Extending the Entropy Stability Measure for Manpower Planning

In manpower planning, it is essential to be able to monitor stability of the length-of-service structure of the staff. Such a stability index is provided by the formula for entropy of a continuous distribution, evaluated for length of service. This measure improves on the previous discrete version by removing the necessity of introducing arbitrary tenure classes, thus facilitating inter-company comparisons. It is closely related to the entropy formula used in demography, and manpower planners may therefore avail themselves of results already used by demographers.     

Dissipativity and asymptotic stability of nonlinear neutral delay integro-differential equations

This paper is concerned with the dissipativity and asymptotic stability of the theoretical solutions of a class of nonlinear neutral delay integro-differential equations (NDIDEs). We first give a generalization of the Halanay inequality which plays an important role in the study of dissipativity and stability of differential equations. Then, we apply the generalization of the Halanay inequality to NDIDEs and the dissipativity and the asymptotic stability results of the theoretical solution of NDIDEs are obtained. From a numerical point of view, it is important to study the potential of numerical methods in preserving the qualitative behavior of the analytical solutions. Therefore, the results, presented in this paper, provide the theoretical foundation for analyzing the dissipativity and the asymptotic stability of the numerical methods when they are applied to these systems.     

On the equilibrium personnel structure in the presence of vertical and horizontal mobility via multivariate Markov chains

The present paper employs the Multivariate Homogeneous Markov System (MHMS) in the context of Markov manpower planning modelling. The system is regulated by an embedded multivariate Markov process that allows us to distinguish employees’ mobility patterns that take place either within or among the existing divisions (departments) of an organization. The motivation behind this step arises from the generalization of univariate Markov manpower planning models in which the organization is considered a single (probably hierarchical) group and from the fact that departmental mobility is actually common in most realistic establishments. The first part of the paper presents the functional relations of the MHMS governing intra/inter-departmental transitions. Using these functional forms, we proceed by studying the system’s equilibrium behaviour. This asymptotic analysis reveals the inherent tendencies of the system to reach the limiting structures of specific forms and properties under conditions imposed in the long run.     

Entropy as a Measure of Stability in a Manpower System

It is important when studying a manpower system to be able to measure stability of the experience distribution and thus evade possible trauma. This paper develops the use of entropy as such a measure, both for the comparison of different companies in steady state, and as a means of monitoring the changes in tenure distribution in time for a particular firm. It is shown for several companies that the entropy measure does in fact reflect the changes in length of service structure taking place within the firm.     

Stability of Functional Equations in Several Variables

We prove a generalization of Hyers＇ theorem on the stability of approximately additive mapping and a generalization of Badora＇s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam＇s problem.     

Entropy as a Measure of the Experience Distribution in a Manpower System

It is important when studying a manpower system to be able to measure stability of the experience distribution and thus evade possible trauma. This paper develops the use of entropy as such a measure, both for the comparison of different companies in steady state, and as a means of monitoring the changes in tenure distribution in time for a particular firm. This is achieved by finding the probability of a person to be in a specific length of service class as t→∞ under the more general assumptions possible.     

On the Asymptotic Behaviour of Age Distributions in Manpower Systems

The literature on supply models for manpower planning shows that an important consideration is the size of the discrepancy between the age or length of service distribution of the population and the age distribution which would be reached if present policies were continued indefinitely. In the present paper we study the asymptotic behaviour of the age distribution in any manpower system. An application to a decision problem in a university system is given.     

Centralized versus Decentralized Manpower Resource Planning: the Case of a Hong Kong Company

This paper considers the problem of planning effective servicing support of a Hong Kong-based company by providing sufficient technicians to repair/service copier machines at numerous customer sites throughout the city. As quality of service depends on its operational responsiveness, there is an urgent need to address the company's present and projected staffing.Mathematical modelling techniques based on the well-tested square-root response distance formulation of Kolesar et al. and a corresponding affine time-distance relationship are successfully applied to quantify the performance measure with respect to manpower resources. The numerical results enable model validation against collected data as well as analyses of different modes of centralized/decentralized, prioritized/non-prioritized service operations. Parametric study of performance versus resource offers further insights and directions towards the goal of optimal manpower planning.The approach is found to be very useful in an actual decision support setting, owing to its ease of adaptation, generalization and robust numerical modelling.     

Lyapunov functionals of constant signs in the stability problem for a functional-differential equation of neutral type

We present a generalization of the Lyapunov functional method and use it to study the stability of nonautonomous functional-differential equations of neutral type with finite delay. This generalization is based on constructing the limit equations and the limit functionals.     

Behavioural modelling of career progression in the European Commission

Though manpower planning models have been part of OR for many years, and simulation has always been acknowledged as a potential approach, there are few reported applications of its use. In this case-based study we report on a micro-simulation model that exploits the structure of the European Commission’s appraisal and promotion rules, and includes regression-based sampling schemes which allow for non-Normal error terms to represent behavioural factors that led to the need for a new system. With a suitably parsimonious formulation the 20,000 person model runs very effectively, and the transparency associated with simulation proves an important factor in the successful use of the model as the basis for designing a promotion box system that was implemented across the Commission in 2009. The simulation modelling incorporates many Markov-type elements, and we reflect on important lessons learned from this combined use of micro-simulation and Markov-based approaches to manpower modelling.     

