scholarly journals Optimal policies for a deterministic continuous-time inventory model with several suppliers: a hyper-generalized (s,S) policy

2021 ◽  
Author(s):  
Lakdere Benkherouf ◽  
Brian H Gilding
Keyword(s):  
Continuous Time ◽  
Control Policy ◽  
Planning Horizon ◽  
Inventory Model ◽  
Inventory Level ◽  
Purchasing Cost ◽  
Continuous State ◽  
Quasi Variational Inequality ◽  
New Type ◽  
Total Inventory

A deterministic continuous-time continuous-state inventory model is studied. In the absence of intervention, the level of stock evolves by a process governed by a differential equation. The inventory level is monitored continuously, and can be adjusted upwards at any time. The decision maker can order from several suppliers, each of which charges a different ordering and purchasing cost. The problem of selecting the supplier and the size of the order to minimize the total inventory cost over an infinite planning horizon is formulated as the solution of a quasi-variational inequality (QVI). It is shown that the QVI has a unique solution. This corresponds to a generalized $(s,S)$ policy under amenable conditions, which have been characterized in an earlier work by the present authors. Under the complementary conditions a new type of optimal control policy emerges. This leads to the concept of a hyper-generalized  (s,S) policy. The theory behind a policy of this type is exposed.

scholarly journals Optimal policies for a deterministic continuous-time inventory model with several suppliers

2020 ◽  
Author(s):  
Lakdere Benkherouf ◽  
Brian Gilding
Keyword(s):  
Unique Solution ◽  
Continuous Time ◽  
Infinite Horizon ◽  
Planning Horizon ◽  
Inventory Model ◽  
Inventory Level ◽  
Discounted Cost ◽  
Continuous State ◽  
Quasi Variational Inequality ◽  
Necessary And Sufficient

This paper is concerned with determining the optimal inventory policy for an infinite-horizon deterministic continuous-time continuous-state inventory model, where, in the absence of intervention, changes in inventory level are governed by a differential evolution equation. The decision maker has the option of ordering from several suppliers, each of which entails differing ordering and purchasing costs. The objective is to select the supplier and the size of the order that minimizes the discounted cost over an infinite planning horizon. The optimal policy is formulated as the solution of a quasi-variational inequality. It is shown that there are three possibilities regarding its solvability: it has a unique solution that corresponds to an $(s,S)$ policy; it does not admit a solution corresponding to an $(s,S)$ policy but does have a unique solution that corresponds to a generalized $(s,S)$ policy; or, it does not admit a solution corresponding to an $(s,S)$ policy or a generalized $(s,S)$ policy. A necessary and sufficient condition for each possibility is obtained. Examples illustrate their occurrence.

Two-Echelon Inventory Stochastic Model of Supply Chain Based on Service Level Constraints

2014 ◽  
Vol 971-973 ◽  
pp. 2448-2451
Author(s):  
Da Li Jiang ◽  
Guang Fu Zhu ◽  
De Li
Keyword(s):  
Supply Chain ◽  
Stochastic Model ◽  
Service Level ◽  
Inventory Model ◽  
Inventory Level ◽  
Effective Algorithm ◽  
Inventory Cost ◽  
Total Inventory

The study on multi-echelon inventory of supply chain is becoming more and more important in E-business era. This paper proposes a two-echelon inventory model with one supplier and several retailers, in which a certain service level has to be satisfied and the goal is to minimize the total inventory cost. In addtion it puts forward an effective algorithm for this model to obtain the optimal replenishment period and inventory level of each supply chain node.

scholarly journals A stochastic inventory model with stock dependent demand items

2001 ◽  
Vol 14 (4) ◽  
pp. 317-328 ◽  
Author(s):  
Lakdere Benkherouf ◽  
Amin Boumenir ◽  
Lakhdar Aggoun
Keyword(s):  
Variational Inequality ◽  
Continuous Time ◽  
Infinite Horizon ◽  
Inventory Model ◽  
Stochastic Inventory ◽  
Stochastic Inventory Model ◽  
Stock Dependent Demand ◽  
Quasi Variational Inequality ◽  
Discounted Costs ◽  
Dependent Demand

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.

scholarly journals Planning Horizon for Production Inventory Models with Production Rate Dependent on Demand and Inventory Level

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jennifer Lin ◽  
Henry C. J. Chao ◽  
Peterson Julian
Keyword(s):  
Production Rate ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Inventory Model ◽  
Inventory Level ◽  
Inventory Models ◽  
New Production ◽  
Production Inventory ◽  
Infinite Planning Horizon ◽  
Finite Planning Horizon

