Secondary bifurcations in systems with all-to-all coupling. Part II.

In a recent paper Dias and Stewart studied the existence, branching geometry, and stability of secondary branches of equilibria in all-to-all coupled systems of differential equations, that is, equations that are equivariant under the permutation action of the symmetric group S_N. They consider the most general cubic order system of this type. Primary branches in such systems correspond to partitions of N into two parts p, q with p + q = N. Secondary branches correspond to partitions of N into three parts a, b, c with a + b + c = N. They prove that except in the case a = b = c secondary branches exist and are (generically) globally unstable in the cubic order system. In this work they realized that the cubic order system is too degenerate to provide secondary branches if a = b = c. In this paper we consider a general system of ordinary differential equations commuting with the permutation action of the symmetric group S_3n on R³ⁿ. Using singularity theory results, we find sufficient conditions on the coefficients of the fifth order truncation of the general smooth S_3n-equivariant vector field for the existence of a secondary branch of equilibria near the origin with S_n × S_n × S_n symmetry of such system. Moreover, we prove that under such conditions the solutions are (generically) globally unstable except in the cases where two tertiary bifurcations occur along the secondary branch. In these cases, the instability result holds only for the equilibria near the secondary bifurcation points. We show an example where stability between tertiary bifurcation points on the secondary branch occurs.     

Fractal properties of percolating film structures

We simulate nucleation and growth processes of thin films on the basis of the so-called rate equation approach allowing “atoms” to diffuse and rearrange whereby enhancing their co-ordination number. The resulting percolating structures are different from those obtained by the “pure” percolation model where “atomic diffusion” is not taken into account. However, the fractal properties for p = p_c are the same as for the percolation model with the fractal dimension of d_f = 1.896 and for random walks of d_w = 2.87. Moreover, d_f and d_w are independent on the diffusion time we choose for our simulations.     

A dynamic game with monopolist manufacturer and price-competing duopolist retailers

The paper considers a dynamic game with a single manufacturer who supplies two retailers. The manufacturer determines his production rate of a specific product, the rate of quality improvement efforts as well as the rate of advertising for the product. Each retailer controls her purchasing rate and the consumer sales price. Payments from a retailer to the manufacturer are determined by a wholesale price or a revenue-sharing scheme. The retailers operate in the same consumer market in which they compete in prices for the consumer demand. Nash equilibrium conditions are derived and numerical methods are employed to characterize equilibrium behavior of the players in a differential game of fixed and finite duration.     

基于风险规避的绿色供应链定价研究

为了解决风险规避型厂商在不同市场结构下的绿色供应链定价问题,首先以由一个风险规避的制造商和一个风险规避的零售商组成的二级绿色供应链为背景,考虑了消费者偏好、产品绿色度、厂商风险规避度等因素,构建厂商的期望效用函数,然后运用博弈论的方法建立了集中决策模型和三种分散决策模型。比较分析了这四种模型下的批发价格、产品绿色度和零售价格,并进一步分析了四种模型在制造商与零售商风险态度不同时的情况。最后通过MATLAB软件数值仿真研究了集中决策模型下的风险规避度对批发价格、产品绿色度、零售价格和供应链效用的影响以及产品绿色度对供应链效用的影响。仿真结果表明：在一定市场条件下,制造商风险规避对批发价格的影响程度要大于零售商,而对于产品绿色度、零售价格和供应链效用的影响程度是相同的且负向相关;同时,在固定制造商和零售商的风险规避度为0.5时,最优产品绿色度在3.3~3.4之间,最大产品绿色度为7.8。     

考虑消费者绿色偏好的竞争性闭环供应链生产决策研究

在消费者对绿色产品存在偏好的背景下,针对由1个绿色产品制造商、1个普通产品制造商以及1个零售商构成的竞争性闭环供应链系统,分别确定了在合作博弈和非合作博弈情形下的最优定价和绿色度决策,并分析了消费者绿色偏好、绿色投资系数和制造商竞争强度对供应链产品选择和各节点企业利润的影响。研究表明,产品零售价、绿色度、供应链企业的利润均与消费者绿色偏好呈正相关而与绿色投资系数呈负相关。制造商的利润随竞争强度增大而减小,零售商的利润却随之增大,并且非合作博弈下绿色产品制造商的利润要高于普通产品制造商。此外,通过数值算例验证了结论。     

Fractal structure and optical properties of semicontinuous silver films

Semicontinuous silver films, prepared by vacuum evaporation on substrate of KBr crystals, have been made with area coverage in the range 0.3–0.8. The morphology of the films were found to change with coverage p. At small or large coverage range, homogeneous films were observed, but when the coverage approaches a critical value p_c (p_c ≈ 0.65), the film was inhomogeneous. The topologic parameters of films such as mean size of cluster S_AV, correlation length ξ and fractal dimension D_f were measured. When the area coverage was close to p_c, S_AV and ξ rapidly diverged and a knee point appeared in the curve of D_f vs. p. The transmittance of films in mid-infrared wave-band (2.5–12.5 m) was measured. For homogeneous films, as wavelength increased, transmittance increased when p < p_c but decreased when p < p_c. On the other hand, transmittance was wavelength independent for inhomogeneous films. The optical percolation phenomenon is observed at a region where the fractal dimension D_f of the film was kept approximately constant while correlation length diverges. These experimental results were compared with existing theory and we interpret the effect of deposition and coalescence on the percolation parameters by considering the growth mechanism of a nano-structured metal film.     

