An application of the system-point method to inventory models under continuous review

This paper derives the stationary probability distribution of inventory level for continuous-review models, by means of the system-point method of level-crossing analysis. We analyze inventory problems with decaying products under (nQ, r) and (s, S) ordering policies and zero lead-time, and derive the relevant cost functions. Our results have implications for the case of positive lead-time and to a non-decaying inventory problem with two types of demand processes.

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The System Point Method in Exponential Queues: A Level Crossing Approach

Mathematics of Operations Research ◽

10.1287/moor.6.1.31 ◽

1981 ◽

Vol 6 (1) ◽

pp. 31-49 ◽

Cited By ~ 54

Author(s):

P. H. Brill ◽

M. J. M. Posner

Keyword(s):

Point Method ◽

Level Crossing ◽

System Point

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Two-Commodity Markovian Inventory System with Set of Reorders

International Journal of Information Systems and Supply Chain Management ◽

10.4018/jisscm.2010040103 ◽

2010 ◽

Vol 3 (2) ◽

pp. 52-67 ◽

Cited By ~ 2

Author(s):

N. Anbazhagan ◽

B. Vigneshwaran

Keyword(s):

Probability Distribution ◽

Lead Time ◽

Inventory System ◽

Poisson Processes ◽

Inventory Level ◽

Numerical Examples ◽

Cost Rate ◽

Continuous Review ◽

Operational Characteristics ◽

Ordering Quantity

This article examines a two commodity substitutable inventory system—two different brands of super computers under continuous review. The demand points for each commodity are assumed to form independent Poisson processes. The reordering policy is to place orders for both the commodities when the total net inventory level drops to any one of the prefixed levels with prescribed probability distribution. Lost sales are assumed during the stock out period. The lead time for a reorder is exponentially distributed with parameter(, depending on the size of the ordering quantity. The limiting probability distribution for the joint inventory levels is also evaluated. Various operational characteristics and total expected cost rate are derived. Numerical examples are provided to find optimal reorder quantity and band width .

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Approximations for the single-product production-inventory problem with compound Poisson demand and service-level constraints

Advances in Applied Probability ◽

10.2307/1427075 ◽

1984 ◽

Vol 16 (2) ◽

pp. 378-401 ◽

Cited By ~ 17

Author(s):

A. G. De kok ◽

H. C. Tijms ◽

F. A. Van der Duyn Schouten

Keyword(s):

Poisson Process ◽

Compound Poisson Process ◽

Service Level ◽

Inventory Level ◽

Inventory Problem ◽

Single Product ◽

Compound Poisson ◽

Poisson Demand ◽

Production Inventory ◽

Random Fluctuations

We consider a production-inventory problem in which the production rate can be continuously controlled in order to cope with random fluctuations in the demand. The demand process for a single product is a compound Poisson process. Excess demand is backlogged. Two production rates are available and the inventory level is continuously controlled by a switch-over rule characterized by two critical numbers. In accordance with common practice, we consider service measures such as the average number of stockouts per unit time and the fraction of demand to be met directly from stock on hand. The purpose of the paper is to derive practically useful approximations for the switch-over levels of the control rule such that a pre-specified value of the service level is achieved.

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Increasing Productivity by Reducing Manufacturing Lead Time through Value Stream Mapping

International Journal of Mechanical and Industrial Engineering ◽

10.47893/ijmie.2012.1044 ◽

2012 ◽

pp. 225-229

Author(s):

Renu Yadav ◽

Ashish Shastri ◽

Mithlesh Rathore

Keyword(s):

Lead Time ◽

Value Added ◽

Value Stream Mapping ◽

Mapping Technique ◽

Inventory Level ◽

Lead Times ◽

Business World ◽

Value Stream ◽

Current State ◽

Future State

To survive in today’s competitive business world, companies require small lead times, low costs and high customer service levels. As such, companies pay more effort to reduce their manufacturing lead times. Value stream mapping (VSM) technique has been used on a broad scale in big companies such as Toyota and Boeing. This paper considers the implementation of value stream mapping technique in manufacturing helical springs by railway spring manufacturing company. It focuses on product family, current state map improvements and the future state map. The aim is to identify waste in the form of non value added activities & processes and then removing them to improve the performance of the company. Current state map is prepared to describe the existing position and various problem areas.. Future state map is prepared to show the proposed improvement action plans. The achievements of value stream implementation are reduction in lead time, cycle time and inventory level. It was found that even a small company can make significant improvements by adopting VSM technology. It was concluded that if we adopt the VSM technique the company could reduce the manufacturing lead time from 36.86 days to 34.06 days.

