Modelling heterogeneity in manpower planning: dividing the personnel system into more homogeneous subgroups

Manpower planning is very useful for human resource management in large organizations. Most manpower models are concerned with the prediction of the future behaviour of the staff: they might leave the organization, get promoted or acquire more and new skills. This behaviour can vary a lot among different employees, what makes prediction difficult. It is common to tackle this problem by dividing the whole heterogeneous personnel system in several more homogeneous subgroups. This approach is often used to develop manpower planning models for prediction, control or optimization. Although the division in homogeneous subcategories is a fundamental and important step in the application of the models, up till now literature neglects to discuss a procedure to deal with this in practice. This paper suggests a general framework to find the distinguished homogeneous subcategories by determining and considering observable sources of personnel heterogeneity. Copyright © 2006 John Wiley & Sons, Ltd.     

Corporate manpower planning: a review of models

Manpower planning has achieved maturity during the past decade. Personnel practitioners have become conversant with the analysis of manpower systems, the use of quantitative techniques, and have developed a sound approach to the whole question of manpower management. But, whilst they no longer rely on the management scientist for using those models and other techniques now widely available, there is a continued contribution to be made in advancing the field. This paper reviews the practical relecance of existing models. It concentrates on techniques for evaluating manpower supply and career management problems, distinguishing especially between the roles played by exploratory and normative models. The author hopes that this article will give management scientists a realistic appraisal of current practice and provide pointers as to where developments are most needed.     

Tactical Manpower Planning via Programming Under Uncertainty

This paper presents models for different types of manpower pooling policies. A multi-grade manpower system with mutually exclusive skills is considered. The work load imposed is a random variable characterized by the known joint distribution of the number of jobs to be performed and of the time to do a job. The basic models are developed as a tool for manpower planning in the jobbing workshops of an oil company. The resulting "two-stage programmes under uncertainty" are shown to reduce to mixed-integer linear programmes. The models are then generalized to permit their use in a larger class of manpower planning problems.     

Hidden heterogeneity in manpower systems: A Markov-switching model approach

In modeling manpower systems, it is of crucial importance to deal with heterogeneity. Until recently, manpower models are dealing with heterogeneity due to observable sources, neglecting heterogeneity due to latent sources. In this paper a two-step procedure is introduced. In the first step personnel groups homogeneous with respect to the transition probabilities are determined in a classical way by taking into account the observable sources of heterogeneity. In the second step heterogeneity caused by latent sources is handled. A multinomial Markov-switching manpower model is introduced that deals with heterogeneity due to latent sources for the internal flows as well as for the wastage flows. The model incorporates the mover-stayer principle. A re-estimation algorithm is presented to estimate the parameters of the Markov-switching manpower model. The switching approach offers a methodology to build a Markov model with personnel groups as states that are more homogeneous, and therefore can contribute to a better validity of the manpower model.     

Approximations for interactive Markov chains in discrete and continuous time

A class of models called interactive Markov chains is studied in both discrete and continuous time. These models were introduced by Conlisk and serve as a rich class for sociological modeling, because they allow for interactions among individuals. In discrete time, it is proved that the Markovian processes converge to a deterministic process almost surely as the population size becomes infinite. More importantly, the normalized process is shown to be asymptotically normal with specified mean vector and covariance matrix. In continuous time, the chain is shown to converge weakly to a diffusion process with specified drift and scale terms. The distributional results will allow for the construction of a likelihood function from interactive Markov chain data, so these results will be important for questions of statistical inference. An example from manpower planning is given which indicates the use of this theory in constructing and evaluating control policies for certain social systems.     

A Survey of Manpower Planning Models and Their Application

Since the late 1950s, much work has been done on developing models of manpower systems which may be used for the purposes of planning. Many organizations have made successful use of such models, but in spite of these successes, manpower planning models are only gradually coming into widespread use. The aim of this paper is to review the models which have been developed, concentrating on their assumptions and applications rather than on mathematical or statistical details. A common theme of successful applications is that good presentation of results and ease of use are more important to users than theoretical sophistication.     

Optimal recruitment strategies in a multi-level manpower planning model

Markov manpower planning models have extensively been analysed in the past in order to find an optimal personnel strategy for which the stocks of the manpower system evolve towards desirable ones. So far, those models do not take into account interactions among different organizational decision levels. In this paper, a multi-level manpower planning model is presented that considers, besides the desirable stock vector at overall level, proposals for the departmental stocks from lower organizational levels. Attainability of the stock vectors at departmental level is examined under control by recruitment and interdepartmental transitions. A multi-level optimization algorithm is presented to determine an optimal recruitment strategy resulting in attainable and acceptable stocks that are a compromise between the proposal from the top and the proposals from the departments.     