This paper discusses why the selection of a finite planning horizon is preferable to an infinite one for a replenishment policy of production inventory models. In a production inventory model, the production rate is dependent on both the demand rate and the inventory level. When there is an exponentially decreasing demand, the application of an infinite planning horizon model is not suitable. The emphasis of this paper is threefold. First, while pointing out questionable results from a previous study, we propose a corrected infinite planning horizon inventory model for the first replenishment cycle. Second, while investigating the optimal solution for the minimization problem, we found that the infinite planning horizon should not be applied when dealing with an exponentially decreasing demand. Third, we developed a new production inventory model under a finite planning horizon for practitioners. Numerical examples are provided to support our findings.

Ordering Policy for Deteriorating Items with Short Shelf Life Based on Lateral Transshipment

2011 ◽  
Vol 204-210 ◽  
pp. 915-918
Author(s):  
Xin Yi Bu ◽  
Fang Zhou Teng
Keyword(s):  
Supply Chain ◽  
Shelf Life ◽  
Conceptual Model ◽  
Planning Horizon ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Inventory Level ◽  
Ordering Policy ◽  
Demand Rate ◽  
Lateral Transshipment

It is usually observed in the supermarkets that display of deteriorating items. These items are with short shelf life and difficult to be transported and stored. A supply chain conceptual model which consists of one supplier and two retailers is structured. Based on analysis of deteriorating inventory model in exist, the transshipment between the two retailers is added into the supply chain conceptual model and a deteriorating model is developed in this paper which can reflect more accurately the relation among inventory level, demand rate, deteriorating rate and lateral transshipment rate. The ordering policy taking into account the shelf life constraint is investigated with two last ordering opportunities on condition that the planning horizon can be modified based on the lateral transshipment. At last, the conclusion implies that the ordering policy for deteriorating items with short shelf life based on the lateral transshipment can improve the profit for the retailer.

scholarly journals Filtering and predicting the cost of hidden perished items in an inventory model

2002 ◽  
Vol 15 (3) ◽  
pp. 235-245
Author(s):  
Lakhdar Aggoun ◽  
Lakdere Benkherouf
Keyword(s):  
Joint Distribution ◽  
Inventory Model ◽  
The State ◽  
Inventory Level ◽  
Discrete State ◽  
History Of ◽  
Accumulated Losses ◽  
The Cost ◽  
State Of The Environment ◽  
Recursive Estimators

This paper is concerned with a discrete time, discrete state inventory model for items of changing quality. Items are assumed to be in one of a finite number, M, 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. The changes of items' quality are dependent on the state of the ambient environment. Furthermore, at each epoch time, items of different classes may be sold or moved to a lower quality class or stay in the same class. These items are priced according to their quality, and costs are incurred as items lose quality. Based on observing the history of the inventory level and prices, we propose recursive estimators as well as predictors for the joint distribution of the accumulated losses and the state of the environment.

scholarly journals Inventory model for deteriorating items with negative exponential demand, probabilistic deterioration and fuzzy lead time under partial back logging

2020 ◽  
Vol 30 (3) ◽  
Author(s):  
Nabendu Sen ◽  
Sumit Saha
Keyword(s):  
Inventory Management ◽  
Lead Time ◽  
Probability Distributions ◽  
Optimal Strategies ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Optimal Time ◽  
Inventory Cost ◽  
Total Inventory ◽  
Negative Exponential

The effect of lead time plays an important role in inventory management. It is also important to study the optimal strategies when the lead time is not precisely known to the decision makers. The aim of this paper is to examine the inventory model for deteriorating items with fuzzy lead time, negative exponential demand, and partially backlogged shortages. This model is unique in its nature due to probabilistic deterioration along with fuzzy lead time. The fuzzy lead time is assumed to be triangular, parabolic, trapezoidal numbers and the graded mean integration representation method is used for the defuzzification purpose. Moreover, three different types of probability distributions, namely uniform, triangular and Beta are used for rate of deterioration to find optimal time and associated total inventory cost. The developed model is validated numerically and values of optimal time and total inventory cost are given in tabular form, corresponding to different probability distribution and fuzzy lead-time. The sensitivity analysis is performed on variation of key parameters to observe its effect on the developed model. Graphical representations are also given in support of derived optimal inventory cost vs. time.

A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (02) ◽  
pp. 473-489
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

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