Water-infrastructure public–private partnerships combine long-duration public-service obligations with incomplete knowledge about governance costs, opportunistic gains, enforcement consequences, and the public-loss implications of hydrological-risk exposure. This study develops a two-population evolutionary game in which government decision makers choose routine governance or enhanced monitoring and private participants choose cooperative performance or opportunistic behavior. Interval grey numbers represent defensible epistemic bounds, while conventional worst-case inequalities establish robust stability over the resulting sets. The reformulated payoff mechanism embeds water risk through public loss, separates latent trust from observable choices, and evaluates all four boundary rest points. Under the maintained assumption that c>0, RC, RO, and MO have nonempty strict stability regions, whereas MC is unstable; the model also yields an interior center. A separable first integral proves that regular interior level sets are closed orbits; the center is not a convergent state. The computational analysis covers 16 effective-box vertices, 50,000 independent-box observations, five linked designs based on a shared 50,000-row whitening sample, and 336 sensitivity cells. In the independent coverage sample, 27,689 rows exhibit the interior center, whereas the midpoint classification disagrees with 22,311 rows (coverage share 0.44622). Positive affine linkage reduces disagreement and improves several worst-case margins, but every baseline robust margin remains negative, so no strict robust regime holds over the full admissible set. The contribution is a water-specific, analytically proved, and reproducibly computed framework that distinguishes grey epistemic representation from robust-set mathematics and supports conditional governance implications tied to named parameters and interval bounds.

Large-scale resource-to-task assignment under nonlinear coupling constraints represents a recurrent computational challenge in industrial engineering, spanning production scheduling, logistics coordination, and multi-agent mission planning. This study addresses a generalized formulation in which heterogeneous agents must be partitioned into coalitions, each assigned to a distinct objective with stringent compatibility and synergistic-effect requirements. A distributed optimization framework, termed the Distributed Coalition Formation Algorithm (DCFA), is developed by recasting the centralized assignment problem as a coalition partition game. Each agent acts as an independent decision-maker, evaluating marginal utility contributions when switching coalitions. The global utility function is proven to constitute an exact potential function, which guarantees finite-step convergence to Nash-stable partitions with a Price of Stability equal to unity over the set of reachable equilibria. A sigmoid-based utility mapping captures nonlinear saturation in cumulative effectiveness, while a Simulated Annealing Better-Response (SABR) mechanism enables systematic escape from suboptimal local partitions. Localized reallocation protocols further equip the framework to accommodate real-time disruptions without triggering full-scale recomputation. Extensive computational experiments, analyzed through Friedman ranking, Nemenyi post-hoc comparisons, and Cohen's d effect sizes, demonstrate that DCFA scales near-linearly with problem size and occupies the optimal compromise point on the utility–time Pareto frontier, achieving order-of-magnitude speedups relative to leading centralized metaheuristics at negligible solution-quality loss. The framework offers a general-purpose computational tool for distributed resource assignment in large-scale industrial systems.

With the deepening of the dual carbon target, the circular economy has become the core direction of manufacturing transformation and upgrading. As its core carrier, closed-loop supply chain still faces core pain points such as conflicts of interest among multiple parties, information asymmetry, high trust barriers, poor reverse recycling cycle, and low contract execution efficiency. This study is based on the tamper-proof and traceable technical characteristics of blockchain, and constructs a closed-loop supply chain lifecycle structure system driven by smart contracts. It characterizes the strategic interaction relationship between manufacturers, retailers, recyclers, and remanufacturing centers, establishes a Stackelberg dynamic game model, and derives the subgame perfect Nash equilibrium. An improved deep deterministic policy gradient algorithm is introduced to achieve multi-objective coordinated optimization in dynamic environments. The research results show that the model achieves a supply chain channel efficiency of 97.2%, a 22.6% increase in total revenue compared to traditional contract models, a contract default rate of 0.8%, a maximum recycling and remanufacturing rate of 92.5%, and a 41.7% decrease in cumulative carbon emissions throughout the entire lifecycle. Its comprehensive performance is significantly better than the four comparative models. Under extreme conditions such as high demand fluctuations, large-scale nodes, and heterogeneous recycling scenarios, the model still maintains strong robustness and scalability, providing theoretical support and a feasible technical path for the digital, trustworthy, and intelligent coordination of closed-loop supply chains in a circular economy.

