Some Models for a Hierarchical Manpower System

This paper is an extension of previous work which described a model for a hierarchical manpower system with two grades. The model is first extended to a system with several grades, and then to a system with several types of entrant or in which the type of entrant has changed over time. Finally, a calculation is described which can be used to determine the best mix of qualifications amongst the entrants.     

The Use of a Simple Multiple-Criteria Model to Assist in Selection from a Shortlist

The use of a simple multiple-criteria model to assist in decision making is described. The model, a hierarchical additive weighted value-function, was used as a part of a decision-making process to select, from a shortlist of three, the company with which to place a contract for the development of a computerized financial management system. The multiple-criteria model and its use are described in detail. To conclude, there is a discussion on the contribution of the model to the decision-making process as perceived by the decision-making group.     

A continuous model for non-closed graded systems and its asymptotic character

The Purpose of the paper is to study the behavior and the asymptotic character of a continuous model for non-closed graded systems. Mathematically, the model is described by a system of volterra integral equations. Then by applying known methods based on the theory of the resolvent kernel and limiting equations we analyze the behavior and the limiting structure of system. Finally, we provide necessary and sufficient conditions for the system to be weakly ergodic     

Solvability of a finite system of parabolic and ordinary differential equations

We generalize a mathematical model of a bimolecular heterogeneous chemical reaction for the case of more than two reactants. The model is described by a finite system of parabolic and ordinary differential equations for which the existence and uniqueness theorem of a classical solution is proved.     

Two-stage least squares based iterative estimation algorithm for CARARMA system modeling

For stochastic systems described by the controlled autoregressive autoregressive moving average (CARARMA) models, a new-type two-stage least squares based iterative algorithm is proposed for identifying the system model parameters and the noise model parameters. The basic idea is based on the interactive estimation theory and to estimate the parameter vectors of the system model and the noise model, respectively. The simulation results indicate that the proposed algorithm is effective.     

Solvability of a mathematical model of dissociative adsorption and associative desorption type

A mathematical model of dissociative adsorption and associative desorption for diatomic molecules is generalized. The model is described by a coupled system of parabolic and ordinary differential equations. The existence and uniqueness theorem of the classical solution is proved.     

Intertemporal General Equilibrium Model of the Russian Economy Based on National Accounts Deaggregation

The paper describes a three-product intertemporal general equilibrium model of the Russian economy. The System Analysis of Evolving Economy (SAEE) approach to modelling economic processes developed in 1975 is described. Based on SAEE Intertemporal Equilibrium Model with Control of Capital (IEMCC) and three-product nonlinear deaggregation of Russian national accounts by consumption are described. The model agents of two types are introduced: mass (rational) and individual (scenario) agents. The former type includes Bank, Producer, Household, Owner, and Trader. The latter type includes State, Central Bank, Exporter, and Importer. The model is reduced to a boundary-value problem for a significantly nonlinear system of equations. These equations are derived from the initial hypothesis by means of the original economic modelling assistance system ECOMOD which is developed in the computer algebra system MAPLE. The model is adjusted with respect to official statistical quarterly data from 2004 till 2010. The calculation results are provided. The model proves the ability to model the Russian economy as a result of interactions of rational and individual macroeconomic agents.     

Mathematical modelling of immune reaction against gliomas: Sensitivity analysis and influence of delays

In the paper we considered a model of immune reaction against malignant glioma. The model proposed by Kronik et al. (Cancer Immunol. Immunother., 2008) describes simplified interactions between tumour cells and five components of the immune system. We studied the effects of uncertainties of the parameters values to the system behaviour. We showed that the tumour growth rate is one of the most important parameters only in case of fast growing tumours, that is for GBM in our case.On the basis of the performed sensitivity analysis we proposed a reduced model in which the role of time delays in loops appearing in the described interactions is considered. The proposed model includes only two main components of the reaction, that is tumour cells and cytotoxic T-lymphocytes. It occurs that although the reduced system is described by several non-linear terms with three time delays, its dynamics is simple and time delays have hardly any influence on it.Both considered models confirmed that the non-linearities present in interactions between tumour cells and CTLs play a major role in the system dynamics, while other components or delays can be taken into account as supplementary elements only.     

Setting expediting repair policy in a multi-echelon repairable-item inventory system with limited repair capacity

Inventory systems with limited repair capacity are affected by congestion externalities, caused by use of a shared service. There is incompatibility between individual and system optimisation in considering congestion externalities. Three models are described that investigate the congestion effect in a multi-echelon inventory system which has two modes of repair, each with a limited repair capacity. An expanding repair policy employed by the bases in order to choose which repair mode to use is described and compared with different expediting policies related to congestion externalities. The expanding repair policy that considers congestion externalities was found to lead to better system performance measurement than an expanding policy with no congestion. The results of the numerical experiment indicate that the model that ignores congestion externalities—that is, the model that measures each base as an individual—leads to poorer performance measurement for every expediting repair policy, and particularly for the optimal expediting repair policy.     