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Explore the Inventory Problem in a System Point of View: A Lot Sizing Policy

Proceedings of the Institute of Industrial Engineers Asian Conference 2013 ◽

10.1007/978-981-4451-98-7_179 ◽

2013 ◽

pp. 1529-1537

Author(s):

Tsung-Shin Hsu ◽

Yu-Lun Su

Keyword(s):

Lot Sizing ◽

Point Of View ◽

Inventory Problem ◽

System Point

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SUPPLY LEAD TIME UNCERTAINTY IN A SUSTAINABLE ORDER QUANTITY INVENTORY MODEL

Management and Production Engineering Review ◽

10.2478/mper-2013-0034 ◽

2013 ◽

Vol 4 (4) ◽

pp. 15-27 ◽

Cited By ~ 14

Author(s):

Salvatore Digiesi ◽

Giorgio Mossa ◽

Giovanni Mummolo

Keyword(s):

Inventory Management ◽

Lead Time ◽

Expected Value ◽

Air Pollutant ◽

Pollutant Emission ◽

Optimal Order ◽

Inventory Level ◽

Order Quantity ◽

Industrial Case Study ◽

Safety Stock

Abstract Transport plays a key role in inventory management since it affects logistic costs as well as environmental performance of the supply chain. Expected value and variability of supply lead time depend on the transportation means adopted, and influence the optimal values of order quantity, reorder level, and safety stock to be adopted. Fast transportation means allow reducing expected value of the lead time; they are characterized by the highest costs of externalities (i.e. air pollutant emission, noise, congestion, accidents). On the contrary, slow transportation means require high inventory level due to large order quantity; in this case costs of externalities tend to decrease. The Sustainable Order Quantity (SOQ) [1] allows identifying optimal order quantity, reorder level, safety stock as well as transportation means which minimize the sum of the logistic and environmental costs in case of stochastic variability of product demand. In this paper, the authors propose a new SOQ analytical model considering stochastic variability of supply lead time (LT). A solution procedure is suggested for solving the proposed model. The approach is applied to a real industrial case study in order to evaluate the benefits of applying it if compared with the traditional one.

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Comparison between continuous review inventory control systems for perishables with deterministic lifetime and lead time

2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO) ◽

10.1109/icmsao.2013.6552713 ◽

2013 ◽

Author(s):

Chaaben Kouki ◽

Zied Jemai ◽

Evren Sahin ◽

Yves Dallery

Keyword(s):

Control Systems ◽

Inventory Control ◽

Lead Time ◽

Continuous Review

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Simulation-Based Optimization of a Two-Echelon Continuous Review Inventory Model with Lot Size-Dependent Lead Time

Processes ◽

10.3390/pr8091014 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1014

Author(s):

Ibrahim Alharkan ◽

Mustafa Saleh ◽

Mageed Ghaleb ◽

Abdulsalam Farhan ◽

Ahmed Badwelan

Keyword(s):

Supply Chain ◽

Lead Time ◽

Shop Floor ◽

Lot Size ◽

Continuous Review ◽

Inventory Costs ◽

Size Dependent ◽

Simulation Based ◽

Simulation Based Optimization ◽

Total Inventory

This study analyzes a stochastic continuous review inventory system (Q,r) using a simulation-based optimization model. The lead time depends on lot size, unit production time, setup time, and a shop floor factor that represents moving, waiting, and lot size inspection times. A simulation-based model is proposed for optimizing order quantity (Q) and reorder point (r) that minimize the total inventory costs (holding, backlogging, and ordering costs) in a two-echelon supply chain, which consists of two identical retailers, a distributor, and a supplier. The simulation model is created with Arena software and validated using an analytical model. The model is interfaced with the OptQuest optimization tool, which is embedded in the Arena software, to search for the least cost lot sizes and reorder points. The proposed model is designed for general demand distributions that are too complex to be solved analytically. Hence, for the first time, the present study considers the stochastic inventory continuous review policy (Q,r) in a two-echelon supply chain system with lot size-dependent lead time L(Q). An experimental study is conducted, and results are provided to assess the developed model. Results show that the optimized Q and r for different distributions of daily demand are not the same even if the associated total inventory costs are close to each other.

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