An Extension to McClean's Steady State Model of Manpower Systems

McClean's model focusses on length of service or stability, making no mention of the size of the system. However, it is shown that size can also be extracted from the same formulation.     

Manpower Planning in the United Kingdom: An Historical Review

The Manpower Planning Study Group of the Operational Research Society was formed on 16th November 1967. This paper traces the growth of manpower planning in the United Kingdom from its origins in the Second World War to the present day. It identifies a series of stages, starting with the beginnings and growing awareness of the 1950s and early 1960s, which led on to an explosive growth between 1965 and 1970, and the lengthy period of consolidation thereafter. It places on record the interest and contributions of many individuals and organizations who laid the foundations of manpower planning in this country, and review trends in methodology and the growing role of computers. The paper concludes with some notes on possible future developments.     

Optimizing State Patrol Manpower Allocation

One of the most difficult tasks of state highway patrol administrators is allocation of manpower; i.e. determining the most effective level of operational manpower for patrol tasks. Typically, administrators resolve the allocation problem by relying on prior statistical data and by employing subjective analysis. In general, only limited systematic analyses have been applied to the problem. This paper presents an integer goal programming model for allocating highway patrolmen to road segments within a patrol region. The model is demonstrated via a case example of the Nebraska State Patrol. The results of the model are valuable to the patrol administrator for considering departmental goals and priority structure, in addition to available historical data, in the assignment of state patrol manpower.     

一类捕食-食饵-互惠模型非常数正平衡解的存在性及分歧

讨论了一类捕食-食饵-互惠反应扩散系统的非常数正平衡解.首先分析了常数正平衡解的稳定性,其次;利用最大值原理和Harnack不等式给出了正解的失验估计.在此基础上,利用积分性质进一步讨论了非常数正解的不存在性,相应地证明了当扩散系数d_2 d_3大于特定正常数且扩散系数d_1有界时此模型没有非常数正解.同时利用度理论证明了当模型的线性化算子的正特征值的代数重数是奇数且扩散系数d_3不小于给定正常数时此模型至少存在一个非常数正解,最后研究了非常数正解的分歧.     

Global Steady State Analytical Solution of Cadmium Uptake Model for Plant Roots

The concentration distribution of cadmium ion in soil is studied by the phytoavailability model. According to the states of the cadmium complex: fully inert, fully labile and partially labile, we establish three corresponding cadmium uptake sub-models, and derive respective global analytical solutions at steady state. In particular, when the complex is partially labile, we give the steady analytical solution of cadmium ion concentration in cylindrical geometry composed of the analytical solutions of partially labile complex and fully inert complex in planar geometry and fully inert complex in cylindrical geometry, that is, the ration approximation method. In this paper, the global analytical solutions are compared with the results of literature and numerical simulations. Therefore, the double check is realized to ensure the rationality of the analytical method. The global concentration profile of cadmium ions in the whole rhizosphere can be described by the steady state analytical solutions: the concentration of cadmium ion increases with the distance from the root surface and finally reaches the initial value; the change rate of cadmium ion concentration is the largest when the complex is fully labile; whatever the state of the complex is, cadmium ions never accumulate on the root surface. Finally, we discuss and compare the effects of moving and fixed right boundaries of the model on the results. The results show that it is more reasonable to take the fixed right boundary, and plant roots can uptake cadmium ions in a wider range.     

A Thermodynamic Model of Manpower Systems

This paper presents a new model of manpower systems which is based on the fundamental concepts of thermodynamics, and which is therefore potentially of very widespread applicability.     

A Manpower Allocation Model of Job Specialization

A major copier machine company in Hong Kong presently faces the problem of providing effective servicing and repairing support to its four service regions. Due to the shortage of skilled technicians and the variety of jobs to be handled by technicians of differing skill levels, its Service Department appears to be understaffed, experiencing substantial daily backlogs. This study concentrates on a new perspective of operation: the assignment of technicians at each skill level to specialize in a single type of job in one of the four regions. The objective is to maximize the overall daily number of completed service calls. A mathematical model is developed to handle this specialized allocation problem, where the average travel time (forming part of the coefficient of one of the model's variables) of a technician servicing a type of job in a region is dependent on the decision variables – the composition of the whole team. This results in what we call a mixed integer non-linear programme with variable coefficients. An exact solution is obtained by an iterative algorithm with an overall dynamic programming approach. Sample numerical results are also reported.     

