Generating optimal production schedules for manufacturing facilities is an area of great theoretical and practical importance. During the last decade, an effort has been made to reconcile the techniques developed by the AI and OR communities. The work described here aims to continue in this vein by showing how a class of well-defined stochastic scheduling problems can be mapped into a general s...

Keqi Yan: Fluid Models for Production-Inventory Systems (Under the direction of Professor Vidyadhar G. Kulkarni) We consider a single stage production-inventory system whose production and demand rates are modulated by a finite state Markov chain called the environment. Supplementary orders can be placed from external suppliers when needed. We model this system by a fluid-flow system and derive...

The generalized Lorenz order and the absolute Lorenz order are used in economics to compare income distributions in terms of social welfare. In Section 2, we show that these orders are equivalent to two stochastic orders, the concave order and the dilation order, which are used to compare the dispersion of probability distributions. In Section 3, a sufficient condition for the absolute Lorenz o...

In this paper, we will investigate two partial orders on classical states∆n that induce a domain theoretic structure. In particular, we will look at the Bayesian order presented by Coecke and Martin (2002) and the implicative order presented by Martin (2004). For both of the domains that arise from these orderings on the classical states, Shannon entropy is a measurement in the domain theoretic...

Any semiorder on a finite set can be reached from any other semiorder on the same set by elementary steps consisting either in the addition or in the removal of a single ordered pair, in such a way that only semiorders are generated at every step, and also that the number of steps equals the distance between the two semiorders. Similar results are also established for other families of relation...

Simulation tools have been used to construct a virtual work/process environment for the purpose of process analyses. The construct of a simulation model uses the processes, resources, process flow, entities etc; coupled together by statistical relationships. Simulation models developed for planning and design are often aggregated models using statistical distributions to model stochastic nature...

After dropping the standard general-equilibrium assumption that preference orders discount future consumption faster than the economy grows and dropping continuity and weakening utility representation, we establish commodity prices and consumptions that approach approximate equilibrium to within any practical tolerance. The Weiza cker-overtaking criterion defines the best-known non-standarddisc...

The state estimation problem, here investigated, regards a class of nonlinear stochastic systems, characterized by having the state model described through stochastic differential equations meanwhile the measurements are sampled in discrete times. This kind of model (continuousdiscrete system) is widely used in different frameworks (i.e. tracking, finance and systems biology). The proposed meth...

Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study stochastic relations, which may be viewed as natural generalizations of stochastic orders. This generalization is motivated by the observation that for the stoc...

We are interested in risk constraints for infinite horizon discrete time Markov decision processes (MDPs). Starting with average reward MDPs, we show that increasing concave stochastic dominance constraints on the empirical distribution of reward lead to linear constraints on occupation measures. An optimal policy for the resulting class of dominance-constrained MDPs is obtained by solving a li...