Lakhdar Aggoun

A diffusion inventory model for deteriorating items

This paper is concerned with finding the optimal impulse control schedule for a stochastic inventory model for deteriorating items that minimizes the total expected discounted cost over an infinite horizon. It turns out that the optimal impulse control policy can be found as a solution of a Quasi-Variational Inequality (QVI) problem of which details are provided. Further, the problem of finding the optimal impulse control policy that minimizes the total expected costs per unit time is addressed.

A hidden Markov model for an inventory system with perishable items

This paper deals with a parametric multi-period integer-valued inventory model for perishable items. Each item in the stock perishes in a given period of time with some probability. Demands are assumed to be random and the probability that an item perishes is not known with certainty. Expressions for various parameter estimates of the model are established and the problem of finding an optimal replenishment schedule is formulated as an optimal stochastic control problem.

ON A STOCHASTIC INVENTORY MODEL WITH DETERIORATION AND STOCK-DEPENDENT DEMAND ITEMS

In this article, we propose a new continuous-time stochastic inventory model with deterioration and stock-dependent demand items. We then formulate the problem of finding the optimal impulse control schedule that minimizes the total expected return over an infinite horizon, as a quasivariational inequality (QVI) problem. The QVI is shown to lead to an (s, S) policy, where s and S are determined uniquely as a solution of some algebraic equations.

A STOCHASTIC INVENTORY MODEL WITH STOCK DEPENDENT DEMAND ITEMS

In this paper, we propose a new continuous time stochastic inventory model for stock dependent demand items. We then formulate the problem of finding the optimal replenishment schedule that minimizes the total expected discounted costs over an infinite horizon as a Quasi-Variational Inequality (QVI) problem. The QVI is shown to have a unique solution under some conditions.

A stochastic jump inventory model with deteriorating items

In this paper, a single product continuous time stochastic inventory model for deteriorating items, driven by a. conditional Poisson process, is suggested. It is assumed the process Zt modulating the jump intensities of the Poisson process is a Markov chain. By observing the history of the inventory level, a finite dimensional filter for the conditional distribution of Zt is found. Further filters are found when the conditional Poisson process is replaced by an integer–valued random measure with predictable compensator depending on a right–constant sample paths process yt

On a stochastic inventory model with deteriorating items

We suggest a new inventory continuous time stochastic model for deteriorating items. We derive optimal operating characteristics of the expected cost per unit time under the assumption that demand in each replenishment cycle forms a regenerative process. We also present numerical examples. 2000 Mathematics Subject Classification. Primary 60K30, 60J10, 90B05.

Optimal adaptive estimators for partially observed numbers of defective items in inventory models

In this paper, three discrete time integer-valued inventory models for perishable items are introduced. In these models, each item in the stock is assumed to perish in a given period with some probability. The dynamics of the models are affected by a demand process, a replenishment process, and perishability. However perished items are not observed while in stock, unless sold. Recursive estimates for the probability of the number of the perished items are derived.

A STOCHASTIC INVENTORY MODEL WITH PERISHABLE AND AGING ITEMS

In this paper, we propose a single-product, discrete time inventory model for perishable items. Inventory levels are reviewed periodically and units in stock have a maximum lifetime of M periods. It is assumed that the dynamics of the inventory level is driven by a parameter process (reflecting perishability) and demands. By observing the history of the inventory level we obtain the conditional distribution of the perishability parameter

Finite-dimensional quasi-linear risk-sensitive control

A discrete-time partially observed stochastic control problem with exponential running cost is considered. The dynamics are linear and the running cost quadratic in the state variable, but the control may enter nonlinearly. Explicit solutions for a forward Zakai equation and a backward adjoint equation are derived in terms of finite-dimensional dynamics. This enables the partially observed problem to be expressed in finite-dimensional terms and a separation principle applied.

M-ary detection of Markov-modulated Poisson processes in inventory models

In this paper M-ary detection filters for discrete-time inventory models are derived. The models considered consist of a discrete-time Poisson process modeling hidden defective items in an inventory and a discrete-time Markov chain modeling the fluctuation of, for instance, the market. These processes are observed through discrete-time Poisson processes modeling the demand and the number of defective items returned to the inventory.