This paper studies the competitive decision-making and collaborative decision-making of the two-level multi-agent supply chain of China's new energy vehicle industry. Based on the differential game theory, this paper constructs the profit model of each subject in the supply chain of the new energy vehicle industry in the case of competitive decision and collaborative decision, and obtains the optimal factor value and profit value of each subject, which is verified by an actual example. The results show that: (1) the optimal sales volume of new energy vehicle manufacturers decreases with the increase of non raw material costs of new energy vehicle manufacturers and the costs of new energy vehicle core parts suppliers, whether in the case of competitive decision-making or collaborative decision-making. (2) The optimal profit of each subject in the supply chain system of the new energy vehicle industry and the overall profit of the supply chain system in the case of collaborative decision-making are significantly better than those in the case of competitive decision-making. (3) Whether it is a new energy vehicle manufacturer, a new energy vehicle core parts supplier or the whole new energy vehicle supply chain, the growth rate of the main profit under the collaborative decision is significantly faster than the optimal profit under the competitive decision.

As e-commerce platforms in Southeast Asia shift toward profitability, they often raise commission rates while providing sellers with free data services that offer three core functions: data mining, traffic profiling, and user profiling. Higher commission rates strengthen platform monetization, while free data services sharpen sellers' operational decisions. This common practice motivates our model construction. This paper develops a supply chain framework consisting of a single e-commerce platform and two brand suppliers that compete from asymmetric market positions. The dominant brand chooses between agency selling and reselling, whereas the weaker brand relies on an agency selling model. We construct four scenarios along two dimensions: (1) channel structure (dual agency versus hybrid mode) and (2) whether the platform adopts the ‘commission rate hikes + free data services’ strategy. Employing a complete Stackelberg game framework, we derive all equilibrium outcomes and analyze the platform's operational tactics, brand suppliers' channel preferences, and the corresponding effects on social welfare. Our findings reveal that the demand-expansion effect of free data services is the primary driver of channel structure decisions. When data service efficiency is sufficiently high, the agency channel absorbs the full incremental demand generated by free data services. Consequently, higher commission rates do not necessarily induce the dominant brand to switch to reselling.

The operation of the automotive supply chain in China is primarily influenced by government subsidy policies and the dual credit policy. Based on a two-echelon automotive supply chain consisting of one manufacturer and one retailer, this paper incorporates the technological decisions regarding battery performance improvement of new energy vehicles, including battery electric vehicles and plug-in hybrid electric vehicles, as well as the energy-saving efficiency improvement of traditional fuel vehicles. Four policy scenarios are considered, namely a baseline scenario with no policy intervention, scenario of government subsidy-only policy, scenario jointing subsidy-dual credit policy, and scenario of dual credit-only policy. A supply chain pricing and technological performance decision model is developed for each policy scenario. Using a Stackelberg game approach, we derive the optimal decisions and profits of supply chain members under the four policy scenarios. The results show that: (1) an increase in the credit trading price generates a stable positive price incentive effect on battery electric vehicles, whereas its impact on the prices of plug-in hybrid electric vehicles and traditional fuel vehicles is jointly moderated by government subsidies and consumers’ green preferences. (2) R&D subsidies and credit trading price effectively promote improvements in the battery performance of new energy vehicles, whereas purchase subsidies may weaken incentives for the battery performance enhancement of new energy vehicles. Meanwhile, the energy-saving efficiency of traditional fuel vehicles exhibits differentiated responses depending on policy instruments and the level of green utility. (3) R&D subsidies and purchase subsidies can simultaneously improve the profits of all members in the automotive supply chain. Moreover, under the scenario joining government subsidy-dual credit policy, the credit trading price can further enhance the profitability of supply chain members. This paper clarifies the differential impacts of various policy instruments on automotive supply chain decisions and benefit incentive mechanisms.