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.     

Stochastic models for air cargo terminal manpower supply planning in long‐term operations

In this research, based on two deterministic‐demand planning models, we established two long‐term stochastic‐demand planning models by incorporating the stochastic disturbances of manpower demands that occur in actual operations. The models are formulated as mixed integer linear programs that are solved using a mathematical programming solver. To compare the performance of the two stochastic‐demand and two deterministic‐demand planning models under the stochastic demands that occur in actual operations, we further develop a simulation‐based evaluation method. Finally, we perform numerical tests using real operating data from a Taiwan air cargo terminal. The preliminary results show that the stochastic models could be useful for planning air cargo terminal manpower supply. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Short-term manpower planning for MRT carriage maintenance under mixed deterministic and stochastic demands

The purpose of this research is to develop two manpower supply planning models and a solution algorithm for mass rapid transit carriage maintenance under mixed deterministic and stochastic demands. These models are formulated as mixed integer programs that are characterized as NP-hard. We employ problem decomposition techniques, coupled with the CPLEX mathematical programming solver, to develop an algorithm that is capable of efficiently solving the problems. The models and the method used currently in actual operations are evaluated by a simulation-based evaluation method. Finally, we perform a case study using real operating data from a Taiwan MRT maintenance facility. The preliminary results are good, showing that the models could be useful for planning carriage maintenance manpower supply.     

Stochastic Programming Applied to Human Resource Planning

This paper shows how state space models for human resource planning may be extended from linear and goal-programming formulations to cover the case where manpower demands and available resources for future periods are not known with certainty. Under reasonable assumptions, the problem can be treated as a multi-period stochastic program with simple recourse. Normal and Beta probability distributions are fitted to the right hand sides, and the equivalent determinstic programme solved using convex separable programming. An application of this methodology to a military human resource planning problem is described. Solution times for the stochastic model compare favourably with those for a goal-programming model of the same human resource system.     

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.     

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.     

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.     

Human resources management at a marine container terminal

We consider the manpower planning problem in the real context of a marine container terminal. The main features of this problem are the uncertainty of workforce demand and the need of ensuring a time continuous efficiency of the terminal, which enforces to decompose the problem into two phases: a long-period planning first and then a daily planning.We propose mathematical programming models for both problems and suitably tailor them to the container terminal at the Gioia Tauro port. We derive solution algorithms by exploiting the mathematical properties of the models: a heuristic approach to a set-covering type problem for the long-term planning, and a branch-and-bound algorithm for the short-term planning. Finally, we report computational results on some real instances.     

A stochastic manpower planning model under varying class sizes

Solution related to different types of manpower planning problems arising in different industries and organizations are very much helpful for proper planning and implementation of different objectives. Previously those type of problems are mostly solved under the deterministic set up. Gradually several scientists have developed different types of stochastic models appropriate for solving such types of problems. The present study is an attempt to develop a stochastic manpower planning model under the set up where the classes are of varying sizes and promotion occurs only on the basis of seniority. The work of second author was supported by a research fellowship from Council of Scientific and Industrial Research (Sanction No. 9/28(611)/2003-EMR-I), India.     

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.     

Corporate manpower planning

In this paper the necessity of corporate manpower planning is discussed and the growing interest in it within many organizations. In particular medium and long term forecasting in rather large and structured organizations are explained and the need for tools to get a survey of the evolution of their personnel strength. These tools should help management and staff-members of a planning or personnel department to design alternative policies concerning promotions, recruitments, etc.We will present a planning method which satisfies these requirements. The interactive manpower planning system FORMASY presents forecasts concerning the evolution of the personnel strength and makes it possible to assess the impacts of alternative policies. This planning system is based on a Markov model and is being used on a general purpose computer in several Dutch organizations, both industrial and governmental.FORMASY has proved its value for practical manpower planning which will be explained by means of a case-study with the Royal Dutch Airforce.     

The multivariate non-homogeneous Markov manpower system in a departmental mobility framework

The present paper proposes a non-homogeneous multivariate Markov manpower system in the general category of mathematical human resource planning. More specifically, we suggest a model, which takes into account the divisions existing in an organization categorizing its employees into several groups (departments). In this context, it considers not only possible transitions within the departments (intra-department transitions), but also, transfers of personnel between departments (inter-department transitions). Additionally, the proposed modeling structure is accompanied by cost and stocks (personnel) objectives which are set and in the sequel could be achieved by controlling either the recruitment policy or the allocation policy of employees transferred to other departments (or both). We use a minmax fuzzy goal-programming approach, under different operating assumptions, in order to keep the operational cost below desired aspiration levels and reach desirable stock structures in the presence of system’s constraints and regulations. The paper concludes with a numerical illustration.