Linear Programming is known to be an important and useful tool for solving Markov Decision Processes (MDP). its derivation relies on the Dynamic Programming approach, which also serves to solve MDP. However, for Markov Decision Processes with several constraints the only available methods are based on Linear Programs. The aim of this paper is to investigate some aspects of such Linear Programs,...

Rangeland ecosystems shift across dynamic thresholds between differentecological states in response to natural or human-induced factors. These differentecological states are the result of interactions among climate, soils, grazing history,and management practices. The notion of a single ‘‘pristine’’ final state is onlyconceptual in nature, and because of this, dynamic thresholds and the effects...

Immediate roof caving in longwall mining is a complex dynamic process, and it is the core of numerous issues and challenges in this method. Hence, a reliable prediction of the strata behavior and its caving potential is imperative in the planning stage of a longwall project. The span of the main caving is the quantitative criterion that represents cavability. In this paper, two approaches are p...

In this chapter we present an approach that leverages linear programming to approximate optimal policies for controlled diffusion processes, possibly with high-dimensional state and action spaces. The approach fits a linear combination of basis functions to the dynamic programming value function; the resulting approximation guides control decisions. Linear programming is used here to compute ba...

In this work, a class of multidimensional stochastic hybrid dynamic models is studied. The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. Closed-form solutions of the syste...