Lakdere Benkherouf

Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand

Abstract In this paper we present optimal and heuristic procedures for the inventory replenishment problem in which items are deteriorating at a constant rate. The demand rates are changing exponentially with time over a known and finite planning horizon. We have developed an iterative numerical procedure to find the optimal replenishment schedule. The first two heuristics are based on the economic order interval approximation. The third heuristic restricts all the replenishment cycles over the planning horizon to be equal over the planning horizon. The last three heuristics are extended versions of the Silver-Meal heuristic, the least cost approach, and the least-unit cost heuristic which were used in the inventory literature for the case of discrete time-varying demand without deterioration. We further assess the cost and computation time effectiveness of the six heuristics. The results of a sample of 1440 problems show that the extended least cost approach is the most cost effective.

A deterministic order level inventory model for deteriorating items with two storage facilities

Abstract Sarma [3] developed an inventory model for a single deteriorating item which is stored in two different warehouses: an owned warehouse (OW) and a rented warehouse (RW). The rented warehouse is used for storing the excess units over the fixed capacity W of the OW and is assumed to offer better preserving facilities than the OW resulting in a lower rate of deterioration. Also, the RW is assumed to charge higher holding cost than the OW. In his paper, Sarma obtained an optimal replenishment schedule when the demand rate is constant over a fixed cycle length where the OW has to stock a specified known quantity. In this paper, we relax the assumptions of fixed cycle length and known quantity to be stocked in the OW. Further, we find the optimal schedule that minimizes the total cost per unit time in a cycle for an arbitrary demand rate function where cycles are assumed to form a regenerative process. We also present numerical examples.

On an inventory model with deteriorating items and decreasing time-varying demand and shortages

In this paper we present an optimal procedure for finding the replenishment schedule for an inventory system with shortages, in which items deteriorate at a constant rate and demand rates are decreasing over a known and finite planning horizon. A numerical example is presented to illustrate the procedure.

A production lot size inventory model for deteriorating items and arbitrary production and demand rates

Abstract In this paper, we present a method for finding the optimal replenishment schedule for the production lot size model with deteriorating items, where demand and production are allowed to vary with time in an arbitrary way and in which shortages are allowed. The method is illustrated by a numerical example.

On the optimal replenishment schedule for an inventory system with deteriorating items and time-varying demand and production rates

In this paper, we present an exact method for finding the optimal replenishment schedule for an inventory system with deteriorating items, and in which demand and production rates are allowed to vary over a finite planning horizon. A numerical example is presented to illustrate the method.

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.

On the generalized Euler distribution

In this paper, a new family of distributions is introduced which we name the generalized Euler distributions. This family arises as a consequence of investigating optimal strategies for drilling in an oil exploration model. Properties of this family are presented.

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.

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