Zaid T. Balkhi

On an inventory model for deteriorating items with stock dependent and time-varying demand rates

In this paper, we present an inventory model for deteriorating items with stock dependent and time-varying demand rates for a finite time planning horizon. We also suggest a procedure for finding the optimal replenishment schedule and show in a rigorous way that the policy suggested is indeed optimal. Further, we present a numerical example and conclude the paper with suggestions for possible future research.

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.

An optimal solution of a general lot size inventory model with deteriorated and imperfect products, taking into account inflation and time value of money

This paper considers a general production lot size inventory model with deteriorated and imperfect products taking into account inflation and time value of money. The production, demand, and deterioration rates are known, continuous, and differentiable functions of time. Shortages are allowed, but only a fraction of the stock out is backordered, and the rest is lost. Under these general assumptions, the inventory model is formulated, and a closed form of the total relevant costs of the underlying inventory system is obtained. Sufficient conditions which lead to a minimal solution of the considered problem are derived. Then, a rigorous mathematical analysis is used to prove that such a minimal solution is unique and global-optimal. A numerical verification of the proposed model is also given.

On a finite horizon production lot size inventory model for deteriorating items: An optimal solution

Abstract A generalized production lot size inventory model for deteriorating items over a finite planning horizon is considered. The demand, production, and deteriorating rates are assumed to be known and continuous functions of time. Shortages are allowed and completely backlogged. The conditions under which the system total cost attains its (unique) global minimum are derived. An example which illustrate the applicability of theoretical results is also introduced.

The effects of learning on the optimal production lot size for deteriorating and partially backordered items with time varying demand and deterioration rates

Abstract In this paper the full transmission of learning for the general production lot size problem with an infinite planning horizon is studied under the following assumptions: (1) Items deteriorate while they are produced or stored. (2) Both demand and deterioration rates are (known) functions of time. (3) Shortages are allowed, but are partially backordered. (4) The production rate is defined as the number of units produced per unit time. A closed form for the total relevant cost as well as a rigorous mathematical method that leads to a minimum total cost of the underlying inventory system are introduced. An illustrative example which explains the applications of the theoretical results as well as its numerical verification are also given.

On the global optimal solution to an integrated inventory system with general time varying demand, production and deterioration rates

In this paper a unified inventory model for integrated production system with a single product is presented. The production, demand and deterioration rates for the finished product and the deterioration rates for raw materials are assumed to be functions of time. A rigorous mathematical proof which shows the global optimality of the solution to the considered inventory system is introduced. A numerical example that illustrates the solution procedure is included.

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.

A generalized economic order quantity model with deteriorating items and time varying demand, deterioration, and costs

A dynamic inventory model with deteriorating items is considered in this paper. Besides the demand and deterioration rates, the cost parameters are also assumed to be general functions of time. Necessary and sufficient conditions for a unique optimal solution are derived. An illustrative example is provided.

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 global optimality of a general economic order quantity model for deteriorating items

In this paper an infinite time horizon inventory model, in which both demand and deterioration rates are functions of time, is considered. Shortages are permitted so that the demand within the stock out period is partially lost. A rigorous mathematical proof showing the global optimality of the solution to the proposed model is presented. Earlier results for similar problems can be shown as special cases of our model.