We studied the single-source capacitated facility location problem (SSCFLP), which can also be viewed as a representative structured binary optimization model with assignment, activation, and capacity constraints. The main difficulty comes from the discrete structure of the model and the coupling constraints, which make large-scale instances hard to solve. To exploit this structure, we introduced a split formulation that separates the original variables into two blocks connected by an equality constraint. For the reformulated model, we proposed an augmented Lagrangian decomposition method with tractable primal subproblems. We further showed that the augmented Lagrangian dual has zero duality gap with the original binary problem when the penalty parameter is sufficiently large. This result provides a theoretical basis for applying the augmented Lagrangian method to this discrete optimization problem. In addition, we used a primal recovery step and a final refinement step to improve feasible solutions. Numerical results demonstrated that the proposed method can produce high-quality feasible solutions on both synthetic and benchmark instances, especially for large instances in time-limited settings.
E-commerce and last-mile growth intensify routing demands, while deterministic demand, independent distribution, and single-mode rescheduling hinder efficiency and realism. To address these issues, we proposed a multi-depot capacity-constrained vehicle routing problem with stochastic demands and joint distribution (MCVRPSD-JD), embedding adaptive skip, reassigning, and redistributing redispatching strategies for failed delivery points. The model integrates chance-constrained programming with cooperative scheduling mechanisms to enhance vehicle utilization and mitigate capacity imbalance under stochastic demand. A hybrid variable neighborhood descent scatter search (HVNDSS) algorithm is developed to balance global search and local refinement across optimization stages. Experimental results demonstrated that the proposed method outperformed baseline algorithms, reducing solution error to 0.17% while achieving notable distribution cost savings. Compared with independent distribution, the joint distribution model lowered costs by an average of 15.91% and reduced failure points. This study contributes a scalable framework for stochastic logistics, offering practical insights for cost-efficient urban distribution systems.
Based on nonlinear model predictive control (NMPC), this paper proposes a novel gait generation method for robot turning movement. Unlike traditional approaches that treat the robot's heading as a fixed parameter, this method explicitly incorporates the sequence of heading angles into the NMPC framework, which enables the unified optimization of the center of mass (CoM) trajectory, footstep sequence, and heading angle sequence. This design allows the robot to adapt to relatively high speeds and large turning angles. Finally, the proposed method was validated through simulations of the BHR-FCR humanoid robot model in the CoppeliaSim. The results demonstrate that the robot can stably and smoothly execute turning movements at speeds up to 0.75 m/s in response to velocity commands, which confirms the effectiveness of the generated gait sequences.
This study examines pricing and green innovation decisions in an e-retail platform supply chain where a national brand (NB) competes directly with a platform-owned private brand (PB). Using a Stackelberg game framework, we analyze four scenarios: No innovation, NB-only innovation, PB-only innovation, and bilateral innovation. The key findings are as follows. Network externalities consistently benefit all supply chain members and enhance green innovation levels across scenarios, but their impact on retail prices is scenario-dependent. The NB manufacturer achieves its highest profit under NB-only innovation, whereas the e-retail platform prefers bilateral innovation, which constitutes the unique Nash equilibrium. This misalignment creates a green innovation prisoner's dilemma: Although bilateral innovation maximizes the total supply chain profit, the manufacturer earns less than under NB-only innovation. Moreover, standalone green innovation by either party yields higher green levels than bilateral innovation. These findings suggest that coordinating bilateral green innovation may require profit-sharing mechanisms, and that innovation strategies should be tailored to the market conditions.
This study investigates the problem of multitype scarce resource distribution using electric vehicles, incorporating practical factors including hybrid time windows, cross-period delivery, and priority-based allocation. We develop a mixed integer programming model to minimize the total distribution costs subject to limits on electric vehicle routing, hybrid time windows, priority, cross-period assignment, load capacity, and battery swapping. A tailored genetic algorithm is designed to solve the proposed model. Numerical experiments demonstrate the model's effectiveness and superiority over benchmark scenarios-including models without priority, demand splitting, battery swapping stations, and region partitioning, as well as intraperiod and soft time windows-in terms of both the distribution cost and demand satisfaction rate. To further balance service fairness across all customers, we introduce an adaptive dynamic priority mechanism based on the cumulative demand satisfaction rate and service start time, and propose a epsilon-adaptive dynamic priority-based multitype scarce resource distribution model with cross-period hybrid time windows. The results show that the enhanced model significantly improves equity performance while maintaining operational efficiency.
This paper investigates a single-machine scheduling problem that integrates cumulative time-dependent learning effects with non-renewable resource allocation, where job processing times are controllable through resource investment. The actual processing time of each job is modeled as a nonlinear function of the allocated resource amount and the cumulative normal processing times of previously processed jobs, thereby reflecting proficiency gains in modern manufacturing environments. The objective is to minimize a weighted aggregate cost consisting of total weighted completion time and total resource consumption. By establishing convexity with respect to the resource variables, we derive an analytical optimal resource allocation policy for any fixed job sequence. This result transforms the original joint continuous-discrete optimization problem into an equivalent combinatorial sequencing problem. To solve the resulting problem, we develop an exact branch-and-bound (B&B) algorithm with a lower-bound scheme based on the monotonicity of the learning term. For larger instances, simulated annealing, tabu search, and genetic algorithms are developed to obtain high-quality feasible solutions within limited computational time. The computational results evaluate the pruning efficiency of the B&B algorithm and the stability of the proposed metaheuristics. The analysis also shows that, under strong learning effects, the classical WSPT rule is no longer universally dominant; in some cases, SPT-type sequences may be preferable. These findings provide useful insights for scheduling decisions in labor-intensive and environments.
