Optimal carbon reduction level and ordering quantity under financial constraints

Carbon tax policy is widely adopted by many countries to curb carbon emissions. In the context of carbon tax policy, firms have more incentive to improve carbon reduction levels by reducing their carbon tax costs. However, firms need to bear carbon reduction costs that may cause shortage of capital. Thus, firms may face problems of financial constraints, which may demotivate firms to produce greener products. To address the decision‐making challenges of firms in the contexts of carbon tax policy and financial constraints, we consider a supply chain with a manufacturer who produces green products and a retailer who sells these products. Our study develops five models to investigate the two firms’ optimal wholesale price, carbon reduction level and ordering quantity, according to the manufacturer and retailer with or without financial constraints. Our goal in this study is to explore how carbon tax policy and banks’ interest rates affect the profits of the two firms, supply chain and consumer surplus. Certain managerial insights are obtained as follows. We demonstrate that carbon tax policy and banks’ interest rates demotivate the manufacturer to produce greener products and demotivate the retailer to order more products. If the interest rate to the manufacturer (retailer) is relatively low, then the manufacturer with financial constraint benefits (harms) the consumers compared with the retailer with financial constraint. Importantly, our analysis suggests that carbon tax policy harms the firms but benefits consumers, and the government in some conditions should reduce unit carbon tax.     

The generalized discrete ‐centroid problem

The ‐centroid problem or leader–follower problem is generalized considering different customer choice rules where a customer may use facilities belonging to different firms, if the difference in travel distance (or time) is small enough. Assuming essential goods, some particular customer choice rules are analyzed. Linear programming formulations for the generalized ‐medianoid and ‐centroid problems are presented and an exact solution approach is applied. Some computational examples are included.     

防振条约束失效对蒸汽发生器传热管面内流弹失稳的影响研究

根据防振条布置以及面内支承连续失效个数，将防振条面内约束失效分析划分为多种工况，分析了不同工况下面内约束失效对传热管面内模态的影响，采用各位置阻尼在振型函数上进行加权平均的方法计算了各阶模态的阻尼比，进而研究了防振条面内不同约束对传热管面内流弹失稳的影响。分析结果表明，随着面内支承连续失效位置的增多，弯管段面内首阶模态频率不断降低，出现在弯管段的振型越加明显；弯管段面内首阶模态不一定是最大流弹失稳比值出现的模态，最大流弹失稳比值出现模态的振型几乎都出现在弯管段；随着面内支承连续失效位置的增多，面内流弹失稳比值不断增大，当连续3个及以上防振条面内约束失效时，将出现流弹失稳现象。     

虚拟手交互中约束类物体操作研究

虚拟手技术是虚拟现实技术中的一种交互方式，是指通过手势识别技术将人的真实手映射到虚拟环境中并与虚拟物体进行交互操作的人机交互方式。主要应用于虚拟训练、虚拟手术和虚拟装配等领域。对虚拟手交互的约束类对象进行了研究，提出了基于运动学的约束类物体操作方法，解决了阀门类有约束物体交互中虚拟手姿态不真实、操作不可控的问题。设计实验验证了基于运动学的方法能以符合实际操作的效果完成虚拟现实系统中的操作任务，可以应用到虚拟训练、虚拟装配等仿真平台。     

A cash-constrained stochastic inventory model with consumer loans and supplier credits: the case of nanostores in emerging markets

We consider a small traditional retailer that is managing its inventory under strict cash constraints, mainly because typically informal loans are offered to customers. These stores are widely present in emerging markets, and we refer to them as nanostores (also called ‘mom-and-pop stores’). As the suppliers require immediate payments for goods delivered, a nanostore can only replenish products to the level for which it has on-hand cash available. To improve delivery efficiency, a supplier might offer a nanostore credit for its replenishments. However, currently, suppliers are often reluctant to do so as these nanostores quickly go bankrupt or disappear, hence defaulting on all outstanding credits. The objective of this paper is to determine when it is beneficial to offer supplier credits. We propose a multi-period, stochastic inventory model, and numerically compare scenarios with and without supplier credits. Our study shows that even in the presence of this risk, suppliers often have good incentives to provide these credits, even if interest is not incurred. For this to hold, the operations of the retailer should be (a little) profitable in the first place, for which we provide analytical conditions.     

