This paper focuses on the total quantity and price of China-US bilateral trade and conducts a time series analysis by comprehensively various econometric methods. By sorting out the China-US trade data from 1980 to 2019, covering variables such as total import and export quantity, price index, the descriptive analysis reveals the growth trend and fluctuation nodes of trade quantity. The unit root test stabilizes the data, the Granger causality test determines the causal relationship between variables, and the cointegration test identifies three cointegration equations, which are then used to construct the least squares regression equation. The impulse response analysis shows that the growth rate index of the total China-US trade quantity, the growth index of consumer prices and ROW have a significant impact on the growth rate index of China's global import and export quantity. The variance decomposition shows that the growth rate index of China's global import and export quantity itself has the greatest impact on it. The research results provide a foundation for a comprehensive understanding of China-US bilateral trade relations and have reference value for the formulation of trade policies and related research.

A multiple objective simulation optimization algorithm named Multiple Objective Probabilistic Branch and Bound with Single Observation (MOPBnB(so)) is presented for approximating the Pareto optimal set and the associated efficient frontier for stochastic multi-objective optimization problems. MOPBnB(so) evaluates a noisy function exactly once at any solution and uses neighboring solutions to estimate the objective functions, in contrast to a variant that uses multiple replications at a solution to estimate the objective functions. A finite-time performance analysis for deterministic multi-objective problems provides a bound on the probability that MOPBnB(so) captures the Pareto optimal set. Asymptotic convergence of MOPBnB(so) on stochastic problems is derived, in that the algorithm captures the Pareto optimal set and the estimations converge to the true objective function values. Numerical results reveal that the variant with multiple replications is extremely intensive in terms of computational resources compared to MOPBnB(so). In addition, numerical results show that MOPBnB(so) outperforms a genetic algorithm NSGA-II on test problems.

Financial subsidies provided by the government have been validated as an effective means to stimulate carbon emission reductions among manufacturers. This paper examines the impact of two types of financial subsidies-namely, one-off subsidies and quantity-based price subsidies-on the bank’s optimal interest rate, the manufacturer’s optimal emission reduction level and wholesale price, and the retailer’s optimal retail price. The benefits of these two subsidy policies are compared from both economic and environmental perspectives. Our findings reveal the following insights: Both subsidy policies effectively enhance market demand and improve the economic performance of the green supply chain. However, when subsidies are below certain thresholds, total carbon emissions increase, leading to reduced environmental benefits. Under a fixed subsidy amount, one-off subsidies result in less environmental harm compared to quantity-based price subsidies. Conversely, at a given level of carbon reduction, quantity-based price subsidies yield higher economic benefits due to greater government expenditure, albeit with lower environmental benefits. These results provide valuable guidance for policymakers: quantity-based price subsidies are preferable when prioritizing economic benefits, whereas one-off subsidies are more suitable for enhancing environmental outcomes.

The number of production companies in the world is growing day by day, and they produce a huge amount of waste that harms the environment. Production companies look for various solutions to manage waste. Additionally, this produced waste can be reused in the remanufacturing process. In this regard, the governments of developed countries provide subsidies to manufacturer on returned products to encourage them to remanufacture. This work proposes a dual-channel closed-loop supply chain model in which products are produced for circuler economics. Dual channel refers to the combination of one direct online channel, where manufacturer sells new products to customers directly through his own E-marketplace with an E-ad platform and the traditional retail channel, where the retailer sells new products to customers offline after purchasing them from the manufacturer. Moreover, customers can resell the used products to the manufacturer's collection center for recycling products at an exchange price. The manufacturer will then remanufacture or rework the goods following inspection and sell them on the secondary market. This work provided a concise idea, supported by precise data (recorded by blockchain technology), about the circular economic index (CEI) of products to address the trust issues of consumers. The primary objective of this study is to maximize the profit of the supply chain while reusing substantial amounts of waste produced every day and conserving natural resources. Here, the return rate is considered linearly dependent on CEI, which helps the manufacturer make the environment sustainable and increases the profit of supply chain members by increasing demand and government subsidies. The proposed model is formulated mathematically, and both centralized and decentralized methods are used to solve the model. In the decentralized model, Stackelberg game theory approach is applied to solve the corresponding maximization problems. Also, the revenue-sharing contract policy is employed to achieve coordination between the retailer and manufacturer. Here, the numerical results indicate that the revenue-sharing contract model is more acceptable from each member's perspective. However, the total supply chain profit is slightly higher in the integrated model than in the contract model. Finally, through sensitivity analysis, we observe which key parameters are more effective for which variables or profitability.

This paper investigates a class of generalized affine fractional programming (GAFP) problems, which emerge as mathematical models in real-world applications such as computer vision and financial portfolio optimization. To develop an effective algorithm for solving problem GAFP, we first employ the Charnes-Cooper transformation to derive an equivalent problem (EP). By relaxing the fractional terms of EP and introducing new auxiliary variables, the linear relaxation of EP is then structured. Furthermore, we propose a novel adaptive branching rule that can dynamically update the lower bound of the optimal value to EP after each iteration of the algorithm. This eliminates a key disadvantage of conventional bisection algorithms, where the redundant computation may arise from improving the lower bound of EP within the selected partitioned region. The theoretical analysis establishes the convergence properties and computational complexity of the algorithm. Finally, the numerical results for several test problems demonstrate the performance of the proposed algorithm.

