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

Adapting to Changing Labor Productivity as a Result of Intensified Heat Stress in a Changing Climate

“…Exploratory models are the analytical tools used to predict the change in the labor system in response to stationary situations. The commonly used exploratory models include renewal models (Chen et al., 2018; De Feyter et al., 2017), Markov (cross‐sectional) models (Di Francesco et al., 2016; Dimitriou & Georgiou, 2019; Knorzer, 2000), and semi‐Markov models (Bastian et al., 2020; Chattopadhyay & Gupta, 2007; Song & Huang, 2008). Moreover, previous studies introduced dynamic programming in a Markov model to generate optimal recruitment and transition patterns to meet various needs in labor requirements and service levels (Dimitriou & Tsantas, 2010).…”

Open Markov Type Population Models: From Discrete to Continuous Time

“…The approach of Markov and semi-Markov processes via kernels if fruitful and so we are lead to the following definitions and results for what we will now follow, mainly, the works in [67] (pp. [7][8][9][10][11][12][13][14][15] and in [33]. Consider a general measurable state space (Θ, A(Θ)).…”

“…Following the pioneering work of Gani, introducing in [6] what now is known as Cyclic Open Markov population models, there were further extensions in [7], for non-homogeneous Markov chains and then, for cyclic non-homogeneous Markov systems or equivalently for non-homogeneous open Markov population processes, by the authors of [8,9]. Let us stress that continuous time non-homogeneous Markov systems have been studied lately in [10]. Furthermore, the recent work in [11] develops an approach to open Markov chains in discrete time-allowing a particle physics interpretation-for which there is a state space of the Markov chain-where distributions are studied by means of moment generating functions-there is an exit reservoir, which is tantamount to a cemetery state and, there is an incoming flow of particles, defined as a stochastic process in discrete time whose properties-e.g., stationarity-condition the distribution law of the particles in the state space.…”

“…We want to determine an extended solution of the Kolmogorov forward equation given in Formula (A11), that is an extended solution of    P t (s 0 , t, λ) = P(s 0 , t, λ)Q(t, λ) P(t, t) = I, (10) an equation which, as seen in Formula (A12), can be read in integral form as, P(s 0 , t, λ) = I + [s 0 ,t] P(s 0 , s, λ)Q(s, λ)ds. (11) As previously said, we will now follow the general idea of successive approximations in the proof of the Picard-Lindelöf theorem for proving existence and unicity of solutions of ordinary differential equations for the forward Kolmogorov equation.…”

Period-Life of a Branching Process with Migration and Continuous Time

“…The theory of Non-Homogeneous Markov systems first introduced in [6]. The case of the Non-Homogeneous Markov systems in continuous time in its latest results exist in Dimitriou and Georgiou [7].…”