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.     

Modelling recruitment training in mathematical human resource planning

This paper deals with mathematical human resource planning; more specifically, it suggests a new model for a manpower‐planning system. In general, we study a k‐classed hierarchical system where the workforce demand at each time period is satisfied through internal mobility and recruitment. The motivation for this work is based on various European Union incentives, which promote regional or local government assistance programs that could be exploited by firms not only for hiring and training newcomers, but also to improve the skills and knowledge of their existing personnel. In this respect, in our augmented mobility model we establish a new ‘training/standby’ class, which serves as a manpower inventory position for potential recruits. This class, which may very well be internal or external to the system, is incorporated into the framework of a non‐homogeneous Markov chain model. Furthermore, cost objectives are employed using the goal‐programming approach, under different operating assumptions, in order to minimize the operational cost in the presence of system's constraints and regulations. Copyright © 2002 John Wiley & Sons, Ltd.     

Modelling heterogeneity in a manpower system: a review

Manpower planning is an essential methodology for business and industry; it allows managers to make more efficient use of human resources. However, human behaviour is highly variable and it is therefore essential for manpower planning that population heterogeneity is successfully modelled. In this paper we review methods of incorporating population heterogeneity into manpower modelling. The analysis of differentials in a manpower system is emphasized since they are a source of aggregation error in stochastic models. Two strategies have been stressed, the use of observable sources of heterogeneity as they affect wastage, and the latent sources which cannot be identified precisely but are known to affect the key parameters of most models. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

The augmented semi‐Markov system and its asymptotic behaviour

This paper suggests a generalized semi‐Markov model for manpower planning, which could be adopted in cases of unavailability of candidates with the desired qualifications/experience, as well as in cases where an organization provides training opportunities to its personnel. In this context, we incorporate training classes into the framework of a non‐homogeneous semi‐Markov system and we introduce an additional, external semi‐Markov system providing the former with potential recruits. For the model above, referred to as the Augmented Semi‐Markov System, we derive the equations that reflect the expected number of persons in each grade and we also investigate its limiting population structure. An illustrative example is provided. Copyright © 2010 John Wiley & Sons, Ltd.     

On the equilibrium personnel structure in the presence of vertical and horizontal mobility via multivariate Markov chains

The present paper employs the Multivariate Homogeneous Markov System (MHMS) in the context of Markov manpower planning modelling. The system is regulated by an embedded multivariate Markov process that allows us to distinguish employees’ mobility patterns that take place either within or among the existing divisions (departments) of an organization. The motivation behind this step arises from the generalization of univariate Markov manpower planning models in which the organization is considered a single (probably hierarchical) group and from the fact that departmental mobility is actually common in most realistic establishments. The first part of the paper presents the functional relations of the MHMS governing intra/inter-departmental transitions. Using these functional forms, we proceed by studying the system’s equilibrium behaviour. This asymptotic analysis reveals the inherent tendencies of the system to reach the limiting structures of specific forms and properties under conditions imposed in the long run.     

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.     

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.     

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.     

Knowledge-based manpower planning

The capacity performance of knowledge-based systems differs essentially from the one of traditional systems. The result is that already today these systems are employed in a number of application areas, and that the intensity of research and development in this field is very high.In this paper the development of a knowledge-based manpower planning system (KBMS) is described. The two main components of this system are a knowledge-based system developed for management planning and a model designed for manpower planning in personnel leasing companies. This model was realized as a KBMPS by applying the knowledge-based system, which was developed for management planning.     

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.     

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.     

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.     

Endogenous optimization fisheries models

This paper deals with a special class of fisheries models referred to as endogenous optimization models. The distinctive feature of these models is that behaviour of the agents in the model is not predetermined by exogenous behavioural rules. In endogenous optimization models, the model agents are merely furnished with objectives such as profit or utility maximization. Given these objectives and the various constraints determined by the state of the model at each point of time, the agents solve their maximization problem. The corresponding values of their control variables then constitute their behaviour.Having generated individual agents' behaviour by endogenous optimization, summing over agents yields aggregate behaviour. Aggregate behaviour must conform with the overall constraints of the model, be they physical or otherwise. Within the market system, individual behaviour or rather plans are made compatible via changes in relative prices. Therefore, outside equilibrium, behavioural plans must be repeatedly modified to become mutually compatible. This implies iteratively solving the maximization problem of a number of different agents. Endogenous optimization models therefore tend to be computationally very demanding.Clearly, the basic principles of endogenous optimization are just as applicable to any model involving maximizing agents.     

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.     

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.     

A linear programming model for an optimum admissions policy in education

This work is a kind of feasibility study mixed with optimization techniques to decide upon the possibility of achieving a certain manpower structure together with a complete removal of illiteracy after a certain planning period. Changing the manpower structure is achieved by controlling the proportions of students who enter the different channels of formal education. The removal of illeteracy is achieved by accepting more and more students into the compulsory stage. It will be found that there is more than one option for achieving these objectives through the many control paths available.It is not easy to fulfil these two aims; the obstacles are the non-availability of teachers as well as the universal budget constraint. This will result in a limited number of feasible opportunity paths to choose from.In this paper the solution to the above problem is given. First the feasibility problem is dealt with by examining the possibility of changing the manpower structure after a certain planning period and subject to the above constraints. Once this is found possible, the optimal path regarding the admission of the students to the compulsory stage is given for the quickest removal of illiteracy.     

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.