and dissatisfaction measures. The resulting single-objective model was implemented in LINGO with its global solver, converting the original bi-objective problem into a computationally tractable optimization task. The selected plan sent 2.0542 quintals from Oragadam to Kanchipuram by automated electric truck on route 1, 57.9457 quintals from Oragadam to Vellore by truck on route 2, 42.9457 quintals from Sriperumbudur to Kanchipuram by truck on route 1, and 7.0542 quintals from Sriperumbudur to Vellore by automated electric van on route 1.

The quantities satisfied the stated supply, demand, vehicle-capacity, battery-range and non-negativity constraints. For this allocation, the estimated transportation cost of ₹148,490 comprised ₹108,901.64 in vehicle movement and distribution expenses, ₹34,575.84 in automation costs and ₹5,012.52 in energy-consumption costs. A separate optimality test found no feasible allocation that could improve both cost and time simultaneously, confirming that the result was Pareto optimal for the two stated objectives.

In a comparison using the same deterministic model and normalization values, the Fermatean fuzzy programming method returned a cost of ₹169,607.90 and a time of 13,076.1 hours. A weighted sum method with equal weights of 0.5 for the normalized objectives returned ₹148,490 and 13,076.1 hours. The hybrid game-theoretic result matched the weighted sum method’s cost but reduced its time estimate by 133.16 hours, or about 1.02%.

Satisfaction levels for the two objectives were 99.32% and 72.60% under the hybrid method, compared with 99.32% and 71.29% under the weighted sum approach. Its degree of closeness was 0.1109, lower than the weighted sum method’s 0.1149 and the fuzzy programming method’s 0.1768; the paper treats a smaller degree of closeness as preferable. These comparisons concern the model’s calculated allocations and objective values, not measured operational performance in a live logistics system.

The computational tests indicated that the method could handle larger arrays of sources, destinations, vehicles and routes. Reported solution times rose from 0.01 seconds for a 2 × 2 × 2 × 2 instance with 16 decision variables and 12 structural constraints to 0.05 seconds for a 3 × 3 × 3 × 3 instance, 0.18 seconds for a 4 × 4 × 4 × 4 instance and 0.76 seconds for a 5 × 5 × 5 × 5 instance with 625 decision variables and 60 structural constraints. Sensitivity tests preserved feasibility when supply increased by 1% to 10% and when demand decreased by 1% to 10%.

With a 10% supply increase, the cost estimate fell by approximately 1.07% while time rose by approximately 0.69%. With a 10% demand reduction, time fell from 12,942.94 hours to 9,606.514 hours, while cost changed from ₹148,490 in the main results to ₹148,032.70 in the sensitivity table. These results describe the mathematical model’s response to parameter changes, not measured changes in an operating logistics network.

The study’s main limitation is that its sustainability and deployability claims extend beyond the variables included in the optimization. The model omits charging-station placement, communication-network requirements, data-transfer security, cybersecurity threats and unauthorized vehicle control. It also treats several uncertainty sources through fuzzy parameters rather than stochastic distributions, handles a limited product case and evaluates routes that are already predefined.

The authors note that lowering energy-related costs and time may indirectly reduce battery consumption and environmental impacts associated with electricity generation, but the case study did not measure emissions, fuel displacement, noise reduction or air-quality changes. They identify charging constraints, intrusion detection, multiple products, multilevel warehouse planning and stochastic uncertainty as possible extensions. Subject to those limitations, the case study shows how a Fermatean fuzzy game-theoretic method can convert uncertain cost and time inputs into one computationally tractable allocation for automated electric vehicle logistics.

Subject of Research: Fuzzy multi-objective optimization for automated electric vehicle transportation planning

Article Title: A sustainable Fermatean fuzzy bi-objective four-dimensional transportation model for automated electric vehicle logistics planning using a Fermatean fuzzy game-theoretic method

Article References: Kumar, E., & Dhanapal, A. (2026). A sustainable Fermatean fuzzy bi-objective four-dimensional transportation model for automated electric vehicle logistics planning using a Fermatean fuzzy game-theoretic method. Frontiers in Sustainability, 7, Article 1944956. https://doi.org/10.3389/frsus.2026.1944956

Image Credits: AI Generated

DOI: 10.3389/frsus.2026.1944956

Keywords: automated electric vehicles, logistics optimization, Fermatean fuzzy sets, game theory, four-dimensional transportation, supply chain management, Pareto optimization, uncertain inputs, smart display units, sustainable logistics, sustainable, Fermatean

The research, led by Jiaxin Tan and corresponding author Xiaohui Huang of East China Jiaotong University in Nanchang, China, together with colleagues Nan Jiang, Xuebo Cheng, Liyan Xiong and Ni Liu, introduces a framework called the Predictive-context Large Language Model Scheduler, or P-LLM. The core idea is deceptively simple. Instead of relying solely on hand-crafted optimization rules or reinforcement learning agents that must be trained for weeks, the framework lets a large language model reason directly over the state of the fleet, the stream of incoming orders, and a forecast of demand that has not yet materialized. The scheduler then proposes vehicle-order assignments that balance immediate profit against the anticipated geography of future demand.

The problem the authors tackle is well known to operations researchers. Traditional scheduling methods, including classical optimization approaches, perform well when the world is static and the rules are clearly defined. Real cities are anything but static. Traffic conditions evolve continuously, order arrival patterns swing between feast and famine, and the best decision for the current moment can be a disaster five minutes later if it strands vehicles in neighborhoods where demand is about to spike. Reinforcement learning, the go-to modern alternative, learns policies through trial and error, but the authors point to persistent challenges with training stability and convergence, particularly in environments as noisy and non-stationary as urban traffic.

