Airport shuttle bus operations are strongly affected by imbalanced directional demand, heterogeneous routes, electric bus charging requirements, and flight-induced service pressure. This paper investigates an integrated vehicle-crew scheduling problem for electric airport shuttle buses with multi-route coordination, time-dependent travel speeds, and flexible service start times. A flight-induced service pressure index (SPI) is developed to measure the temporal concentration of flight arrivals and departures and to define trip-specific time-window flexibility. A mixed-integer linear programming model is formulated to jointly optimize vehicle schedules, charging decisions, service start times, and driver duties. The model considers trip coverage, battery feasibility, vehicle-driver synchronization, working-time limits, and workload-balance requirements. To solve large-scale instances, a two-stage variable neighborhood search algorithm is designed, in which electric bus paths, charging decisions, and service start-time adjustments are first optimized, and driver duties are then constructed and improved. Computational experiments are conducted on instances derived from real-world shuttle bus operations at Xianyang International Airport. The results show that the valid inequalities reduce the mean CPLEX solution time from 107.70 s to 25.46 s. The proposed algorithm achieves an average objective gap of 2.08% relative to CPLEX on small-scale instances. It also reduces the objective value by 2.90% compared with ALNS on large-scale instances. The results further show that multi-route collaboration reduces operating costs and balances workloads, while SPI-based time windows enhance service stability during flight-intensive periods.
The stochastic recursive gradient algorithm (SARAH) has garnered considerable attention owing to its implementation of a straightforward recursive framework for stochastic gradient updates. Motivated by this, we propose to integrate the importance sampling strategy with mini-batch techniques into the SARAH framework, developing a variant termed SARAH-MI-RBB. During each inner iteration of SARAH-MI-RBB, the mini-batch technique and importance sampling method are employed to dynamically adjust the Barzilai-Borwein (BB) step size and update the iterates. We establish the linear convergence in expectation of the outer iterates to the unique optimal solution for strongly convex problems. Furthermore, we establish the complexity analysis of the algorithm. Numerical experiments demonstrate that the proposed algorithm outperforms existing state-of-the-art methods in its class.
Last-mile delivery platforms operating in quick-commerce settings face an inherent tension between operational efficiency and equitable distribution of work among riders. We propose a multi-objective optimization framework for the dynamic, real-time assignment of delivery orders to a rider fleet, governed by a tunable parameter [Formula: see text] that interpolates between pure efficiency and perfect fairness. This reduces the dual objective to a unified minimum-cost assignment problem, solved at scale via a two-stage architecture that decouples route generation (VRP) from optimal rider assignment (Hungarian algorithm). Validated on real-world trip data from the NYC Yellow Taxi dataset over a simulated 24-hour horizon, the framework demonstrates that a 4–5[Formula: see text]% increase in mean delivery time relative to an efficiency-only baseline reduces earnings inequality measured by the Gini coefficient by 33[Formula: see text]%. The empirically convex shape of the fairness-efficiency frontier reveals that early gains in fairness are nearly cost-free, while the marginal efficiency cost accelerates only as perfect equality is approached. This convexity implies the existence of a principled operating point at which platforms capture the bulk of the equity benefit while preserving service guarantees, offering operators a transparent and quantifiable lever to balance customer service levels against sustainable rider welfare, a trade-off of growing regulatory significance in the gig economy.
This study examines how artificial intelligence (AI) adoption by manufacturers or retailers impacts operational decisions and expected profits in a two-tier supply chain. Through the newsvendor framework, we analyze three scenarios: no adoption (N), manufacturer adoption (MA), and retailer adoption (RA). Our findings indicate that AI adoption contributes to enhancing service levels and order quantities. However, the adopting party does not always secure higher profits, as benefits are partially transferred to the non-adopting counterpart through free-riding effects. By comparison, we observe that manufacturer adoption is preferable when its cost-saving advantages exceed the demand-enhancing advantages of retailer adoption, and vice versa. Furthermore, we explore the impact of stockout on the effectiveness of AI adoption. Our results show that optimal order quantities increase with the intelligence level of AI, while the presence of stockout costs weakens this relationship. Interestingly, stockout costs reduce the positive effect of AI adoption on manufacturers’ profits but amplify its benefits for retailers. Finally, we examine the scenario where both the manufacturer and the retailer adopt AI (MRA) and find that simultaneous adoption is not necessarily a better choice.