The constrained two-dimensional guillotine cutting problem with defects: an ILP formulation,a Benders decomposition and a CP-based algorithm

This paper addresses a variant of two-dimensional cutting problems in which rectangular small pieces are obtained by cutting a rectangular object through guillotine cuts. The characteristics of this variant are (i) the object contains some defects, and the items cut must be defective-free; (ii) there is an upper bound on the number of times an item type may appear in the cutting pattern; (iii) the number of guillotine stages is not restricted. This problem commonly arises in industrial settings that deal with defective materials, e.g. either by intrinsic characteristics of the object as in the cutting of wooden boards with knotholes in the wood industry, or by the manufacturing process as in the production of flat glass in the glass industry. We propose a compact integer linear programming (ILP) model for this problem based on the discretisation of the defective object. As solution methods for the problem, we develop a Benders decomposition algorithm and a constraint-programming (CP) based algorithm. We evaluate these approaches through computational experiments, using benchmark instances from the literature. The results show that the methods are effective on different types of instances and can find optimal solutions even for instances with dimensions close to real-size.     

Impact of industrial virtual power plant on renewable energy integration

An industrial park is one of the typical energy consumption schemes in power systems owing to the heavy industrial loads and their abilities to respond to electricity price changes. Therefore, energy integration in the industrial sector is significant. Accordingly, the concept of industrial virtual power plant (IVPP) has been proposed to deal with such problems. This study demonstrates an IVPP model to manage resources in an eco-industrial park, including energy storage systems, demand response (DR) resources, and distributed energies. In addition, fuzzy theory is used to change the deterministic system constraints to fuzzy parameters, considering the uncertainty of renewable energy, and fuzzy chance constraints are then set based on the credibility theory. By maximizing the daily benefits of the IVPP owners in day-ahead markets, DR and energy storage systems can be scheduled economically. Therefore, the energy between the grid and IVPP can flow in both directions: the surplus renewable electricity of IVPP can be sold in the market; when the electricity generated inside IVPP is not enough for its use, IVPP can also purchase power through the market. Case studies based on three wind-level scenarios demonstrate the efficient synergies between IVPP resources. The validation results indicate that IVPP can optimize the supply and demand resources in industrial parks, thereby decarbonizing the power systems.     

Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes

This study proposes a method of constructing type II generalized angulated elements (GAEs II) Hoberman sphere mechanisms on the basis of deployment axes that intersect at one point. First, the constraint conditions for inserting n GAEs II into n deployment axes to form a loop are given. The angle constraint conditions of the deployment axes are obtained through a series of linear equations. Second, the connection conditions of two GAEs II loops that share a common deployable center are discussed. Third, a flowchart of constructing the generalized Hoberman sphere mechanism on the basis of deployment axes is provided. Finally, four generalized Hoberman sphere mechanisms based on a fully enclosed regular hexahedron, arithmetic sequence axes, orthonormal arithmetic sequence axes, and spiral-like axes are constructed in accordance with the given arrangement of deployment axes that satisfy the constraint conditions to verify the feasibility of the proposed method.     

Isogeometric topology optimization based on energy penalization for symmetric structure

We present an energy penalization method for isogeometric topology optimization using moving morphable components (ITO–MMC), propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures, and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint. The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads. Topology optimization problems of asymmetric, bilateral symmetric, and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach. Compared with the conventional ITO–MMC, the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6% to 44.5% for the optimization of the asymmetric structure. For the ITO–MMC under a bilateral symmetric constraint, the proposed method can reduce the objective value by 5.6% and obtain a final optimized topology that has a clear boundary with decreased iterations. For the ITO–MMC under a periodic symmetric constraint, the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.     

Mathematical representation of radiality constraint in distribution system reconfiguration problem

Distribution systems are most commonly operated in a radial configuration for a number of reasons. In order to impose radiality constraint in the optimal network reconfiguration problem, an efficient algorithm is introduced in this paper based on graph theory. The paper shows that the normally followed methods of imposing radiality constraint within a mixed-integer programming formulation of the reconfiguration problem may not be sufficient. The minimum-loss network reconfiguration problem is formulated using different ways to impose radiality constraint. It is shown, through simulations, that the formulated problem using the proposed method for representing radiality constraint can be solved more efficiently, as opposed to the previously proposed formulations. This results in up to 30% reduction in CPU time for the test systems used in this study.