Optimal filters for a hidden Markov random field model

A Markov random field (MRF) is a useful technical tool for modeling dynamics systems exhibiting some type of spatio-temporal variability. In this paper, we propose optimal filters for the states of a partially observed temporal Markov random field. We also discuss parameters estimation. This generalizes an earlier work by Elliott and Aggoun [1].     

On an inventory model for deteriorating items and time-varying demand

In this paper, we present an optimal procedure for finding the replenishment schedule for the inventory system in which items deteriorate over time and demand rates are increasing over a known and finite planning horizon.     

Recursive Estimation of Inventory Quality Classes Using Sampling

In this paper we propose a new discrete time discrete state inventory model for perishable items of a single product. Items in stock are assumed to belong to one of a finite number of quality classes that are ordered in such a way that Class 1 contains the best quality and the last class contains the pre-perishable quality. By the end of each epoch, items in each inventory class either stay in the same class or lose quality and move to a lower class. The movement between classes is not observed. Samples are drawn from the inventory and based on the observations of these samples, optimal estimates for the number of items in each quality classes are derived.     

On an Inventory Model for Deteriorating Items With Increasing Time-varying Demand and Shortages

In this paper we present an exact solution for the inventory replenishment problem with shortages, in which items are deteriorating at a constant rate. The demand rates are increasing with time over a known and finite planning horizon. We also present a dynamic programming solution to the problem. Both these methods provide a net improvement over existing methods.     

Optimality of (s, S) policies for jump inventory models

This paper is concerned with the optimality of (s, S) policies for a single-item inventory control problem which minimizes the total expected cost over an infinite planning horizon and where the demand is driven by a piecewise deterministic process. Our approach is based on the theory of quasi-variational inequality.     

Oil Exploration: A Property of Beale's Model

In this paper we assume that an oil company has k areas in which to drill and occurrences of undiscovered oilfields are represented by the model of Beale. The company is seeking a strategy for drilling that maximizes its expected return under the constraint that the total amount spent on drilling in all areas must not exceed R. This leads to an integer programming problem. We establish that the expected return functions for the separate areas are concave and that this property can be used to reduce the computational effort required to find an optimal solution.     

Filtering of continuous-time Markov chains

This paper discusses finite-dimensional optimal filters for partially observed Markov chains. A model for a system containing a finite number of components where each component behaves like an independent finite state continuous-time Markov chain is considered. Using measure change techniques various estimators are derived.