A scheduling problem comprising time-dependent durations, sequence-dependent setup times, batch scheduling, precedence constraints and job selection is studied. Applications of the scheduling problem could be in the testing of aircraft in a multifunctional testing facility, the distribution of resources to different areas and the repairing and maintenance of vehicles in a workshop. An integer programming formulation for this problem is presented. As CPLEX was unable to find a feasible solution for the majority of the generated test cases within one hour, metaheuristics such as variable neighborhood search (VNS) and tabu search have been developed, employing eight neighborhood strategies to search for solutions. Tabu search performs the best in solving the scheduling problem. It was able to solve all test cases while CPLEX and VNS could solve only 25% of the test cases. In terms of total weighted profit, tabu search performed 40% and 9% better than CPLEX and VNS, respectively, for test cases solvable by all three algorithms.
In this paper, we investigate multi-agent alliance strategies in the emerging "autonomous-vehicle (AV) + courier" delivery system for instant retail. Motivated by the rapid expansion of instant retail and the widespread industry practice, we develop five game-theoretic decision models that capture the optimal options: a benchmark non-cooperative mode and four cooperative modes among the instant retailer, the AV and courier delivery firms. It turns out that cooperative models consistently yield higher aggregate service levels and market demand than the non-cooperative benchmark. Besides, any member is willing to form an alliance that yields higher joint profit compared with the non-cooperation mode. Additionally, alliance preferences depend on costs: retailers prefer the higher-cost partner to mitigate double marginalization, while AV and courier firms prefer allying with the retailer to increase their decision power. Our results shed light on alliance formation and governance in AV-enabled last-mile systems and provide theoretical guidance for designing cooperative arrangements that improve service performance and economic outcomes in instant retail.
In this paper, a new bundle trust region method for nonsmooth and nonconvex sem-infinite programming (SIP) problems is presented. This newly developed method imposes weaker assumptions on the structure of the objective function in comparison with the existing numerical methods for solving SIP. Furthermore, in contrast to most of the existing bundle methods, such as proximal bundle methods, level bundle methods, and bundle trust region methods, which all necessitate the solution of quadratic programming subproblems, the new algorithm proposed herein only requires the solution of linear programming subproblems. This substitution can reduce the computational cost. The new bundle trust region method addresses the challenge of SIP having infinitely many constraints by leveraging a relaxation approach to derive an upper bound problem of SIP. Based on this upper bound problem, a local approximation model is constructed. At each iteration, by virtue of the approximation model, the trust region technique, and the infinity norm, a linear subproblem is formulated. Under reasonable assumptions, the iteration sequence generated by the new algorithm converges to an epsilon-KKT point of the SIP. The numerical results confirm the effectiveness of the new algorithm.
In this paper, a kind of stochastic tensor absolute value equation with discrete distribution is considered. Using the expected value method in the discrete probability space, we transform it into a minimization problem with non-negative constraints. To solve this constrained optimization problem, we develop a projected trust region method which combines the quasi-Newton method with the trust region method. And the convergence result is also established under mild conditions. Finally, we present some numerical experiments to illustrate the effectiveness of our method.
This paper explores the application of differential privacy (DP) to alternating direction method of multipliers (ADMM) with symmetric proximal strategy for convex (non)smooth federated learning problems. We introduce a Differential Privacy Symmetric ProximalADMMAlgorithm (DP-SPADMM) that incorporates time-varying penalty perturbations at each local client to ensure (ϵ, δ)-differential privacy. Utilizing the Gaussian mechanism and the relationship between Rényi Differential Privacy (RDP) and (ϵ, δ)-DP, we perform a vital privacy analysis and establish the convergence for the proposed algorithm. Experimental results on two real-world datasets demonstrate the improved performance and faster convergence of the proposed algorithm.
