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.     

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 Hierarchical Model for Control of Flexible Manufacturing Systems

Flexible Manufacturing Systems (FMSs) are usually composed of general purpose machines with automatic tool changing capability and integrated material handling. The complexity of FMSs requires sophisticated control. In this paper we present a four-level control hierarchy and outline computationally feasible control algorithms for each level. The top level is concerned with the choice of part types and volumes to be assigned to the FMS over the next several months. The second level plans daily or shift production. Production levels are set and tools are allocated to machines so as to minimize holding and shortage costs. Various FMS environments are presented. The third level determines process routes for each part type in order to minimize material handling. Additional tools are loaded on machines when possible to maximize alternate routeing. Routes are then assigned to parts to minimize workload assignment, and these are used by level four for actual routeing, sequencing and material handling path control. The level three model is formulated as a linear program, and heuristics are used for level four. An example is provided to illustrate the completeness of the decision hierarchy and the relationships between levels.     

A Grade-Specific Stochastic Model for the Analysis of Wastage in Manpower Systems

A stochastic model for a hierarchically-structured company is presented which accounts for the effect on wastage of the internal structure of the company and the promotion experience of its employees. We differentiate two main reasons for leaving, owing to the company's internal structure, and the model is formulated on the basis of the joint probabilities of the employee being in service or having left the company because of either reason by time t and his promotion experience up to t. It is shown that the model provides a good fit to a variety of observed leaving patterns of five large companies, explains the relationship between a number of important occupational variables and is useful for planning purposes in predicting future developments.     

A Network Optimization Model for Budget Planning in Multi-Objective Hierarchical Systems

This paper presents a planning/budgeting scheme for hierarchical systems. A multi-objective network optimization model for multilayer budget allocation is suggested. The network presents the hierarchical structure of the system. The budget allocations are the flows in the network. Each component in the system (arc in the network) has lower and upper bounds. The model maximizes the additive utility function of the system, expressed as a weighted summation over the preferences of the system's components in the various levels. The preferences are evaluated by using a multigoal approach, utilizing the Analytical Hierarchy Process (AHP). Finally, the model is conceptually compared with other known budgeting procedures and models, such as ZBB, PBBS and cost benefit analyses.     

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.     

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.     

Stability of Manpower Systems

Members of an organization belong to one of the grades (1, 2,... k), and movements between grades are governed by a substochastic matrix P. The model can be deterministic, stochastic, or partially stochastic; and we may or may not insist that the total size be restored to a fixed quantity each year. Various notions of the stability of a structure x = (x₁, x₂, … x _k ), where x _i represents the number, or proportion, in grade i are considered. Mainly, but not exclusively, the case when P is upper triangular is considered.     

Linear-Feedback Recruitment polices for Constant-Size Manpower Systems

Feedback control principles are used to develop recruitmentpolicies for manpower systems, with and without vacancies beingconsidered. The problem of reaching a desired steady-state distributionis also formulated and discussed as a linear programming problem.     

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.     

A Parallel Projection for the Multicommodity Network Model

We present an application of parallel computing techniques to the solution of a quadratic programme that arises in the resource-directive decomposition method for multicommodity problems. A sequential algorithm for the quadratic programme is discussed, and its extension to a parallel implementation is given. Computational testing of the sequential and parallel algorithms was done on the Sequent Symmetry S81 parallel computer located in the Parallel Processing Laboratory at Southern Methodist University. On several large test problems the parallel version achieved a speed-up of 10 with 12 processors.     

Block Projection Methods for Linear Systems

The aim of this paper is to provide a theory of block projection methods for the solution of a system of linear equations with multiple right-hand sides. Our approach allows to obtain recursive algorithms for the implementation of these methods.     

A Note on Stability in Gani-Type Models in Manpower Systems

The paper provides a generalization of a result given by Feichtinger on the stability in Gani-type models in manpower systems. This generalization on the important question of stability is important from the practical point of view, because it can be used for any Markovian manpower system.     

基于DNA微阵列数据分析的分级Bayes模型

如何分离出少量区别不同组织类型的特异性基因是DNA微阵列数据分析中的主要问题,特别是构建恰当的统计模型来刻画这些不同组织类型的DNA表达形式尤为重要.为此,基于基因DNA微阵列数据的特点,我们假定对数变换后的微阵列数据服从混合正态分布.我们采用分级Bayesian先验刻画不同基因的相关性,利用分级Bayesian方法构建模型,给出了刻画不同组织基因表达的差异的一个标准,用MCMC迭代计算该标准.模拟计算表明我们的模型具有较好的识别能力.     

Two-Subspace Projection Method for Coherent Overdetermined Systems

We present a Projection onto Convex Sets (POCS) type algorithm for solving systems of linear equations. POCS methods have found many applications ranging from computer tomography to digital signal and image processing. The Kaczmarz method is one of the most popular solvers for overdetermined systems of linear equations due to its speed and simplicity. Here we introduce and analyze an extension of the Kaczmarz method that iteratively projects the estimate onto a solution space given by two randomly selected rows. We show that this projection algorithm provides exponential convergence to the solution in expectation. The convergence rate improves upon that of the standard randomized Kaczmarz method when the system has correlated rows. Experimental results confirm that in this case our method significantly outperforms the randomized Kaczmarz method.     

The Prospect Award 1981: A Manpower Planning Model for Mobile Repairmen

The country's largest vending machine operators and distributors were faced with the problem of evaluating manpower requirements and structure for the repair and maintenance work force, and of deciding where additions to this force should be located. This paper describes the formulation and application of a solution to the problem which has had beneficial effects far beyond the scope originally envisaged.The work force concerned operates a breakdown repair service which requires random journeys within each individual's prescribed area. The developed model evaluates the work content, and thus manpower requirements, of a region based on the number of machines, the breakdown rates, the repair times and the journey time. The travel component is automatically adjusted for growth in the work force.Analysis of the model's sensitivity to the key factors and the development of the relationship between utilisation and service level have enabled the company to improve service performance by 15% while also achieving a 67% increase in productivity.