scholarly journals Comparison of Inventory Systems with Service, Positive Lead-Time, Loss, and Retrial of Customers

2007 ◽  
Vol 2007 ◽  
pp. 1-23 ◽  
Author(s):  
A. Krishnamoorthy ◽  
K. P. Jose
Keyword(s):  
Steady State ◽  
System Performance ◽  
Lead Time ◽  
Inventory Systems ◽  
Inventory Level ◽  
Analytic Method ◽  
Finite Capacity ◽  
Inventory Models ◽  
Time Loss ◽  
Linear Rate

We analyze and compare three (s,S) inventory systems with positive service time and retrial of customers. In all of these systems, arrivals of customers form a Poisson process and service times are exponentially distributed. When the inventory level depletes to s due to services, an order of replenishment is placed. The lead-time follows an exponential distribution. In model I, an arriving customer, finding the inventory dry or server busy, proceeds to an orbit with probability γ and is lost forever with probability (1−γ). A retrial customer in the orbit, finding the inventory dry or server busy, returns to the orbit with probability δ and is lost forever with probability (1−δ). In addition to the description in model I, we provide a buffer of varying (finite) capacity equal to the current inventory level for model II and another having capacity equal to the maximum inventory level S for model III. In models II and III, an arriving customer, finding the buffer full, proceeds to an orbit with probability γ and is lost forever with probability (1−γ). A retrial customer in the orbit, finding the buffer full, returns to the orbit with probability δ and is lost forever with probability (1−δ). In all these models, the interretrial times are exponentially distributed with linear rate. Using matrix-analytic method, we study these inventory models. Some measures of the system performance in the steady state are derived. A suitable cost function is defined for all three cases and analyzed using graphical illustrations.

Steady State Analysis of Impulse Customers and Cancellation Policy in Queueing-Inventory System

Processes ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 2146
Author(s):  
V. Vinitha ◽  
N. Anbazhagan ◽  
S. Amutha ◽  
K. Jeganathan ◽  
Gyanendra Prasad Joshi ◽  
...  
Keyword(s):  
Steady State ◽  
Lead Time ◽  
Arrival Process ◽  
Inventory Level ◽  
Stationary Probability ◽  
Probability Vector ◽  
Steady State Analysis ◽  
Proposed Model ◽  
Stationary Probability Vector ◽  
Bernoulli Schedule

This article discusses the queueing-inventory model with a cancellation policy and two classes of customers. The two classes of customers are named ordinary and impulse customers. A customer who does not plan to buy the product when entering the system is called an impulse customer. Suppose the customer enters into the system to buy the product with a plan is called ordinary customer. The system consists of a pool of finite waiting areas of size N and maximum S items in the inventory. The ordinary customer can move to the pooled place if they find that the inventory is empty under the Bernoulli schedule. In such a situation, impulse customers are not allowed to enter into the pooled place. Additionally, the pooled customers buy the product whenever they find positive inventory. If the inventory level falls to s, the replenishment of Q items is to be replaced immediately under the (s, Q) ordering principle. Both arrival streams occur according to the independent Markovian arrival process (MAP), and lead time follows an exponential distribution. In addition, the system allows the cancellation of the purchased item only when there exist fewer than S items in the inventory. Here, the time between two successive cancellations of the purchased item is assumed to be exponentially distributed. The Gaver algorithm is used to obtain the stationary probability vector of the system in the steady-state. Further, the necessary numerical interpretations are investigated to enhance the proposed model.

An upper bound on the performance of queues with returning customers

1987 ◽  
Vol 24 (02) ◽  
pp. 466-475 ◽  
Author(s):  
Betsy S. Greenberg ◽  
Ronald W. Wolff
Keyword(s):  
Steady State ◽  
Upper Bound ◽  
System Performance ◽  
Finite Capacity ◽  
Multiple Channel ◽  
Poisson Arrivals ◽  
Time Averages ◽  
Steady State Probabilities

Multiple channel queues with Poisson arrivals, exponential service distributions, and finite capacity are studied. A customer who finds the system at capacity either leaves the system for ever or may return to try again after an exponentially distributed time. Steady state probabilities are approximated by assuming that the returning customers see time averages. The approximation is shown to result in an upper bound on system performance.