This study deals with an [Formula: see text]-machine flowshop problem with the DeJong’s learning effect, in which [Formula: see text] is the number of machines. The goal is to identify a permutation that minimizes the maximum completion time, i.e., the makespan. We derive several properties, lower bounds, and initial upper bounds, and then propose a branch-and-bound algorithm. Additionally, we develop several heuristic algorithms. Computational tests are presented to evaluate the effectiveness and performance of these algorithms.
As e-commerce platforms become a dominant retail channel and environmental sustainability becomes an urgent managerial concern, firms increasingly face the dual challenge of coordinating green initiatives and selecting appropriate sales modes. Motivated by this practical issue, this paper investigates the strategic interplay between green cooperation and sales mode selection in a platform-based supply chain that comprises a manufacturer and an e-tailer, both engaged in green initiatives. We develop game-theoretic frameworks to examine how cooperation structures (non-cooperative vs. cooperative) and sales modes (wholesale vs. agency) influence firms’ outcomes. We find that green cooperation always raises the green effort levels and market demand, but its impact on each firm’s profitability depends on their green investment efficiencies. A win–win outcome from cooperation emerges when the manufacturer’s green investment efficiency lies in an intermediate range. Besides, one firm’s increasing investment efficiency might hurt itself due to the free-rider effects enjoyed by the other firm. Furthermore, green cooperation alters the manufacturer’s preference for sales modes. Without cooperation, when the e-tailer’s green investment efficiency is high enough, the manufacturer prefers wholesale mode at very low or very high commission rates and finds agency mode advantageous only at intermediate commission rates. However, with cooperation, agency mode becomes optimal at low commission rates and wholesale mode is preferable at high commission rates. These findings provide managerial insights for firms on when to pursue green cooperation and how to select the suitable sales mode.
A retailer’s capital constraints not only influence its own operations but also significantly affect the operational decisions of its competitors. This study focuses on two competing retailers selling homogeneous products in the same market, who engage in both service-level and retail-price competition. When a retailer faces a capital constraint, it resorts to external financing. The core objective is to analyze how capital constraints affect competitive dynamics and profitability. The findings reveal that under mild capital constraints, profits may be higher than when retailers have ample capital. Additionally, when one retailer is capital-constrained and the interest rate is high, the constrained retailer with smaller potential market demand may set a higher retail price than its larger rival, depending on the service cost coefficient. Moreover, when the larger retailer suffers a severe capital constraint, the smaller retailer can achieve a profit advantage: if the small retailer is well-funded, it does so by raising its service and price; if the small retailer is also mildly constrained but much better off than the larger rival, it does so by keeping low service and low price and relying on its cost advantage.
Agricultural supply chains have been experiencing an increasing number of disruptions due to natural disasters, extreme weather events, geopolitical disturbances, and animal or plant diseases, amplifying concerns about the resilience of food supply. This paper focuses on the supply of commercial seeds, the key input into agricultural supply chains. We examine how supply chain disruptions affect the optimal production decisions of seed manufacturers, the expected revenue of farmers that are part of the production process, and the resilience of food supply. We model the seed production process as a discrete-time stochastic dynamic optimization problem where, in each period, the seed manufacturer solves an optimization problem with two stages: The planting stage, where the manufacturer chooses the quantity of hybrid seeds to produce through a network of independent farmers, and the allocation stage, where the manufacturer allocates the resulting yield to different markets with varying profit margins. We then examine how changes in the likelihood of a disruptive event affect the supply chain’s performance. We prove that, as the probability of disruption increases, [Formula: see text] the manufacturer’s expected profits decrease while the optimal planting quantity grows; [Formula: see text] the expected total yield decreases, reducing the expected profit of the farmers who are under contract with the manufacturer; [Formula: see text] the expected allocation quantity to different markets decreases with a more significant drop in smallholder markets. Finally, we present a simulation model calibrated to industry data where we find that even a small increase in the likelihood of supply volatility can dramatically change the optimal production decisions and have significantly negative effects on the profitability of commercial seeds, on the availability of seeds in smallholder markets, on the profits earned by contacted farmers, and on the value of typical operational improvements such as delayed differentiation.
