呼叫中心坐席人员排班问题优化模型与算法研究

国内呼叫企业在保证每个坐席人员周内当值相同班次情况下,通过灵活安排周内当班日期与班次来制定排班方案。针对该实际排班场景,构建问题整数规划模型。通过对问题数据特征及优化性质分析,以及对班次人力有效满足区段电话服务需求的量化指标表征,分别提出两个构造性启发式算法。使用企业实例数据对模型算法进行计算实验。实验结果显示,整数规划模型适合于求解小规模排班问题最优解,而启发式算法能够以小计算成本获得大规模排班问题优化解。最后讨论保证员工上班规律性的同班次用工制度对企业人力成本控制的影响。     

考虑时滞效应与均值-方差效用的非零和投资与再保险博弈

在考虑时滞效应的影响下研究了非零和随机微分投资与再保险博弈问题.以最大化终端绝对财富和相对财富的均值-方差效用为目标,构建了两个相互竞争的保险公司之间的非零和投资与再保险博弈模型,分别在经典风险模型和近似扩散风险模型下探讨了博弈的Nash均衡策略.借助随机控制理论以及相应的广义Hamilton-Jacobi-Bellm...     

Study of radiation background at the north crossing point of the BEPCⅡ in collision mode

Understanding the radiation background at the north crossing point (NCP) in the tunnel of BEPCII is crucial for the performance safety of the High Purity Germanium (HPGe) detector, and in turn of great significance for long-term stable running of the energy measurement system. Therefore, as the first step, a NaI(Tl) detector is constructed to continuously measure the radiation level of photons as background for future experiments. Furthermore, gamma and neutron dosimeters are utilized to explore the radiation distribution in the vicinity of the NCP where the HPGe detector will be located. Synthesizing all obtained information, the shielding for neutron irradiation is studied based on model-dependent theoretical analysis.     

Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system

We consider a model for the flow of a mixture of two viscous and incompressible fluids in a two or three dimensional channel-like domain. The model consists of the Navier-Stokes equations governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids. We prove the instability of certain stationary solutions for such a system endowed with periodic boundary conditions on elongated domains (0,2π/α₀)×(0,2π) or (0,2π/α₀)×(0,2π)×(0,2π/β₀) for a special class of periodic body forces, provided that α₀ and β₀ are small enough. As a consequence, we deduce a lower bound for the Hausdorff dimension of the global attractor.     

Axial instability of double-nanobeam-systems

This Letter considers the axial instability of double-nanobeam-systems. Eringen's nonlocal elasticity is utilized for modelling the double-nanobeam-systems. The nonlocal theory accounts for the small-scale effects arising at the nanoscale. The small-scale effects substantially influence the instability (or buckling) of double-nanobeam-systems. Results reveal that the small-scale effects are higher with increasing values of nonlocal parameter for the case of in-phase (synchronous) buckling modes than the out-of-phase (asynchronous) buckling modes. The increase of the stiffness of the coupling elastic medium in double-nanobeam-system reduces the small-scale effects during the out-of-phase (asynchronous) buckling modes. Analysis of the scale effects in higher buckling loads of double-nanobeam-system with synchronous and asynchronous modes is also discussed in this Letter. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the instability analysis of complex-nanobeam-system such as complex carbon nanotube system.     

电商平台主导的E-闭环供应链定价、服务决策与回收模式

E-闭环供应链(E-CLSC)管理须有科学的定价与服务决策支撑。针对集中和分散回收模式,构建电商平台主导的Stackelberg博弈模型,研究E-CLSC定价与平台服务决策。通过对产品销售价格、平台服务水平等均衡策略分析,揭示回收主体投资有效性、回收转移价格等对E-CLSC均衡策略影响。研究表明:集中回收模式优于分散回收模式;在分散回收模式下,若回收主体投资有效性相同,制造商、平台均偏好制造商回收模式;平台回收与第三方回收模式相比,产品销售价格、平台服务水平相同,前者回收渠道效率较高;平台回收模式下,单位佣金与回收转移价格负相关,产品销售价格、平台服务水平、废旧产品回收率均与回收转移价格无关;若回收主体投资有效性差异程度较大,制造商回收模式并非总是最优的,回收主体投资有效性差异显著影响产品销售价格、回收渠道效率、平台服务水平和E-CLSC各成员利润。上述结论通过数值仿真进行了验证。     

Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy

We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on each subinterval. The method is shown to be unconditionally stable, and for general nonlinear equations, the uniform sharp numerical order 3 − $ν$ can be rigorously proven for sufficiently smooth solutions at all time steps. The proof provides a general guide for proving the sharp order for higher-order schemes in the nonlinear case. Some numerical examples are given to validate our theoretical results.     

Two problems in the 筭數書 Suanshu shu (Book of Mathematics): Geometric relations between circles and squares and methods for determining their mutual relations

Much research has been devoted to two problems, Yi yuancai fang (From a circular timber [find] a square) and Yi fangcai yuan (From a square timber [find] a circle), both of which appear in the Suanshu shu, an early Han dynasty mathematical work written on bamboo slips, excavated from tomb 247 at Zhangjiashan in Hubei Province, China. In this article, the geometric relations between circles and squares and the methods for determining their mutual relations in these two problems are interpreted in a different way, and an alternative approach is offered for reconciling these two problems.     

Pre-university students square-root from squared things: A commognitive account of apparent conflicts within learners' mathematical discourses

This study explores the grasp of square roots among eleven students in a remedial mathematics course, with a special focus on where the same student generated apparently conflicting responses. Building on the commognitive framework, the analysis distinguished between routines that individual students consistently implemented in situations where roots “stood alone” and where they were incorporated in more compound exercises, where roots were extracted from square numbers and from squared radicands, where roots were applied to monomials and binomials, and where parameters named with different letters were involved. Differences were found in routines’ degree of objectification, procedures, and tasks. These differences are explained with a theoretical account, suggesting that what may seem as a conflict within a student’s discourse could be a sensible difference of actions taken in situations that this student construed as different. The contribution of this study to the body of knowledge on teaching and learning of roots and to commognitive research is discussed.     

Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media

This paper presents a new nonlinear reaction–diffusion–convection system coupled with a system of ordinary differential equations that models a combustion front in a multilayer porous medium. The model includes heat transfer between the layers and heat loss to the external environment. A few assumptions are made to simplify the model, such as incompressibility; then, the unknowns are determined to be the temperature and fuel concentration in each layer. When the fuel concentration in each layer is a known function, we prove the existence and uniqueness of a classical solution for the initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. We construct monotone iterations of upper and lower solutions and prove that these iterations converge to a unique solution for the problem, first locally and then, in time, globally.