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.     

Balancing attainability,desirability and promotion steadiness in manpower planning systems

A Markov manpower planning model with fixed internal transition probabilities, enables assessing the feasibility to attain the most desirable personnel structure. In case the desirable personnel structure is not attainable under control by recruitment, the internal personnel flows can be modified while not disrupting the career progression expectations. This paper introduces the promotion steadiness degree to quantify the personnel policy deviation from the career progression expectations. As a result, this paper focuses on a model that balances three criteria, that is, the desirability degree, the attainability degree and the promotion steadiness degree, formulated by fuzzy membership functions. A new set of instances is introduced, and the algorithms are evidenced in a set of experiments.     

Personnel Recruitment Policies and Long-Term Production Planning

Any organization or industry operating in a market where there is unmet demand will be under considerable pressure to meet the demand as quickly as possible. This short-term objective can be met by rapidly expanding productive capacity in terms of both plant or other equipment and also manpower. If the commodity in demand is durable—e.g. housing, cars, computers—then when the initial requirement is met, further output is for replacement purposes. Production during the expansion phase, planned to eliminate the backlog of demand may be much greater than that needed for the next phase, meeting recurrent replacement demand. If capacity is allowed to run down, a later increase in demand will possibly find the organization with too little capacity. There follows a potentially continuing cycle of under- and over-production. Since manpower comprises a significant part of the capacity, this creates a possible cycle of under- and over-employment.Mathematical models of manpower systems can be adapted to investigate the consequences of controlling recruitment policies over fairly long periods of time. If costs can be ascribed to both under- and over-production it is possible to combine the manpower models with mathematical programming techniques to produce optimal longterm recruitment policies.The possible development of the telephone network in the Republic of Ireland is used as an illustrative example. Here it has already been established by government operational research scientists that meeting the original target number of installations for the early 1980's would require impossibly large levels of recruitment immediately. Our model shows that, if the target were achieved, an intolerably large proportion of the workforce would be redundant in a few years time. We use a linear programming model to illustrate viable policies trading off present delays in satisfying demand against future overmanning.     

An extended and tractable approach on the convergence problem of the mixed push-pull manpower model

In this paper, the asymptotic behavior of the time-homogeneous mixed push-pull manpower model is studied under the assumption that the desired stock vector and the recruitment policy are fixed over time. In the mixed push-pull manpower model, the internal mobility of a personnel system can be regulated by both pull and push transitions. Based on those characteristics, we express and examine the dynamics of the personnel system by formulating the mixed push-pull manpower model by means of particular transition matrices, which we demonstrate to have interesting properties. We show that under certain conditions the stock vector converges. An explicit analytical form for this limiting personnel stock vector is found.     

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.     

Safety stocks in multi-stage inventory systems under different service measures

In this paper, we treat the problem of determining safety stocks in multi-stage inventory systems with normally distributed demands. The system follows a periodic review base-stock control policy. Assuming that every stockpoint satisfies a service level constraint and that no internal delays occur, we formulate the optimization problem for a general inventory system and derive properties of the optimal policy, which depend on the structure of the multi-stage system and the service measure used. Considering stockout occurrence related service levels, we find that the safety stock coverage times can only obtain values resulting from the extreme points of the solution set. Service levels representing size and duration of stockouts need less protection and are connected with problem reduction properties. The analysis of the reduced problems leads to similar extreme point properties as for stockout occurrence related service.     

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.     

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.     

A model for promotion rate control in hierarchical manpower systems

In optimization models of hierarchical manpower systems, thenumbers promoted from each of the grades in a time period arenormally considered as decision variables. As a result, promotionrates, defined in terms of the proportions of staff promoted,can vary substantially from period to period in these models.Policies of this type may be unacceptable in practice becauseof their adverse impact on staff morale. In this paper, a mixedinteger programming (MIP) manpower planning model is developedfor determining minimum-cost manpower policies in which promotionrates remain stable while satisfying specified manpower requirementsover the planning period. In this MIP model, promotion ratesare considered as decision variables by using binary variables,and the model is solved by using an iterative procedure. Theuse of the approach is illustrated with representative datafor a military system.     

A Method of Estimating Craft Manpower Requirements at Industry Level

Accurate estimation of future craft manpower requirements is essential to an industry if shortage of manpower on the one hand and unemployment on the other are to be avoided. Such estimation should allow for the fact that there is a range of likely outcomes, should permit modification with the passage of time and should be objective.This article proposes a method, based on studies of the printing industry, of obtaining a probabilistic forecast of future manpower requirements by treating changes in individual technical and economic factors as random variables and combining them in a statistical model. The implications of this are then examined for various policies, using a cost utility model and calculations of the expected value of unemployment resulting from different levels of recruitment.     

Sensitivity Analysis of Promotion Opportunities in Graded Organizations

This paper extends earlier work on manpower mobility in hierarchical organizations and is concerned especially with the effects of changes in hiring and separation on opportunities for internal advancement. We make use of a fractional flow model of personnel to highlight the links between personnel flows and vacancy flows, and then derive formulae that can be used to simulate the impact of changes in grade-size targets, hiring policy and attrition rates on promotion opportunities for staff. The model is then illustrated by application to data on faculty staffing in a large university.     

