With a decentral and global economy, distributed scheduling problems are getting a lot of attention. This paper addresses a distributed flexible job shop scheduling problem (DFJSP) with minimizing makespan, in which three subproblems, namely operations sequencing, factory selection and machine selection must be determined. To solve the DFJSP, a novel mixed-integer linear programming (MILP) model is first developed, which can solve the small-scaled instances to optimality. Since the NP-hard characteristic of DFJSP, a hybrid algorithm (GA-VNS-CP) of genetic algorithm (GA), variable neighborhood search (VNS) and constraint programming (CP). Specifically, the GA-VNS-CP is divided into two stages. The first stage uses the hybrid meta-heuristic algorithms of GA and VNS (GA-VNS), and the VNS is designed to improve the local search ability of GA. In GA-VNS, the encoding only considers the factory selection and the operations sequencing problems, and the machine selection problem is determined by the decoding rule. Because the solution space may be limited by the decoding rule, the second stage uses the CP to extend the solution and further improve the solution. Numerical experiments based on benchmark instances are conducted to evaluate the effectiveness of the MILP model, VNS, CP and GA-VNS-CP. The experimental results show effectiveness of the MILP model, VNS and CP. Moreover, the GA-VNS-CP algorithm has better performance than traditional algorithms and improves 6 current best solutions for benchmark instances

With the annual promotion of the international “dual carbon” goals, countries attach great importance to the development and innovation of clean energy. The United States, Japan, and China have all created many policies for the research and market development of photovoltaic energy. This article incorporates market dynamic regulation capability into a two-dimensional system of government subsidy policies and photovoltaic revenue, constructs a three-dimensional dynamic nonlinear model based on market dynamic regulation capability, government subsidies, and enterprise revenue, and numerically simulates and analyzes the impact of parameter and initial value changes in the equation on enterprise revenue. The market dynamic regulation capability is obtained from Chaotic attractors and dynamic evolution graphs of the nonlinear evolution between government subsidies and corporate profits in different scenarios. Research has shown that: (1) Rapidly improving the dynamic regulation ability of the market cannot continuously increase the revenue of the photovoltaic industry; (2) The changes in market dynamics affect the dependence of enterprises on government subsidies; (3) The demand for government subsidies by enterprises gradually decreases with the increase of their own profits.

With the continuous upgrading of industrial technology and information technology, consumers can deeply participate in the whole life cycle of products and realize customized production. These unprecedented changes have brought consumers and manufacturers closer together, resulting in the intelligent business model of "Internet + Customized Production" and "Customer to Manufacturer (C2M)". C2M has been adopted by more and more companies. However, the transition from traditional business models to C2M is a problem that every company must face and solve. Personalized orders of many varieties and small lots put enormous pressure on the production of mainly labor-intensive electronic assembly companies. The theoretical findings of Industry 4.0 and Lean Manufacturing show that people play a central role in assembly operations. As an important element of the production system, worker scheduling has a direct impact on delivery time and cost. Worker scheduling requires not only matching people to jobs, but also considering flexible employment. According to the "Learning Curve" theory, workers with learning potential can continuously enrich their skills and work efficiency will show dynamic changes. Therefore, under the condition of shortest order delivery time and lowest cost, worker scheduling considering the learning effect becomes a challenge for enterprise decision makers. Firstly, the production method of manufacturing industry in C2M environment is studied. Then, based on single-skill task and multi-skill task, respectively, a learning curve-based model of dynamic change in worker skill level is constructed. And this model is used as the input of the assembly line worker scheduling model. Secondly, an Elite Non-dominant Sorting Whale Optimization Algorithm (ENS-WOA) is designed for this multi-objective optimization problem. The correctness and feasibility of the proposed algorithm are verified by selecting classical arithmetic cases for experimental comparison with other algorithms. Finally, the established worker efficiency change model, worker scheduling model and the proposed algorithm are applied to optimize the assembly line of water pump products of Company B, which is being transformed to C2M, and solved by MATLAB software. The results show that the model proposed in this paper is effective, stable and practical compared with the worker costs and delivery period required to complete the order in the original assembly line. Worker costs were reduced by 29.02% and orders were completed approximately 10 days earlier.

With the increasing complexity of the distribution environment, customers usually propose higher requirements, such as independent loading of local and foreign cold-chain items in the event of an emergency. Moreover, minimum fuel volume plays an important role in the process of transportation with different speeds and different kinds of vehicles. In this paper, we present a new mathematical model to characterize cold-chain vehicle routing optimization with independent loading of local and foreign items and minimum fuel volume. To address the above mathematical model, an extended particle swarm optimization (PSO) algorithm is proposed by combining original PSO with 2-opt optimization to improve diversity and reduce convergence speed. Six sets of experiments are set to verify the practical performance and stability of the extended PSO algorithm based on three standard datasets of C201, R201, and RC201 from Solomon.

To promote the development of the new energy vehicle industry, China has introduced many subsidy policies. Existing policies rarely consider the difference in market share of new energy vehicle enterprises, but the difference in market share will directly affect consumer demand, and then affect the development of the new energy vehicle industry. Therefore, we consider the difference of the market share and endurance of the new energy vehicle firms at the same time, establishing a Stackelberg model and considering three most common subsidy forms, which are quantity-based subsidies, price-based subsidies, and endurance-based subsidies to derive the optimal differentiated subsidies of the government. The analysis of this paper shows that for the new energy vehicle firms with different market share and endurance, differentiated subsidies can achieve higher social welfare. In addition, for any subsidy form of the sale-based subsidies, price-based subsidies, and endurance-based subsidies, the final cost for consumers will be reduced, and the total sales quantity of the new energy vehicles in the market will increase, but the profits of firms and the sales quantity of one firm could increase or decrease. Lastly, under the assumption of this paper, the optimal price of both firms and social welfare are the same under the three aforementioned subsidy forms.