A note on linear θ-derivations on JB1-triples

In this paper we prove a generalization of the stability of the functional equation in the spirit of Hyers, Ulam and Rassias. Also we introduce the concept of linear θ-derivations on JB¹-triple, and prove the generalization of the stability of the functional equation in the spirit of Hyers, Ulam and Rassias of linear θ-derivations on JB¹-triple. For resent results see [1], [2], [3].     

基层部队人力资源优化配置的动态规划模型研究

军事人力资源管理是我军政治工作的重要组成部分。在给出军事人员价值评价指标体系的基础上,对军事人员价值贡献度进行了研究。运用动态规划模型对一定条件下基层部队人力资源按照级别层次进行分配,力求综合价值贡献度最高,人力成本最少,实现与部队级别层次结构的结合,从整体上提高基层部队人力资源的优化配置。     

Stability and bifurcation in a discrete system of two neurons with delays

In this paper, we consider a simple discrete two-neuron network model with three delays. The characteristic equation of the linearized system at the zero solution is a polynomial equation involving very high order terms. We derive some sufficient and necessary conditions on the asymptotic stability of the zero solution. Regarding the eigenvalues of connection matrix as the bifurcation parameters, we also consider the existence of three types of bifurcations: Fold bifurcations, Flip bifurcations, and Neimark–Sacker bifurcations. The stability and direction of these three kinds of bifurcations are studied by applying the normal form theory and the center manifold theorem. Our results are a very important generalization to the previous works in this field.     

On approximate ring homomorphisms

We prove the stability of a generalization of the Bourgin's result on approximate ring homomorphisms.     

企业家人力资源培训问题的整数规划模型

本文强调了企业家人力资源在企业核心能力和可持续成长能力生成中的重要作用和地位。基于时间和费用指标,研究了企业家人力资源培训问题,利用0-1线性整数规划建立了一个带有培训时间约束的最小培训费用模型,给出了求解模型的基于Lagrange松弛的分解算法,计算实例表明给出的算法是有效的。     

Stability of equilibrium solutions of Hamiltonian systems under the presence of a single resonance in the non-diagonalizable case

The problem of knowing the stability of one equilibrium solution of an analytic autonomous Hamiltonian system in a neighborhood of the equilibrium point in the case where all eigenvalues are pure imaginary and the matrix of the linearized system is non-diagonalizable is considered. We give information about the stability of the equilibrium solution of Hamiltonian systems with two degrees of freedom in the critical case. We make a partial generalization of the results to Hamiltonian systems with n degrees of freedom, in particular, this generalization includes those in [1].      

Halanay type inequalities on time scales with applications

This paper aims to introduce Halanay type inequalities on time scales. By means of these inequalities we derive new global stability conditions for nonlinear dynamic equations on time scales. Giving several examples we show that besides generalization and extension to q-difference case, our results also provide improvements for the existing theory regarding differential and difference inequalities, which are the most important particular cases of dynamic inequalities on time scales.     

Dynamics of a hysteretic neuron model

A mathematical model of a single isolated artificial neuron with hysterisis is formulated by means of a neutral delay differential equation. The asymptotic and exponential stability of such a model are investigated. Sufficient conditions for the exponential stability of a linear integral difference inequality are obtained. In the absence of hysterisis effect, our model reduces to a known model of a single neuron. Usually asymptotic stability of neutral delay differential equations is studied by means of degenerate Lyapunov–Kravsovskii functionals. In this article, perhaps for the first time exponential stability of a class of neutral differential equations are studied by means of the exponential stability of an affiliated difference inequality. While generalization to Hopfield type hysteretic neural networks is possible, such a generalization is not considered in this article.     

Defence Manpower Studies<Superscript>†</Superscript>

The Defence Manpower Studies Unit (DMSU) has been created to co-ordinate and develop manpower planning and research for the Armed Forces. Some of its objectives and modes of operation are described.An important characteristic of the Unit is that it seeks to be both an operational research unit and an integral part of management. The arguments for this dual role are based on experience and particularly on the experience of the Naval Manpower Department. The relevant history of this Department is described, and examples of its tasks given.The Armed Forces, taken together, absorb a substantial part of the national manpower resources at the recruiting ages, but also contribute to national trained manpower. The DMSU, therefore, is paying considerable attention to macro-scale aspects. Some of the work of the new Unit is relevant to the work of other government departments, universities, and industry. Examples are given.     

Evaluation of staffing policies in Markov manpower systems and their extension to organizations with outsource personnel

This paper takes up the problem of the evaluation of manpower policies followed in an organization, and examines it in relation to the career growth facilitation afforded by the system to its members. The method proposes and constructs a quantitative measure of effectiveness for manpower policies based on the career growth facilitation afforded to the members, which can then be used for comparative evaluation of different policies. The models are then extended to organizations which outsource work through outsource manpower, and which seek to control the blend of internal and outsource manpower. The models and analyses developed herein will be of relevance to all manpower systems, and in particular, to organizations which outsource work, and those that attempt to achieve desired blends of the outsource staff with their own.