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Journal ArticleDOI: 10.1080/03610926.2019.1648827

Introduction, analysis and asymptotic behavior of a multi-level manpower planning model in a continuous time setting under potential department contraction

04 Mar 2021-Communications in Statistics-theory and Methods (Taylor & Francis)-Vol. 50, Iss: 5, pp 1173-1199
Abstract: A mathematical model in a multi-level manpower planning setting is developed and analyzed incorporating the divisions of an organization’s personnel into several homogeneous groups. The proposed fr...

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7 results found


Open accessJournal ArticleDOI: 10.3390/MATH9131496
25 Jun 2021-
Abstract: We address the problem of finding a natural continuous time Markov type process—in open populations—that best captures the information provided by an open Markov chain in discrete time which is usually the sole possible observation from data. Given the open discrete time Markov chain, we single out two main approaches: In the first one, we consider a calibration procedure of a continuous time Markov process using a transition matrix of a discrete time Markov chain and we show that, when the discrete time transition matrix is embeddable in a continuous time one, the calibration problem has optimal solutions. In the second approach, we consider semi-Markov processes—and open Markov schemes—and we propose a direct extension from the discrete time theory to the continuous time one by using a known structure representation result for semi-Markov processes that decomposes the process as a sum of terms given by the products of the random variables of a discrete time Markov chain by time functions built from an adequate increasing sequence of stopping times.

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Topics: Markov chain (71%), Markov process (69%), Discrete time and continuous time (67%) ... show more

4 Citations


Open accessJournal ArticleDOI: 10.3390/MATH9080868
15 Apr 2021-
Abstract: The homogeneous branching process with migration and continuous time is considered. We investigated the distribution of the period-life τ, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time. The probability generating function of the random process, which describes the behavior of the process within the period-life, was obtained. The boundary theorem for the period-life of the subcritical or critical branching process with migration was found.

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Topics: Branching process (69%), Stochastic process (57%), Moment (mathematics) (54%) ... show more

2 Citations



Open accessJournal ArticleDOI: 10.3390/MATH9151745
24 Jul 2021-
Abstract: Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena. The aim of this paper is to provide closed analytic forms for three types of probabilities which describe attributes of considerable research interest in semi-Markov modeling: (a) the number of transitions to a state through time (Occupancy), (b) the number of transitions or the amount of time required to observe the first passage to a state (First passage time) and (c) the number of transitions or the amount of time required after a state is entered before the first real transition is made to another state (Duration). The non-homogeneous in time recursive relations of the above probabilities are developed and a description of the corresponding geometric transforms is produced. By applying appropriate properties, the closed analytic forms of the above probabilities are provided. Finally, data from human DNA sequences are used to illustrate the theoretical results of the paper.

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Topics: Markov chain (59%), First-hitting-time model (59%)

1 Citations


Open accessJournal ArticleDOI: 10.1029/2020GH000313
Jinxin Zhu1, Shuo Wang2, Boen Zhang2, Dagang Wang1Institutions (2)
01 Apr 2021-
Abstract: The intensification of heat stress reduces the labor capacity and hence poses a threat to socio-economic development. The reliable projection of the changing climate and the development of sound adaptation strategies are thus desired for adapting to the decreasing labor productivity under climate change. In this study, an optimization modeling approach coupled with dynamical downscaling is proposed to design the optimal adaptation strategies for improving labor productivity under heat stress in China. The future changes in heat stress represented by the wet-bulb globe temperature (WBGT) are projected with a spatial resolution of 25 × 25 km by a regional climate model (RCM) through the dynamical downscaling of its driving global climate model (GCM). Uncertain information such as system costs, environmental costs, and subsidies are also incorporated into the optimization process to provide reliable decision alternatives for improving labor productivity. Results indicate that the intensification of WBGT is overestimated by the GCM compared to the RCM. Such an overestimation can lead to more losses in working hours derived from the GCM than those from the RCM regardless of climate scenarios. Nevertheless, the overestimated heat stress does not alter the regional measures taken to adapt to decreasing labor productivity. Compared to inland regions, the monsoon-affected regions tend to improve labor productivity by applying air conditioning rather than working overtime due to the cost differences. Consequently, decision-makers need to optimally make a balance between working overtime and air conditioning measures to meet sustainable development goals.

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Topics: Downscaling (56%), Productivity (53%), Climate model (52%) ... show more

1 Citations


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37 results found


Open accessBook
01 Nov 2008-
Abstract: Finite Non-Negative Matrices.- Fundamental Concepts and Results in the Theory of Non-negative Matrices.- Some Secondary Theory with Emphasis on Irreducible Matrices, and Applications.- Inhomogeneous Products of Non-negative Matrices.- Markov Chains and Finite Stochastic Matrices.- Countable Non-Negative Matrices.- Countable Stochastic Matrices.- Countable Non-negative Matrices.- Truncations of Infinite Stochastic Matrices.

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Topics: Integer matrix (70%), Matrix (mathematics) (68%), Matrix analysis (66%) ... show more

2,736 Citations


Journal ArticleDOI: 10.2307/3213839
Abstract: In this paper we study the asymptotic behavior of Markov systems and especially non-homogeneous Markov systems. It is found that the limiting structure and the relative limiting structure exist under certain conditions. The problem of weak ergodicity in the above non-homogeneous systems is studied. Necessary and sufficient conditions are provided for weak ergodicity. Finally, we discuss the application of the present results in manpower systems.

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Topics: Markov property (61%), Markov chain (61%), Markov kernel (61%) ... show more

86 Citations


Open access
01 Feb 2005-
Abstract: : This report presents the review of workforce planning applications of operations research and explores potential modelling of military training. We classify the operations research techniques applied in workforce planning into four major branches: Markov chain models, computer simulation models, optimisation models and supply chain management through System Dynamics. For each of these, we outline the underlying mathematical formalism and concepts, overview models published and discus potential limitations. The prospect of modelling training forces via System Dynamics is demonstrated by a causal-loop analysis of the military officer system and a simulation model based on a stock-flow diagram for a one-rank officer training system.

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69 Citations


Open accessJournal ArticleDOI: 10.1016/0024-3795(94)90470-7
Abstract: We study the asymptotic behavior of a nonhomogeneous semi-Markov system (population) in discrete time. After a series of definitions, lemmas, and theorems, we firstly establish the conditions under which the ergodic behavior of a nonhomogeneous semi-Markov chain exists and then find the limit of the basic matrix of the chain Q(n, s) in closed form. Finally, the existence of the asymptotic population structure of the nonhomogeneous semi-Markov system is studied, and the limit is provided in closed analytic form.

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Topics: Population (54%), Series (mathematics) (52%), Ergodic theory (51%) ... show more

51 Citations


Journal ArticleDOI: 10.1002/ASMB.454
Andreas C. Georgiou1, N. TsantasInstitutions (1)
Abstract: 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.

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48 Citations


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