An analysis of p-median location problem: Effects of backup service level and demand assignment policy

Any solution to facility location problems will consider determining the best suitable locations with respect to certain criteria. Among different types of location problems, involving emergency service system (ESSs) are one of the most widely studied in the literature, and solutions to these problems will mostly aim to minimize the mean response time to demands. In practice, however, a demand may not be served from its nearest facility if that facility is engaged in serving other demands. This makes it a requirement to assign backup services so as to improve response time and service quality. The level of backup service is a key, strategic-level planning factor, and must be taken into consideration carefully. Moreover, in emergency service operations conducted in congested demand regions, demand assignment policy is another important factor that affects the system performance. Models failing to adopt sufficient levels of backup service and realistic demand assignment policies may significantly deteriorate the system performance.Considering the classic p-median problem (pMP) location model, this paper investigates the effects of backup service level, demand assignment policy, demand density, and number of facilities and their locations on the solution performance in terms of multiple metrics. For this purpose, we adopt a combined optimization and simulation approach. We will first modify the classic pMP to account for distances to backup services. Next, we employ a discrete event simulation to evaluate the performance of location schemes obtained from the deterministic mathematical model. Our results provide insights for decision-makers while planning ESS operations.     

Managing the supply and demand uncertainty in workforce recruitment: planned or just-in-time acquisition

Managing knowledge workers is highly complex because of the need to balance the costs associated with their training and holding costs against the need to meet market demand as quickly as possible. Unlike previous approaches to this problem in the workforce management literature, this paper develops a stochastic optimization model to examine the impact of not only uncertainty of the demand of knowledge services but also that of the supply of knowledge workers on a recruiting strategy. Hypotheses on optimal recruiting decisions that this paper suggests include: (1) high holding and training costs decrease recruitment of apprentices; (2) high mobility of skilled workers decreases recruitment of apprentices; (3) high elasticity of the supply of skilled workers decreases recruitment of apprentices; (4) high volatility of the demand of knowledge services decreases recruitment of apprentices; and (5) in high seasonal effect on the demand, the decision policy based on decision thresholds proportional to seasonal demands outperforms the decision policy based on a constant decision threshold. Suggested hypotheses are supported by a simulation of the model. Model parameters in the simulation are estimated based on the survey of information security consulting service companies in South Korea.     

Modelling personnel sustainability: a tool for military force structure analysis

This paper describes the mathematical formulations that have underpinned the development of a strategic-level, personnel sustainability planning tool for the Australian Army. The tool considers personnel sustainability in terms of the dynamics of progression through career profiles and the requirements of the force to meet operational capability demands. It assists in analysing the ability of a force structure (current or future) to meet forecast operational deployments, providing insights into: likely problem areas with regard to sustainability, the effect of changing personnel policies, resource/cost implications and force expansion issues. Utilised in shorter-term planning, the tool allows for rapid force options testing and, in longer-term planning, for detailed sustainability analysis of proposed future force structures. The paper focuses on the basic construction of the model and its mathematical underpinnings, while giving insights into its utility and to how it has been applied.     

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.     

Efficient Scheduling Rules in a Combined Make-to-Stock and Make-to-Order Manufacturing System

In this paper, we consider a mixed MTS/MTO policy to manage a single manufacturing facility producing two classes of end-products. A few end-products have high volume demands, whereas a fairly large number of end-products have low volume demands. In this situation, it is appealing to try to produce the high volume products according to an MTS policy and the low volume products according to an MTO policy. The purpose of this paper is to analyze and compare the impact of the choice of the scheduling policy on the overall performance of the system. We consider two policies: the classical FIFO policy and a priority policy (PR). The PR policy gives priority to production orders corresponding to low volume products over production orders corresponding to high volume products. Under some simple stochastic modeling assumptions, we develop analytical/numerical solutions to optimise each system. We then provide insights regarding this issue with the help of numerical examples. It appears that for some range of parameters, the PR rule can outperform the FIFO rule in the sense that, to achieve the same service level constraint, the corresponding cost under the PR rule is much lower. This situation is encountered when the low volume products can be managed with an MTO policy under the PR scheduling rule, while they have to be managed according to an MTS policy under the FIFO scheduling rule. We also derive some theoretical properties that support our empirical findings.     

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.     

A Manpower Planning Study

The paper describes a technique which has been applied in practice to predict the movements of the staff of a large undertaking over the next 20 years. The exercise shows the future promotion pattern and the recruitment required to fill the posts which become vacant as a result of promotion or wastage.By feeding in alternative assumptions about the future demand for staff in each department, corresponding to different levels of business activity, it is possible to see in advance which situations are likely to give rise to the greatest staff problems.It is thought that the same basic technique could be used for manpower planning in other firms.     

Optimal EOQ Models for Deteriorating Items with Time-Varying Demand

In this paper, optimal inventory lot-sizing models are developed for deteriorating items with general continuous time-varying demand over a finite planning horizon and under three replenishment policies. The deterioration rate is assumed to be a constant fraction of the on-hand inventory. Shortages are permitted and are completely backordered. The proposed solution procedures are shown to generate global minimum replenishment schedules for both general increasing and decreasing demand patterns. An extensive empirical comparison using randomly generated linear and exponential demands revealed that the replenishment policy which starts with shortages in every cycle is the least cost policy and the replenishment policy which prohibits shortages in the last cycle exhibited the best service level effectiveness. An optimal procedure for the same problem with trended inventory subject to a single constraint on the minimum service level (maximum fraction of time the inventory system is out of stock during the planning horizon) is also proposed in this paper.     

A multi-period,multiple criteria optimization system for manpower planning

This paper discusses a multi-period, multiple criteria optimization system for manpower supply forecasting. The system is used to identify recruitment and promotion strategies for managing the enlisted force of the U.S. Navy. With the criteria modeled as trajectories of goal values over the multiple time periods, the system uses the interactive augmented weighted Tchebycheff method as its solution procedure. Illustrative computer results are presented.