TWO COMMODITY COORDINATED INVENTORY SYSTEM WITH MARKOVIAN DEMAND

2006 ◽  
Vol 23 (04) ◽  
pp. 497-508 ◽  
Author(s):  
V. S. S. YADAVALLI ◽  
G. ARIVARIGNAN ◽  
N. ANBAZHAGAN
Keyword(s):  
Probability Distribution ◽  
Inventory System ◽  
Poisson Processes ◽  
Expected Cost ◽  
Numerical Examples ◽  
Cost Rate ◽  
Continuous Review ◽  
Long Run ◽  
Operational Characteristics ◽  
The One

This paper considers a two commodity continuous review inventory system. The demand points for each commodity are assumed to form Poisson processes. It is further assumed that the demand for the first commodity require the one unit of second commodity in addition to the first commodity with probability p1. Similarly, the demand for the second commodity require the one unit of first commodity in addition to the second commodity with probability p2. This assumption model the situation in which a buyer who intends to buy one particular commodity may also go for another commodity. The limiting probability distribution for the joint inventory levels is computed. Various operational characteristics, expression for the long run total expected cost rate is derived. The results are illustrated with numerical examples.

Two-Commodity Markovian Inventory System with Set of Reorders

2012 ◽  
pp. 231-244
Author(s):  
N. Anbazhagan ◽  
B. Vigneshwaran
Keyword(s):  
Probability Distribution ◽  
Inventory System ◽  
Poisson Processes ◽  
Inventory Level ◽  
Lost Sales ◽  
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 .

Two-Commodity Markovian Inventory System with Set of Reorders

2010 ◽  
Vol 3 (2) ◽  
pp. 52-67 ◽  
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 .

Two-Way Substitutable Inventory System with N–Policy

2010 ◽  
pp. 253-260
Author(s):  
N. Anbazhagan
Keyword(s):  
Inventory System ◽  
Inventory Level ◽  
Unit Size ◽  
Cost Rate ◽  
Continuous Review ◽  
Time Points ◽  
Stochastic Inventory ◽  
Ordering Policy ◽  
Long Run ◽  
Operational Characteristics

This article presents a two commodity stochastic inventory system under continuous review. The maximum storage capacity for the i-th item is fixed as Si (i = 1, 2). It is assumed that demand for the i-the commodity is of unit size and demand time points form Poisson distribution with parameter i = 1, 2. The reorder level is fixed as si for the i-th commodity (i = 1, 2) and the ordering policy is to place order for items for the i-th commodity (i = 1, 2) when both the inventory levels are less than or equal to their respective reorder levels. The lead time is assumed to be exponential. The two commodities are assumed to be substitutable. That is, if the inventory level of one commodity reaches zero, then any demand for this commodity will be satisfied by the item of the other commodity. If no substitute is available, then this demand is backlogged up to a certain level Ni, (i = 1, 2) for the i-th commodity. Whenever the inventory level reaches Ni, (i = 1, 2), an order for Ni items is replenished instantaneously. For this model, the limiting probability distribution for the joint inventory levels is computed. Various operational characteristics and expression for long run total expected cost rate are derived.

Stochastic Inventory System with Compliment Item and Retrial Customers

2016 ◽  
pp. 148-164
Author(s):  
N. Anbazhagan
Keyword(s):  
Inventory System ◽  
Inventory Level ◽  
Unit Size ◽  
Maximum Capacity ◽  
Numerical Examples ◽  
Continuous Review ◽  
Time Points ◽  
Stochastic Inventory ◽  
Operational Characteristics ◽  
Main Item

In this chapter, the author consider a two commodity stochastic inventory system under continuous review with maximum capacity of i-th commodity is Si(i=1,2). In this two commodity one is main item and the other is compliment item. It is assumed that demand for the i-th commodity is of unit size and demand time points form a Poisson process. The compliment item is supplied as a gift whenever the demand occurs for the main item, but no main item is provided as a gift for demanding a compliment item. Reordering for supply is initiated as soon as the on-hand inventory level of the main item reaches a certain level s1, and there is a lead time until the reorder arrives but instantaneous replenishment for the compliment item. The arriving any primary demands enter into an orbit, when the inventory level of main item is zero. The limiting probability distribution for both commodities and the number of demands in the orbit, is computed and various operational characteristics are derived. The results are illustrated with numerical examples.

Substitutable Inventory System with Partial Backlogging under Continuous Review

2016 ◽  
pp. 183-199
Author(s):  
B. Vigneshwaran ◽  
N. Anbazhagan ◽  
V. Perumal
Keyword(s):  
Inventory System ◽  
The Other ◽  
Inventory Level ◽  
Partial Backlogging ◽  
Numerical Examples ◽  
Cost Rate ◽  
Continuous Review ◽  
Time Points ◽  
Negative Exponential Distribution ◽  
Negative Exponential