P-LLM addresses this by combining three cooperating modules. The first is an Order Demand Prediction Module, which mines historical order data to forecast how many orders are likely to appear in each zone of the city in upcoming time steps. The second is the LLM-Based Scheduling Module, the heart of the system, which receives structured, machine-readable descriptions of current orders, vehicle availability, estimated arrival times, and the demand forecast, and then generates candidate assignments. The third is a Scheduling Output Verification Module, a safety net that checks whether the language model’s decisions are actually reasonable and feasible before they are executed.

That verification module matters more than it might first appear. Large language models are famously fluent but not always reliable, and a scheduler that assigns the same vehicle to two orders at once, or accepts an order that no vehicle can reach within its time window, would be worse than useless. The published framework enforces hard feasibility constraints through this separate verification layer, while the language model itself is instructed to follow softer reasoning principles. According to the prompt design documented in the paper’s appendix, the model is cast as an autonomous vehicle scheduling expert for smart cities, instructed to reason about the economic value of each order using rewards and travel costs, to promote efficient use of idle vehicles, and to avoid over-allocating vehicles to regions expected to see high future demand.

One of the more intriguing design choices is what the authors call demand-aware selective rejection. The scheduler is explicitly permitted to decline orders that are economically unfavorable or clearly infeasible. Under conditions of limited vehicle availability, it may reject low-value orders while weighing the predicted future demand in the same zone, effectively deciding that a vehicle parked in a soon-to-be-busy district is worth more than the marginal profit of a cheap fare right now. This kind of judgment, blending immediate economics with spatial foresight, is precisely the sort of contextual reasoning that language models excel at, and it is difficult to encode in a fixed reward function.

The decision loop itself follows a structured workflow. At each time step, the model analyzes current orders and vehicle states, interprets the demand predictions and zone-level demand rankings, generates candidate vehicle-order assignments guided by profit, feasibility and future demand awareness, performs a self-consistency check to catch obvious violations such as repeated vehicle usage, and only then outputs its final assignment. The output must conform to a consistent structured format, which allows the downstream verification module to parse and validate every decision mechanically. In effect, the system treats the language model as a powerful but fallible reasoning engine, wrapped in guardrails that catch its mistakes before they reach the road.

The experimental results reported in the paper are striking. The proposed method outperformed both traditional scheduling methods and existing reinforcement learning baselines. More importantly for real-world deployment, performance remained stable and consistent across different real-world scenarios, time periods, fleet sizes and order volumes. That robustness addresses one of the most common criticisms of learned scheduling systems, which often excel in the specific conditions they were trained on but degrade when demand patterns shift, a fleet grows, or a new service area is added. A scheduler that generalizes across these axes is far more attractive to operators of delivery fleets and ride-hailing services, whose operating conditions change daily.

The study arrives amid a rapidly growing body of work applying large language models to transportation. Recent research has explored LLMs as decision makers for autonomous driving, as agents for adaptive traffic signal control, as generators of reward functions for highway driving, and as reasoning engines for traffic scene risk assessment. A closely related preprint, LLM-ODDR, applies language models to joint order dispatching and driver repositioning in ride-hailing. The new work extends this line into fleet scheduling with an explicit spatio-temporal demand forecast feeding the model’s context, which the authors argue is what allows the scheduler to act on the future rather than merely react to the present.

The implications reach beyond academic benchmarks. Unmanned delivery vehicles and autonomous taxis are already being deployed in smart cities, and fleet management is where their economics are won or lost. A framework that can incorporate predicted demand, respect operational constraints, and adapt to changing conditions without lengthy retraining could shorten the path from pilot projects to profitable services. The authors have released their simulator code on the Gitee platform, inviting other researchers to build on the approach. The study’s underlying datasets, which contain sensitive vehicle trajectory information, cannot be publicly shared due to privacy constraints but are available from the corresponding author upon reasonable request with data provider approval.

There are, of course, open questions. Large language models are computationally expensive, and the paper does not claim to have resolved every challenge of latency and cost at massive fleet scale. The verification module, while essential, also means the language model’s suggestions are constrained rather than fully autonomous, a design that reflects a broader consensus in AI safety research: powerful generative models are best deployed where their outputs can be checked. Still, the work offers a compelling glimpse of a new architecture for urban logistics, one in which forecasting, reasoning and verification are stitched together around a language model that can read the city’s pulse and position its fleet accordingly. If the reported gains hold up in deployment, the chatbot’s cousin may soon be deciding where your delivery van goes next.

Subject of Research: Large language model-based scheduling of autonomous vehicle fleets in smart cities

Article Title: A spatio-temporal context-aware LLM-centric framework for autonomous vehicle scheduling

Article References: Tan, J., Huang, X., Jiang, N., Cheng, X., Xiong, L., & Liu, N. (2026). A spatio-temporal context-aware LLM-centric framework for autonomous vehicle scheduling. Applied Intelligence, 56(14), Article 423. https://doi.org/10.1007/s10489-026-07451-3

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07451-3

Keywords: large language models, autonomous vehicles, vehicle scheduling, fleet management, demand prediction, reinforcement learning, smart cities, ride-hailing, logistics optimization, LLM decision-making, order dispatching, Applied Intelligence