考虑价格和时间敏感性需求的两周期供应链鲁棒优化模型

在不确定需求下,考虑需求的时间和价格敏感性,研究两周期供应链定价及订货联合决策问题。利用分段函数构建需求的价格和时间敏感性,并采用区间不确定集描述需求不确定性。根据制造商是否给予零售商回扣,分别建立主从对策鲁棒优化模型,并转化为可解的数学规划。结果表明,需求不确定性以及需求的时间和价格敏感性对双方的定价、订货和利润具有影响。具有回扣的主从策略使双方获得更高利润,需求的不确定性以及需求的时间和价格敏感性增加会降低双方利润。     

Magnetism of epitaxial Ru and Rh monolayers on graphite

Recently, Pfandzelter et al. (1995) reported the first observation of monolayer ferromagnetism of a 4d metal, namely in a Ru monolayer grown on graphite. Using the tight-binding linear-muffin-tin-orbital (TB-LMTO) method we have calculated the electronic and magnetic structure of epitaxial Ru and Rh monolayers on graphite with the experimentally determined atomic density. Monolayers of the other 4d elements were found to be non-magnetic already in the free-standing limit. The magnetic structure of the Ru and Rh monolayers is studied as a function of metal-graphite interlayer distance h. They become magnetic at h = 4.5 a.u. (Ru) and h = 4.8 a.u. (Rh) in a first-order transition. In the assumed p(2 × 2) super-structure, the moments on the “hollow” site atoms are up to four times bigger than those on the “on-top” site atoms. For h > 5.4 a.u. (Ru) and h > 5.1 a.u. (Rh) the site dependence vanishes and the moments of the free monolayers are approximately reached (1.9 μ_B and 1.2 μ_B, respectively).     

Refractive indices of Zn-doped lithium niobate

We measured the index of refraction n(λ) of Zn-doped LiNbO₃ grown from a congruent melt as a function of the Zn concentration in the crystal. The Zn concentration c_Zn in a sample was determined by electron microprobe technique. The refractive index n(λ, c_Zn) is described by a generalized Sellmeier equation for 400 < λ < 1200 nm and c_Zn up to 8 mol% ZnO. Calculated phase-matching conditions of nonlinear effects like second-harmonic generation are in excellent agreement with experimental results obtained with the same set of crystals.     

Alcohol use, driving records, and crash culpability among injured motorcycle drivers

Alcohol use, driving records, crash culpability, and crash conviction rates for 165 injured motorcycle drivers (MTCDs) were studied. Of the 165 MTCDs, 53.3% tested positive for alcohol (BAC+). Culpability determinations (n = 150) revealed that 83% of BAC+ and 46% of BAC- MTCDs caused their crashes (p < 0.001). Driving records (n = 145) revealed the following prevalence of one or more convictions for BAC+ and BAC- MTCDs: impaired driving (29% vs. 7%, p < 0.001); speeding (74% vs. 58%, p < 0.05); and reckless driving (68% vs. 44%, p < 0.002). Of the surviving culpable impaired MCTDs (n = 48), 16.7% received crash-related convictions, 12.5% received alcohol-related convictions. The reasons for the low conviction rates are probably multifactoral.     

闭环供应链广告协调机制研究

为了研究闭环供应链中零售商回收与制造商回收时两种情形下价格决策与广告协调策略,在广告既能影响市场需求又能影响回收率的条件下,运用博弈论分别建立制造商回收与零售商回收时的广告分摊协调策略数学模型,结果表明制造商回收模式有利于零售商,零售商回收模式有利于制造商。零售商所分摊的广告费用比例在制造回收时小。制造商回收时零售商所分摊的广告费用比例与广告回收效率因子负相关,与广告营销效率因子正相关。零售商将回收时零售商所分摊的广告费用比例与回收效率因子、营销效率因子无关。最后通过仿真证明了相关结论。本文的研究为闭环供应链在不同回收模式下广告回收效率与营销效率的变化时提供相应的协调策略。     

Impact of demand price elasticity on advantages of cooperative advertising in a two-tier supply chain