Start-up of multi-species anaerobic digestion systems: extrapolation of the single species approach

This paper presents a brief evaluation of a start-up strategy for multi-species anaerobic digestion systems modelled as two-step reaction systems, where acidogenesis is described by Monod kinetics while the methanogenesis is described by Haldane kinetics. The start-up policy has been developed originally for single species systems with the aim of maximizing the biogas outflow rate. It consists of switching the dilution rate from minimum to maximum and then to the optimal value (bang-bang control) in order to bring the system from an arbitrary initial condition to the optimal set-point. This start-up strategy is applied to the multi-species system using an averaged model, which is usually the only model that can be identified for a multi-species system, as measuring individual biomasses is almost impossible in practice. Even the development of an accurate averaged model, fully characterizing the system dynamics based on the variation of the species proportions is difficult. The averaged models used in this study are built based on a more or less accurate knowledge of the species proportions and their kinetics at the start-up instant and used as such in the application of the start-up policy. It is shown that the start-up policy leads to an efficient ecosystem, characterized by high outflow rate of biogas, which is very close to the maximum even in the case of an inaccurate averaged model. The influence of the model accuracy on the system stability and its productivity is discussed. This study can also be viewed as a robustness evaluation with respect to model inaccuracy of the single species start-up strategy, as the process changes from the averaged kinetics to the kinetics of the winning species during species selection.     

Knowledge-based manpower planning

The capacity performance of knowledge-based systems differs essentially from the one of traditional systems. The result is that already today these systems are employed in a number of application areas, and that the intensity of research and development in this field is very high.In this paper the development of a knowledge-based manpower planning system (KBMS) is described. The two main components of this system are a knowledge-based system developed for management planning and a model designed for manpower planning in personnel leasing companies. This model was realized as a KBMPS by applying the knowledge-based system, which was developed for management planning.     

Mathematical modeling of seismic and acousto-gravitational waves in a heterogeneous earth-atmosphere model

A numerical-analytical solution to problems of seismic and acoustic-gravitational wave propagation is applied to a heterogeneous Earth-Atmosphere model. The seismic wave propagation in an elastic half-space is described by a system of first order dynamic equations of the elasticity theory. The propagation of acoustic-gravitational waves in the atmosphere is described by the linearized Navier-Stokes equations. The algorithm proposed is based on the integral Laguerre transform with respect to time, the finite integral Bessel transform along the radial coordinate with a finite difference solution of the reduced problem along the vertical coordinate. The algorithm is numerically tested for the heterogeneous Earth-Atmosphere model for different source locations.     

Implementation of a visual interactive consensus decision support system

The development of a consensus production, distribution of finance decision support system for HP Bulmer PLC is described. The DSS is implemented on a micro computer, uses high resolution colour graphics for its display output and supports both a data base and a software model bank. This model bank allows different production and distribution planning models to be run, in context during the same interactive planning session. The paper also comments on the elementary learning capabilities of the system.     

Nonlinear dynamical analysis of hydro-turbine governing system with a surge tank

This paper brings attention to a new nonlinear mathematical model of a hydro-turbine governing system with a surge tank. The nonlinear mathematical model, which is described by state-space equations, is composed of Francis turbine system, electrical generator system, conduit system and governor system. Furthermore, the nonlinear dynamical behaviors of the system with different parameters are studied exhaustively including bifurcation diagrams, time waveforms, phase orbits, Poincare maps, spectrograms and power spectrums. Fortunately, some interesting phenomenons are found from numerical simulation results. More important, all of the above analyses supply some theory bases for designing and running of a hydro-turbine governing system.     

The Stochastic Quasi-chemical Model for Bacterial Growth: Variational Bayesian Parameter Update

We develop Bayesian methodologies for constructing and estimating a stochastic quasi-chemical model (QCM) for bacterial growth. The deterministic QCM, described as a nonlinear system of ODEs, is treated as a dynamical system with random parameters, and a variational approach is used to approximate their probability distributions and explore the propagation of uncertainty through the model. The approach consists of approximating the parameters’ posterior distribution by a probability measure chosen from a parametric family, through minimization of their Kullback–Leibler divergence.     

利用传递函数——噪声模型表达经济变量间的动态影响机制

传递函数———噪声模型是一类多变量时间序列模型,它在表达系统动态影响机制方面有着独到的优势。本文将这种模型的建模方法应用于经济系统,建立了一个表达产值和出口间动态关系的传递函数———噪声模型。近几个月的实际数据表明模型的拟合是理想的。     

Numerical solution to a two-dimensional hypersingular integral equation and sound propagation in urban areas

A mathematical model of sound propagation from a noise source in urban areas is constructed. The exterior Neumann problem for the scalar Helmholtz equation is reduced to a system of hypersingular integral equations. A numerical method for solving the system of integral equations is described. The convergence of the quadrature formulas underlying the numerical method is estimated. Numerical results are presented for particular applications.     

半导体瞬态问题特征变网格有限元法和分析

1 引 言考虑平面区域Ω　R2上的二维问题,其数学模型为[1]-△ψ=α（p-e+N（x））,（x,t）∈Ω×J,J（0,T],（1.1）     

Determination of Stock for Sales Promotions

This paper describes the solution of the practical problems encountered by a Company when a product is made and sold for a limited promotional period only. The production and inventory control aspects are considered and a system aimed at the reduction of obsolescence costs is described which is based on a model of the demand pattern which uses a Gompertz exponential growth curve. Under pressure for an early improvement from the organisation, a system based on an empirical model was implemented, as an interim measure, which achieved a considerable improvement in performance. The Gompertz model has now been put into operation and the results of a simulation model are presented indicating that further improvements can be achieved.     

多周期多种设备公用工程系统优化模型的改进及应用

本文提出了多周期多种设备公用工程系统改进的混合整数双线性优化模型,它含有两种优化变量和系统运行过程的离散动态约束,期望系统总设备投资(含设备折旧)与全周期运行操作费用之和最小。针对改进优化模型求解上的困难,给出将改进优化模型分解成有限多个关于连续变量的线性规划。论述了改进优化模型与分解模型的等价性以及两种模型的主要数学性质,并在此基础上提出了求解策略。最后将改进优化模型应用于某石化企业的蒸汽动力系统最优设计与运行优化集成实例。