An upper bound on the performance of queues with returning customers

1987 ◽  
Vol 24 (2) ◽  
pp. 466-475 ◽  
Author(s):  
Betsy S. Greenberg ◽  
Ronald W. Wolff
Keyword(s):  
Steady State ◽  
Upper Bound ◽  
System Performance ◽  
Finite Capacity ◽  
Multiple Channel ◽  
Poisson Arrivals ◽  
Time Averages ◽  
Steady State Probabilities

Multiple channel queues with Poisson arrivals, exponential service distributions, and finite capacity are studied. A customer who finds the system at capacity either leaves the system for ever or may return to try again after an exponentially distributed time. Steady state probabilities are approximated by assuming that the returning customers see time averages. The approximation is shown to result in an upper bound on system performance.

Decoupled Lead Time in finite capacity flowshop: a feedback loop approach

2019 ◽  
Author(s):  
Guillaume Dessevre ◽  
Guillaume Martin ◽  
Pierre Baptiste ◽  
Jacques Lamothe ◽  
Robert Pellerin ◽  
...  
Keyword(s):  
Lead Time ◽  
Feedback Loop ◽  
Finite Capacity

scholarly journals Increasing Productivity by Reducing Manufacturing Lead Time through Value Stream Mapping

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.

scholarly journals Perishable Inventory System with Postponed Demands and Negative Customers

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Paul Manuel ◽  
B. Sivakumar ◽  
G. Arivarignan
Keyword(s):  
Steady State ◽  
Joint Probability ◽  
Inventory System ◽  
Arrival Process ◽  
Inventory Level ◽  
Joint Probability Distribution ◽  
Time Interval ◽  
Negative Customers ◽  
Perishable Inventory System ◽  
Number Of Customers

This article considers a continuous review perishable (s,S) inventory system in which the demands arrive according to a Markovian arrival process (MAP). The lifetime of items in the stock and the lead time of reorder are assumed to be independently distributed as exponential. Demands that occur during the stock-out periods either enter a pool which has capacity N(<∞) or are lost. Any demand that takes place when the pool is full and the inventory level is zero is assumed to be lost. The demands in the pool are selected one by one, if the replenished stock is above s, with time interval between any two successive selections distributed as exponential with parameter depending on the number of customers in the pool. The waiting demands in the pool independently may renege the system after an exponentially distributed amount of time. In addition to the regular demands, a second flow of negative demands following MAP is also considered which will remove one of the demands waiting in the pool. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are calculated and the total expected cost per unit time is also considered. The results are illustrated numerically.

Analysis of Some Stochastic Inventory System in Supply Chain

2016 ◽  
pp. 124-147
Author(s):  
Bakthavachalam Rengarajan
Keyword(s):  
Steady State ◽  
Lead Time ◽  
Distribution Center ◽  
Setup Cost ◽  
Steady State Probability ◽  
Stochastic Inventory ◽  
Replenishment Policy ◽  
System States ◽  
Policy Supply ◽  
The Cost

In this chapter we consider a three echelon inventory control system which is modeled as a warehouse, single distribute and one retailer system handling a single product. A finished product is supplied from warehouse to distribution center which adopts one-for-one replenishment policy. The replenishment of items in terms of packets from warehouse to distribution center with exponential lead time having parameter µ1. Then the product is supplied from distribution center to retailer who adopts (s, S) policy. Supply to the retailer in packets of Q (= S - s) items is administrated with exponential lead time having parameter µ0. The demand at retailer node follows a Poisson with mean lambda. The steady state probability distribution of system states and the measures of system performance in the steady state are obtained explicitly. The Cost function is computed by using numerical searching algorithms, the optimal reorder points are obtained for various input parameters. Sensitivity analysis are discussed for various cost parameter such as holding cost, setup cost etc.

scholarly journals Inventory models for perishable items with inventory level dependent demand rate

2012 ◽  
Vol 36 (10) ◽  
pp. 5015-5028 ◽  
Author(s):  
Yongrui Duan ◽  
Guiping Li ◽  
James M. Tien ◽  
Jiazhen Huo
Keyword(s):  
Inventory Level ◽  
Inventory Models ◽  
Perishable Items ◽  
Demand Rate ◽  
Dependent Demand Rate ◽  
Dependent Demand
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