Two-stage flowshop scheduling has been extensively studied in the scheduling community. Unlike traditional objectives, which focus on minimizing job completion time objectives such as makespan or total tardiness, this study addresses the minimization of total job rejection costs while ensuring that the makespan remains within a specified threshold. This problem is motivated by outsourcing practices in certain make-to-order scenarios, where a cost is incurred if the manufacturer opts to reject a job and outsource it instead. For the single two-stage flowshop case, a polynomial time approximation scheme is proposed, utilizing a guessing strategy combined with a linear programming rounding technique. For the parallel two-stage flowshops case, when the number of flowshops is a fixed constant, a bicriteria [Formula: see text]-approximation algorithm is introduced, i.e., the total rejection cost does not exceed the minimum possible value, but the schedule is relaxed to possibly exceed the bound on the makespan by a factor of [Formula: see text], where [Formula: see text] is a given arbitrarily small positive constant. The algorithm is derived from a pseudo-polynomial time dynamic programming algorithm coupled with a trimming technique. When the number of flowshops is part of the input, a bicriteria [Formula: see text]-approximation algorithm is proposed. The problem formulation and algorithmic results offer production managers greater flexibility in managing job outsourcing decisions.

Against the increasingly severe global pollution and greenhouse effect, strengthening environmental governance and cutting carbon emissions has become a universal consensus. Under China’s “carbon peak and carbon neutrality” goals, this paper focuses on a dual-channel green supply chain comprising a manufacturer and a retailer, where market demand correlates linearly with retail price, carbon emissions and green sales efforts. We establish game models to derive and compare optimal decisions and profits of supply chain members under centralized and decentralized decision-making. Taking the decentralized model as a benchmark, we propose three coordination mechanisms: bidirectional cost sharing, government subsidy, and their combination. We further obtain optimal coordination factors to realize Pareto improvement, reduce carbon emissions and boost social welfare. Results show that an optimal direct sales ratio maximizes supply chain profit under decentralization; bidirectional cost sharing aligns carbon emissions and sales efforts with centralized decision-making; the integrated mechanism minimizes carbon emissions and sales efforts with minimal government subsidies. This paper innovates by proposing the integrated coordination mechanism and exploring the optimal combination of key factors to achieve a multi-win situation.

In this paper, we are devoted to investigating a parametric setvalued variational-hemivariational inequality (PSVHI), where its data including the constraint set and the involved mappings or functions are perturbed by two independent parameters. By using the Clarke subdifferential of the involved locally Lipschitz continuous function, we introduce a gap function for PSVHI and derive a kind of local continuity for the gap function under the assumption of Hölder continuity for the involved mappings or functions, based on which an error bound result for PSVHI is established under the condition of stable (ϕ; h)-pseudomonotonicity for the involved set-valued mapping. Then, with the assumption of solvability for PSVHI, we prove the Hölder continuity of the set-valued solution mapping of PSVHI with the help of the obtained error bound result and the local continuity for the gap function.

In the live streaming (LS) environment, there are currently two types of streamers: human influencer streamers and virtual streamers. The time and energy of influencer streamers are limited, making it difficult to meet the audiences’ continuous demand for LS. Therefore, many manufacturers, while collaborating with influencer streamers, have also introduced virtual streamers. The manufacturers have two options: have influencer streamers and virtual streamers appear on the same screen (S-mode), or to arrange them live-stream in different time slots (peak-shifting LS, P-mode). For an influencer streamer, he can choose between different contracts: revenue-sharing contract (RS-contract) and hybrid contract (H-contract). In this paper, we investigate the manufacturer’s choice of LS modes, with considering the influencer streamer’s contract strategies. Our research indicates that the manufacturer’s choice of LS modes depends on the technical cost of virtual live streaming (VLS). Additionally, under the same technical cost, an increase in the platform commission rate will prompt the manufacturer to choose the P-mode, while the growth in the influencer streamer’s traffic will encourage it to choose the S-mode. The influencer streamer’s choice of contracts is influenced by the manufacturer’s LS strategy. The influencer streamer can perform better under either contract, depending on specific conditions.

This research presents a multi-period, two-stage stochastic mobile facility (MF) location problem (2S-SMFLP) related to fresh food harvesting. The objective is to determine the optimal locations for MFs and allocate personnel prior to the delivery of fresh food to designated facilities. This comprehensive methodology encompasses two levels: the design level, which addresses the location of MFs, staffing, and mobile routing decisions, and the operational level, which focuses on transportation and penalties for non-compliance. We calibrate decisions to minimize expected costs associated with the location and transportation scheme within the harvesting system, accounting for uncertain yields. This study considers a planning horizon characterized by fluctuating yields of fresh produce across multiple periods. As a result, the 2S-SMFLP under stochastic yield presents a complex multistage decision problem. We employ a two-stage stochastic harvesting approach with linear recourse, which is suitable given the strategic nature of the problem. The size of the stochastic set is adjusted using the sample average approximation (SAA) method. The Benders Decomposition (BD) technique is utilized to efficiently decompose and solve the two-stage stochastic model. Computational experiments are conducted based on various distributions to validate the model. We compare the deterministic harvesting model with the stochastic harvesting model for fresh food. The results of the computations demonstrate that this method holds practical value for the harvesting of fresh food.