An Approach to Optimal Recruitment and Transition Strategies for Manpower Systems using Dynamic Programming

In this paper, concepts of dynamic programming are used within a discrete time Markovian model for the development of a graded population. Optimal recruitment and transition patterns are determined by minimizing expected discrepancies between actual states and preferred goals.     

Recruitment Effects on Manpower Structures

Recruitment is one of the dynamics of manpower systems that can usually be most effectively controlled, always assuming that there is at any time an adequate supply of recruits to a system. In this situation, recruitment can be fixed to meet immediate demands, or it can be part of long-term planning programmes designed perhaps to alleviate a skewness in the length of service profile without reducing the strength of the system greatly. In general, recruitment levels will necessarily be connected with wastage and promotion in a system as well as with the desired growth of the system. The process of determining manpower-planning policies, hereunder recruitment levels, is open to a variety of options with regard to the underlying assumptions that are made: observed experience can be assumed to continue; promotion policies can be adjusted and the consequences estimated; recruitment levels can be allowed to meet immediate demands but with the restriction of some maximum level; or recruitment levels are pre-fixed on the basis of some perhaps even arbitrary management desires. Each of these options and each accompanying recruitment policy will affect the internal structure of the system, with regard to both rank and length of service profiles. This paper employs established projection and promotion models for hierarchical manpower systems to consider recruitment policies and their effects on internal structures. Various policy models are outlined and results presented for a particular application.     

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.     

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.     

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 Dynamic Programming Approach to Determine Optimal Manpower Recruitment Policies

The manpower planning models available in the literature have dealt with how changes take place in a manpower planning system, under various operating and policy constraints. However, none of these models has identified the manpower system costs. In this paper we have identified various manpower system costs. Further, we have developed a manpower planning model with the objective of minimizing the manpower system costs. The model has been found to be analogous to the Wagner-Whitin model in production/inventory management. A numerical example has been given to illustrate the model.     

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.     

Evaluating Recruitment Strategies Using Fuzzy Set Theory in Stochastic Manpower Planning

Abstract

One aspect of Manpower Planning is the investigation of wastage and internal transitions for homogeneous groups of employees in a Manpower system. In the relevant literature, the attainability of a desired stock vector was studied under control by recruitment for time-discrete Markov models. These approaches allow choosing a proper recruitment strategy, resulting in an attainable vector most similar to a desired one. In this article, this problem will be discussed under stochastic assumptions for attainability after one step. Based on fuzzy set theory, a procedure is introduced that allows evaluating and comparing recruitment strategies, resulting in the determination of a most preferable strategy.     

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 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.     

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.     

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.     

Attainable and Maintainable Structures in Markov Manpower Systems with Pressure in the Grades

Some of the problems of attaining and maintaining structures with given values of a quantity called ‘pressure’, which can be generated in the grades of a manpower system as a result of delays in expected promotions, have been considered in this paper. The research is focused on determining structures with given values of the total size and pressures and which can be attained and maintained by fixed recruitment policies.     

Optimal excess-of-loss reinsurance and investment polices under the CEV model

This paper focuses on risk control problem of the insurance company in enterprise risk management. The insurer manages its financial risk through purchasing excess-of-loss reinsurance, and investing its wealth in the constant elasticity of variance stock market. We model risk process by Brownian motion with drift, and study the optimization problem of maximizing the exponential utility of terminal wealth under the controls of reinsurance and investment. Using stochastic control theory, we obtain explicit expressions for optimal polices and value function. We also show that the optimal excess-of-loss reinsurance is always better than optimal proportional reinsurance. And some numerical examples are given.     

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.     

Manpower planning procedures for hierarchical manpower systems

In this paper, a model which describes manpower planning procedures for a hierarchical system having certain desired properties to be achieved is presented. These properties will act as constraints on the system. It will be assumed that eventual, desired properties are achieved gradually over a period of time. Promotion policies will be wastagelinked and designed to satisfy vacancy-expansion demands. The model will be applied to data from a group of English County Police Constabularies.