A logistics distribution path optimization method based on soft time windows and hill climbing genetic algorithms is proposed to reduce costs and achieve low-carbon transport. Experimental results show the improved algorithm converges after 20 iterations with a fitness of 4.93×10⁵, lower than others. It averages 20 iterations and 3.1 seconds, indicating high efficiency. In example C105, the path length is 843.70 km, below others. In a practical test with a chain supermarket, the delivery path length is 367.5 km, reduced by at least 14.9%. Total cost is 1873.6 yuan and carbon emissions are 109.1 kg, both lower. Vehicle load capacity exceeds 80%, improving utilization. Under multiple distribution centers, delivery time is shorter and demand coverage averages 96.5%, better than others. The algorithm effectively reduces costs, emissions, and enhances efficiency, with high application value.

Insufficient prepositioning of relief supplies before a disaster and inefficient allocation after it are two major causes of post-disaster shortages. Such shortages can impose substantial suffering on disaster-affected populations, particularly when critical supplies are unavailable. Therefore, in addition to logistics costs, governments should pay attention to human suffering when designing relief supply systems. However, limited research has examined how human suffering affects prepositioning and supply strategies of relief supplies. To address this gap, this study develops a model grounded in option contracts for the prepositioning of relief supplies that explicitly incorporates human suffering. We derive the respective optimum strategies for the two contracting parties (the public authority and the private supplier), and further characterize the superiority conditions of the contract prepositioning model over the government‑only reserve model. Furthermore, analytical results and numerical examples are used to examine how key parameters affect the optimal decisions of both players, together with the corresponding social cost borne by the government and profit earned by the supplier. The results show that the pre-paid fee for emergency purchases can be set within a flexible range such that the minimum requirements of both parties can be satisfied. Finally, sensitivity analyses of several key parameters further provide managerial insights into government-supplier contractual cooperation, supplier selection, and pricing strategies. It shows that the model of relief supplies prepositioning under an option contract is more closely aligned with the people-centered principles of emergency response in China.

While supplier encroachment has been extensively studied, existing research has largely overlooked two important market elements: the segment of used products owners and the peer-to-peer (P2P) resale market. We bridge this gap by building game-theoretic models featuring a retailer who distributes its supplier’s products to both new customers and existing owners through a trade-in program. Additionally, we incorporate a P2P resale platform that permits direct used-good exchanges between new consumers and owners. The supplier’s encroachment strategies and the P2P resale market’s effects are investigated. Our research indicates that the supplier’s optimal strategy can be either partial encroachment on new customers (Strategy N) or full encroachment on both segments (Strategy B). Furthermore, the supplier systematically favors Strategy B over Strategy N. The owner ratio, new product durability and the P2P platform’s commission rate serve as key moderators, capable of either amplifying or diminishing the supplier’s motivation to encroach and the resulting positive spillovers. Intriguingly, when the platform commission rate meets certain thresholds, Strategy N invariably enhances the retailer’ profitability. The emergence of the P2P resale market consistently reduces the supplier’s profitability and dampens encroachment incentives. Yet, it can mitigate the supply chain double marginalization effects and enhance the retailer's sales, thereby benefiting both the retailer and the overall supply chain when encroachment occurs.

For the flexible job shop scheduling problem (FJSP), this study develops a multi-objective optimization model that simultaneously minimizes makespan and total energy consumption. To address the limited generalizability of conventional metaheuristic algorithms in scheduling applications, a Bi-Level Dynamic Metaheuristic Algorithm Framework (BLDMA) is proposed. Within this framework, the outer-layer metaheuristic optimizes the operation sequence, whereas the inner-layer metaheuristic dynamically adjusts the weights assigned to different machine-assignment rules. Through the interaction between the two layers, the framework can adapt its search strategy to the characteristics of the problem and the evolving search process. Computational results show that, compared with the corresponding baseline metaheuristic algorithms, the BLDMA framework achieves better non-dominated solution sets on the tested instances. These findings demonstrate the effectiveness and adaptability of the proposed framework for energy-aware flexible job shop scheduling.