This paper focuses on pricing and vertical cooperative advertising decisions in a two-tier supply chain. Using a Stackelberg game model where the manufacturer acts as the game leader and the retailer acts as the game follower, we obtain closed-form equilibrium solution and explicitly show how pricing and advertising decisions are made. When market demand decreases exponentially with respect to the retail price and increases with respect to national and local advertising expenditures in an additive way, the manufacturer benefits from providing percentage reimbursement for the retailer’s local advertising expenditure when demand price elasticity is large enough. Whether the manufacturer benefits from cooperative advertising is also closely related to supply chain member’s relative advertising efficiency. In the decision for adopting coop advertising strategy, it is critical for the manufacturer to identify how market demand depends on national and local advertisements. The findings from this research can enhance our understanding of cooperative advertising decisions in a two-tier supply chain with price-dependent demand.     

A shelf-space-dependent wholesale price when manufacturer and retailer brands compete

We propose a game-theoretic model involving the manufacturer of a national brand and a retailer selling her private label along with the national brand. The retailer can use either a differentiation strategy or an imitation strategy for offering her store brand. We consider two cases: the benchmark case, where both players have symmetric information and play a Nash game, and the incentive case, where the national brand’s manufacturer, acting as a leader, offers an incentive to the retailer in order to benefit from a larger proportion of the shelf space, which ultimately increases her own profit. By comparing both situations, we attempt to derive the conditions under which it is profitable for the manufacturer to implement such an incentive strategy and investigate if the results are idiosyncratic to the PL concept. These conditions are fourfold, and include the private label’s image, the price competition between the national brand and the private label, the transfer price level and the shelf-space allocated to the national brand in the benchmark case.     

Optimal replenishment cycle for perishable items facing demand uncertainty in a two-echelon inventory system

We consider a two-echelon supply chain with an upstream manufacturer and a downstream retailer for a single perishable product. The manufacturer processes raw materials into finished products, which are purchased by the retailer in each replenishment cycle. The raw materials of the manufacturer are highly perishable (i.e. perishing within hours or days), and the finished goods at the retailer face demand uncertainty and obsolescence. We model the manufacturer–retailer relationship as a Stackelberg game where the retailer is the leader and decides the replenishment cycle that minimises its mismatch cost between supply and uncertain demand. The manufacturer is the follower and decides its processing rate to minimise its unit cost for finished goods. Our results show that the raw material and finished goods lifetimes, which are interrelated through the duration of the replenishment cycle, have a significant impact on supply chain costs. Although raw material spoilage cost by itself is low, we show that short raw material lifetimes have a significant impact on the costs of both parties. Additionally, we find that while high manufacturer markups increase retailer costs, they reduce the manufacturer's costs due to large production batches.     

多供应链间的Nash和Stackelberg博弈决策模型

以N条包含一个制造商和一个零售商的单链式供应链为研究对象,分别讨论了多供应链间Nash博弈和Stackelberg博弈问题,对N条供应链间博弈均衡解进行了分析和求解,证明了N条供应链博弈下均衡解的存在性和唯一性。在实例分析中,以两条供应链为例,比较了不同博弈框架下定价策略和系统利润的差异。结果表明,对于供应链1来说,链间Nash博弈时的零售商利润、制造商利润和供应链利润均大于链间Stackelberg博弈情形,也即无论从零售商、制造商还是整条供应链的角度,他们均乐于放弃作为领导者的先动优势;对于供应链2来说,情况则相反,也即无论从零售商、制造商还是整条供应链的角度,他们均乐于作为追随者发挥后动优势。     

Inventory competition and incentives to back-order

In this paper we consider the issue of inventory control in a multi-period environment with competition on product availability. Specifically, when a product is out of stock, the customer often must choose between placing a back-order or turning to a competitor selling a similar product. We consider a competition in which customers may switch between two retailers (substitute) in the case of a stock-out at the retailer of their first choice. In a multi-period setting, the following four situations may arise if the product is out of stock: (i) sales may be lost; (ii) customers may back-order the product with their first-choice retailer; (iii) customers may back-order the product with their second-choice retailer; or (iv) customers may attempt to acquire the product according to some other more complex rule. The question we address is: how do the equilibrium stocking quantities and profits of the retailers depend on the customers' back-ordering behaviors? In this work we consider the four alternative back-ordering scenarios and formulate each problem as a stochastic multi-period game. Under appropriate conditions, we show that a stationary base-stock inventory policy is a Nash equilibrium of the game that can be found by considering an appropriate static game. We derive conditions for the existence and uniqueness of such a policy and conduct a comparative statics analysis. Analytical expressions for the optimality conditions facilitate managerial insights into the effects of various back-ordering mechanisms. Furthermore, we recognize that often a retailer is willing to offer a monetary incentive to induce a customer to back-order instead of going to the competitor. Therefore, it is necessary to coordinate incentive decisions with operational decisions about inventory control. We analyze the impact of incentives to back-order the product on the optimal stocking policies under competition and determine the conditions that guarantee monotonicity of the equilibrium inventory in the amount of the incentive offered. Our analysis also suggests that, counterintuitively, companies might benefit from making their inventories “visible” to competitors' customers, since doing so reduces the level of competition, decreases optimal inventories and simultaneously increases profits for both players.     