This paper addresses the supply chain financing and ordering problem, where the retailer acts as an intermediary to provide guarantees for the supplier's loans. Traditional supply chain financing investigations usually assume that the demand distribution is known, whereas such complete information cannot be obtained for problems with high uncertainty. In addition, high uncertainty often makes decision-makers pay more attention to the robustness of the strategy. To address these challenges, this paper combines subjective judgment with robust optimization, using fuzzy sets to express expert judgment, and constructs a new robust optimization objective. This optimization objective incorporates risk aversion through a worst-case optimization framework, which can be more in line with decision-makers' behavioral characteristics. Through comparative analysis, it is concluded that the fuzzy robust ordering strategy proposed in this paper is more reasonable than the traditional optimal expected strategy and the Max-Min robust strategy. Also, it mitigates the extreme conservatism of traditional robust models, providing a more pragmatic approach to handling uncertainty.
The continued development of media platforms has given rise to alternative revenue models. Unlike the advertising-sponsored strategy, under which a media platform earns revenue exclusively from advertisers, the freemium strategy enables the platform to generate revenue from both consumers and advertisers by offering a paid ad-free subscription tier and a free ad-supported tier. This study develops a game-theoretic framework to compare these two revenue models while incorporating content quality into the analysis. We find that the platform adopts the freemium strategy when consumers’ price sensitivity is low, but prefers the advertising-sponsored strategy when price sensitivity is high. With respect to content provision, the freemium strategy does not necessarily lead to greater investment in content quality. Although subscriptions broaden the platform’s revenue sources, content quality exceeds that under the advertising-sponsored strategy only when the freemium strategy yields a sufficiently large profit advantage. From the advertiser’s perspective, the freemium strategy does not necessarily reduce profit. In particular, advertiser profit under the freemium strategy first decreases and then increases as consumers’ price sensitivity rises. When price sensitivity is low, it even exceeds that under the advertising-sponsored strategy. In terms of joint outcomes, the freemium strategy can increase profits for both the platform and the advertiser when consumers’ price sensitivity is low.
This paper focuses on the total quantity and price of China-US bilateral trade and conducts a time series analysis by comprehensively using 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.
Online shopping festivals (OSFs) are among the most important promotional activities in the online retail industry. While OSFs offer customers significant discounts and enhance online retailers’ performance, they also cause severe logistics challenges. This paper focuses on the operational management of OSFs. To help online retailers increase profits and mitigate logistics challenges, we examine the solution of jointly considering the product pricing, temporary warehouse location, and order fulfillment operations. We develop an optimization model for the problem which is shown to be NP-hard. An efficient solution method is proposed to obtain near-optimal solutions within reasonable computational time. Extensive numerical experiments are conducted to evaluate the method and solutions. By using the optimization model, we address a number of crucial questions emerging from the OSFs and derive managerial insights. For example, we find that the popular strategy that charges customers a distance-dependent fee for order shipment is suboptimal in most cases, since such a fee would largely limit online retailers to adjust the demand of customers, especially those in remote areas.
Measuring productivity is crucial for analyzing organizational performance and assessing development. Malmquist-Luenberger productivity index (MLPI) is a prominent method for evaluating Total factor productivity (TFP), accounting for both desirable and undesirable outputs. This study advances productivity analysis through the development of an advanced MLPI model within a network DEA framework (NMLPI), while employing window analysis separately to assess efficiency patterns across time periods. Using a directional distance function (DDF)-based approach, the model handles negative data and undesirable resources, assessing efficiency and productivity across overlapping periods. To advance network DEA, Machine learning algorithms, including Support vector regression (SVR), Least-squares SVR, and Twin SVR, are integrated to reduce computational complexity and enable predictive analysis. The practical applicability of this approach (three-year window width) is demonstrated on the Information Technology (IT) sector (2018-23), structured as a two-stage system encompassing operational effectiveness and financial viability. Findings indicate that operational effectiveness significantly impacts overall efficiency compared to financial viability. Sensitivity analysis reveals the influence of variables on divisions and overall efficiency. Results demonstrate steady productivity growth in IT companies, driven by technological progress and efficiency improvements, reflected in high NMLPI, TCH (Technological change), and TECH (Technical efficiency change) values. The hybrid model delivers precise efficiency predictions with minimal error rates for the window W-4, validating its robustness and potential for strategic decision-making.
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.