As the expert gear of the emergency rescue system, drones are frequently utilized to distribute supplies following a calamity. The cost and effectiveness of rescue efforts as well as equitable distribution should be taken into account when allocating emergency supplies to disaster-affected areas. This work explores the emergency material allocation problem for truck-drone joint transportation with dynamic energy restrictions based on taking the fairness of emergency material allocation into consideration. In order to guarantee the equitable distribution of materials, the psychological stress experienced by the victims at each catastrophe site is measured using the relative deprivation cost. An adaptive large-scale neighborhood search method serves as the foundation for the creation of a two-stage heuristic algorithm, which reduces the overall cost of the system. The integer programming model MIP is built for this purpose. The research findings can serve as a useful guide for developing a just and effective emergency drone rescue system, and the testing results demonstrate the viability and effectiveness of the two-stage heuristic algorithm.

The hybrid flow shop scheduling problem (HFSP) is an extension of the classic flow shop scheduling problem and widely exists in real industrial production systems. In real production, sequence-dependent setup times (SDST) are very important and cannot be neglected. Therefore, this study focuses HFSP with SDST (HFSP-SDST) to minimize the makespan. To solve this problem, a mixed-integer linear programming (MILP) model to obtain the optimal solutions for small-scale instances is proposed. Given the NP-hard characteristics of HFSP-SDST, an improved artificial bee colony (IABC) algorithm is developed to efficiently solve large-sized instances. In IABC, permutation encoding is used and a hybrid representation that combines forward decoding and backward decoding methods is designed. To search for the solution space that is not included in the encoding and decoding, a problem-specific local search strategy is developed to enlarge the solution space. Experiments are conducted to evaluate the effectiveness of the MILP model and IABC. The results indicate that the proposed MILP model can find the optimal solutions for small-scale instances. The proposed IABC performs much better than the existing algorithms and improves 61 current best solutions of benchmark instances.

This paper analyzes practical production characteristics, including customer's stringent quality requirements and uncertain processing time in aircraft shaft parts manufacturing. Considering the above characteristics, we propose a multi-objective fuzzy aircraft shaft parts production scheduling problem considering the maximization of production quality. We define this problem as a multi-objective fuzzy flexible job shop scheduling problem (MO-fFJSP) with fuzzy processing time. To address this problem, we developed an improved multi-objective spider monkey optimization (IMOSMO) algorithm. IMOSMO integrates strategies such as genetic operators, variable neighborhood search and Pareto optimization theory on the framework of the conventional Spider Monkey Optimization (SMO) framework and discretize the continuous SMO algorithm to solve MO-fFJSP. To enhance the efficiency of the algorithm, we further adjust the sequence of the local leader learning phase and the global leader learning phase within the proposed IMOSMO framework. We conduct a comparative analysis between the performance of IMOSMO and NSGA-Ⅱ using 28 cases of varying scales. The computational results demonstrate the superiority of our algorithm over NSGA-Ⅱ in terms of both solution diversity and quality. Moreover, the performance of the proposed algorithm upgrades as the problem scale increases.

In the context of multichannel retailing, the phenomenon of web-rooming, where consumers research online and purchase offline, has become widespread. Therefore, we consider supply chain consisting of a manufacturer, an e-commerce platform, and an offline retailer, we study the impact of consumer web-rooming effect on the three sales modes of online channels, which are directly operated by the manufacturer, resold by the e-commerce platform, or co-exist with direct operation and resale, and comparatively analyze the pricing, demand, and profit of each channel under the three modes. The conditions for optimal pricing decisions are further explored through numerical simulation. It is found that profit always increases whether the online channel is opened by the manufacturer or the e-commerce company. The coexistence of direct sales and resale does not always increase profit for offline retailers, which must be discussed in the context of the sales model before channel expansion. The existence of web-rooming not only affects the decision-making of manufacturers and e-commerce platforms, but also always harms the interests of e-commerce platforms, and as the intensity of web-rooming deepens, the revenue of e-commerce platforms becomes smaller. Offline retailers benefit from web-rooming and experience a slowdown in profit growth as the intensity of the phenomenon increases. For manufacturers, the impact of changes in the intensity of the web-rooming is analyzed in relation to platform commission rates and online retail prices.

This paper considers a dual-channel supply chain with two members, comprising a manufacturer and an online platform. We mainly investigate the influence of various key system variables on manufacturer encroachment strategy and all members’ optimal decisions through Stackelberg game models. Our findings show that, regardless of the size of each parameter, the encroachment strategy is always optimal to the manufacturer; the manufacturer may be motivated to choose the direct selling channel and the platform may opt for the agency selling channel due to a high commission rate. Moreover, when the inter-channel substitution rate is high, the encroachment strategy has a diminishing positive effect on the manufacturer and an increasing negative effect on the platform so that the platform may temporarily benefit from the manufacturer encroachment; in cases where the inter-channel substitution rate is not high, the encroachment strategy always yields advantages for the manufacturer while causing disadvantages for the platform. In addition, if the elasticity coefficient is large, both the manufacturer and the platform are inclined to the reselling channel, that is, if the platform service cost is high, it is advisable for the platform to reduce its investment of service to avoid negative effect.