A mechanistic model for the effect of stress ratio on the LEFM fatigue crack growth behavior of metals and alloys—II. Crack-brittle materials

A recently proposed mechanistic model for the effect of stress ratio, R, on the LEFM (long) fatigue crack growth behavior of “crack-ductile” materials is extended here to explain and predict similar behavior under similar conditions of “crack-brittle” materials characterised by the presence of “static” modes of fatigue fracture in stages II and III. It is shown that in these materials the stage I behavior is similar, but the stages II and III behave differently from crack-ductile materials. Mechanism-based existence of two types of stage II curves characterised respectively by “ pure shear mode ” (SM-II) and “mixed-mode” (MM-II), both plotting linear but having different slopes, is introduced. It is shown that while stage SM-II is insensitive, stage MM-II is significantly sensitive to R, in the same material. Similar to stage I, another “ moving pivot-point ” exists at the transition from SM-II to MM-II, which slides down the “ master shear-curve ” with increasing R. Assuming a critical K_max for the initiation of static modes, a critical R for saturation of these modes, and Paris-type growth relations, a quantitative predictive model containing growth equations for stages SM-II and MM-II, has been developed. Stage III is discussed only qualitatively. Reasonably good agreement was found between predicted curves at selected R-values and a relatively large volume of experimental data for steels, Al-alloys and Ti-alloys. This simple, alternative model may be used for obtaining quick, fairly accurate and conservative estimates of R-influenced crack growth rates for design applications in preference to crack-closure which frequently requires elaborate and tedious experimental procedures.     

The impact of strategic inventory and procurement strategies on green product design in a two-period supply chain

This study analyses the impact of power structures and strategic inventory on the development-intensive and marginal-cost-intensive green product types under three procurement strategies. The results suggest that (i) in the manufacturer-Stackelberg game, the retailer retains strategic inventory to earn higher profits. The retailer's decision improves profit for the manufacturer and greening level of the product; (ii) for the marginal-cost-intensive green product, the power structures and procurement strategies cannot make any impact on the greening level and the retailer cannot build up strategic inventory under retailer-Stackelberg game; (iii) under the Nash game, the procurement decision creates conflict between the supply chain members for marginal-cost-intensive green products; (iv) if the retailer does not maintain strategic inventory or procures product in a single lot, then the manufacturer prefers to produce marginal-cost-intensive products and retailer prefers to sale development-intensive products to receive maximum profits under manufacturer-Stackelberg game. The optimal preferences are concurrent under retailer-Stackelberg game, but not under the Nash game; (v) single-period equilibrium solutions may exhibit sub-optimal characteristics, but two-period planning can lead to exemplary outcomes in the perspective of the greening level and profits of the supply chain members.     

信息不对称下多供应商与单零售商的退货策略

研究由多个提供互补组件的供应商和一个组装商组成的报童型供应链中,零售商将需求信息私有化时,供应商如何制定克服信息不对称的退货策略,使得零售商订货量和信息对称情况下供应链最优订货量相等。假设需求分高需求和低需求两种状态,供应商在需求状态未知的情况下给出针对不同需求状态的两个子契约,使得零售商按照实际需求状态而确定相应订货量。首先分析集权型供应链中整个供应链的最优订货量,再分析分权型供应链中零售商的订货决策,进一步分析信息不对称情况下供应商间的博弈及批发价和回收价契约参数的确定方法。通过算例,说明激励零售商按照真实需求状态选择子契约的合理性,供应商制定的退货策略可以克服信息不对称。     

基于均值-CVaR的回购契约供应链创新协调机制

为了研究制造商创新情形下回购契约供应链的订货及协调机制,构建了回购契约Stackelberg博弈模型,运用均值-CVaR的方法探讨了回购契约供应链创新协调问题。研究表明,均值-CVaR方法比CVaR度量准则更能提高零售商的订货量,指出零售商的风险规避程度影响供应链的创新和需求。当零售商喜好风险,将使制造商的创新投入度增大,供应链渠道的总需求增加。考虑到零售商过度订购的潜在风险,通过对回购商品数量的限制,改进制造商创新投入回购契约供应链,结果表明,改进的制造商创新投入回购契约能够降低零售商的订货量,同时,在一定条件下能够使供应链协调。最后通过数值算例分析了β和λ对最优订货量和创新投入度的影响。