On the Steady State Relativistic Euler-Poisson Equations

We are concerned with the mathematical analysis of the relativistic Euler-Poisson equations in one dimensional case. The existence and uniqueness of the related smooth steady state solutions are proved. The non-relativistic limit and zero-relaxation limit of the model as well as their convergence rates are also obtained.     

GA状态空间的代数模型

以遗传算子的代数模型为基础 ,以矩阵的初等变换及初等矩阵为基本工具 ,给出了遗传算法状态之间的代数通达概念 ,分析了杂交、变异、选择及保优等算子的通达性 ,建立了遗传算法状态空间的代数通达关系 ,给出了返祖操作、退化操作等遗传操作的代数基础 .     

混沌优化算法在不可分稳态大系统优化中的应用

讨论了整体目标函数关于各子系统不具有可加形式的大规模稳态系统的优化问题,将混沌优化算法应用于其最优值的求解,利用混沌运动的遍历性来得到优化问题的全局最优值.仿真结果表明,该算法简单易行,求解精度和可靠性较高,是解决不可分稳态大系统优化问题的一种有效方法.     

A Projection Model for Hierarchical Manpower Systems

This paper presents a projection model for a hierarchical manpower system, viz. a combined group of English County Police Constabularies. The model is designed to describe how observed wastage and promotion rates will shape the internal structure of the system should these persist. Employees in the system are classified according to rank and completed length of service. The model also determines recruitment rates necessary to achieve desired manning levels.     

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。     

An Optimal Reduced-Order Model by Orthogonal State Variables

A zero-input linear time-invariant system is considered. A setof state variables are formulated. The location of zeros ofsuch state variables are used to demonstrate some concepts incontrol theory. Applications to reduced-order models are discussed.The concept of orthogonal state variables—first introducedby the author—is shown, in a particular case, to be superiorto some other concepts in model-reduction analysis.     

The Use of Derivatives for Optimizing Steady State Queues

To design queueing systems in an optimal way, one needs derivatives of the main queueing measures, such as the average number in the system and the throughput. In this paper we show how such measures can be obtained in a Markovian environment. For simplicity, we restrict our attention to queues with Poisson arrivals, having either a finite buffer capacity or a finite calling population. For these queues, we first determine the derivatives of their steady state probabilities, which allow us to find the derivatives of throughput and average number in the system. A number of examples show how these derivatives can be used for the purpose of optimization.     

A Bivariate Model for Markov Manpower Planning Systems

Markov models are being extensively used for analysis of manpower planning systems. Most of these models concentrate either on estimating the gradewise distribution of future manpower structure, given the existing structure and promotion policies, or on deriving policies towards promotion, given the required future structure. However, in many large organizations, agreements between employee unions and management result in the framing of policies towards promotion based either on seniority (length of service in the grade) or on performance (as in the case of ‘high fliers’). In this paper these two criteria are considered in a bivariate distribution framework. The transition probabilities for promotion obtained from the Markov model are further translated into required seniority and performance rating. The procedure is illustrated through an example.     

Positive Steady States of a Competitor- Competitor-Mutualist Model

In this paper we deal with the positive steady states of a Competitor-Competitor-Mutualist modelwith diffusion and homogeneous Dirichlet boundary conditions.We first give the necessary conditions,and thenestablish the sufficient conditions for the existence of positive steady states.     

An Optimal Reduced-Order Model by Discrete Orthogonal State Variables

A linear discrete autonomous (i.e. unforced and time-invariant)systems is considered, and a set of discrete state variablesformulated. The location of zeros of such state variables isused to demonstrate some concepts in control theory. Applicationsto reduced-order models are discussed. The concept of discreteorthogonal state variables is shown, in a particular case, tobe superior to some other concepts in model-reduction analysis.     

关于具有状态变量的HJM模型的实证分析

采用能有效地将期限结构数据中的时间序列和截面信息结合起来的成组数据方法 ,并借助于 Kalman过滤器通地假性最大可能性对模型的系数进行估值并提炼出隐含的状态变量     

Note on a Stochastic Manpower Smoothing and Production Model

It is shown that the optimal policy for a stochastic manpower smoothing and production model, with regular and overtime hours can be characterized by a set of four critical numbers for each state and each period, resulting in substantial computational simplifications.