Consider a two-commodity substitutable inventory system with storage capacity Si for commodity i, (i=1,2) under continuous review. The demand time points for each commodity are assumed to form independent Poisson processes. The two commodities are assumed to be substitutable. That is when any one of the commodity's inventory level reaches zero, then the demand for that commodity will be satisfied by the other commodity. If no substitute is available, then this demand is backlogged up to the level Ni, for commodity i, (i=1,2). The reordering policy is to place an order for both the commodities, when both inventory levels are less than or equal to their respective reorder levels. If the inventory level drops to N1 or N2, then both inventory levels are pulled back to their maximum levels S1 and S2 immediately and the previous order gets canceled. The lead time is assumed to follow negative exponential distribution. Various stationary measures of system performances have been derived and total expected cost rate is computed. Numerical examples are provided.

scholarly journals On the equivalence of various definitions of mixed poisson processes

2019 ◽  
Vol 69 (2) ◽  
pp. 453-468
Author(s):  
Demetrios P. Lyberopoulos ◽  
Nikolaos D. Macheras ◽  
Spyridon M. Tzaninis
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Random Variable ◽  
Poisson Processes ◽  
Counting Processes ◽  
Mixing Parameter ◽  
Mixed Poisson Process ◽  
Probability Spaces ◽  
The One

Abstract Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing probability distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of “canonical” probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions for the characterization of mixed Poisson processes in terms of disintegrations cannot be omitted.

scholarly journals Optimal Maintenance of a Production-inventory System With Continuous Repair Times and Idle Periods

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Preventive Maintenance ◽  
Average Cost ◽  
Inventory System ◽  
Control Limit ◽  
Raw Material ◽  
Production Unit ◽  
Numerical Examples ◽  
Long Run ◽  
Production Inventory ◽  
Production Inventory System

In this paper two similar models for the maintenance of a production-inventory system are considered. In both models, an input generating installation supplies a buffer with a raw material and a production unit pulls the raw material from the buffer. The installation in the first model and the production unit in the second model deteriorate stochastically over time and the problem of their optimal preventive maintenance is considered. In the first model, it is assumed that the installation, after the completion of its maintenance, remains idle until the buffer is evacuated, while in the second model, it is assumed that the production unit, after the completion of its maintenance, remains idle until the buffer is filled up. The preventive and corrective repair times of the installation in the first model and the preventive and corrective repair times of the production unit in the second model are continuous random variables with known probability density functions. Under a suitable cost structure, semi-Markov decision processes are considered for both models in order to find a policy that minimizes the long-run expected average cost per unit time. A great number of numerical examples provide strong evidence that, for each fixed buffer content, the average-cost optimal policy is of control-limit type in both models, i.e. it prescribes a preventive maintenance of the installation in the first model and a preventive maintenance of the production unit in the second model if and only if their degree of deterioration is greater than or equal to a critical level. Using the usual regenerative argument, the average cost of the optimal control-limit policy is computed exactly in both models. Four numerical examples are also presented in which the preventive and corrective repair times follow the Exponential, the Weibull, the Gamma and the Log-Normal distribution, respectively.

Random Age Replacement Policies with Periodic Planning Times

2019 ◽  
Vol 26 (05) ◽  
pp. 1950023 ◽  
Author(s):  
Satoshi Mizutani ◽  
Xufeng Zhao ◽  
Toshio Nakagawa
Keyword(s):  
Weibull Distribution ◽  
Failure Time ◽  
Optimal Solutions ◽  
Expected Cost ◽  
Numerical Examples ◽  
Cost Rate ◽  
Modeling Approaches ◽  
Maintenance Policies ◽  
Age Replacement

The random age replacement policies discussed in literatures are helpful to complete the nonstopping works with random working cycles, however, maintenance policies are more easily performed at periodic times in real applications. For such a viewpoint, this paper proposes that age replacement policies are planned at periodic times while considering the random working cycles. Using the modeling approaches of replacement first and last policies, we discuss two models such that the unit is replaced at periodic times [Formula: see text] and working cycles [Formula: see text], whichever occurs first and whichever occurs last. The expected cost rate models are obtained and their optimal solutions for [Formula: see text] and [Formula: see text] are discussed. The comparisons between the policies of [Formula: see text] and [Formula: see text], and replacement first and last are made from the point of cost. Numerical examples are illustrated when the failure time has a Weibull distribution.

A COMPARISON STUDY OF REPLACEMENT POLICIES FOR A CUMULATIVE DAMAGE MODEL

2014 ◽  
Vol 21 (04) ◽  
pp. 1450021
Author(s):  
ALFONSUS JULANTO ENDHARTA ◽  
WON YOUNG YUN
Keyword(s):  
Damage Model ◽  
Cumulative Damage ◽  
Replacement Policy ◽  
Model Parameters ◽  
Comparison Study ◽  
Expected Cost ◽  
Numerical Examples ◽  
Cost Rate ◽  
Periodic Inspection ◽  
Cumulative Damage Model

A comparison study in basic preventive replacement (PR) policies based on a cumulative damage model is done. Three well-known PR policies (time-based, shock number-based, cumulative damage-based policies) are considered and the expected cost rate is used as the objective function to determine the optimal policy. Each policy requires certain information in the cumulative damage model. We evaluate the expected values of information by numerical examples and investigate the effect of model parameters and cost terms on the optimal expected cost rate. A damage-based replacement policy with periodic inspection is also proposed and compared with the three PR policies by numerical examples.

On optimal life extension for degrading systems

2020 ◽  
Vol 234 (3) ◽  
pp. 487-495
Author(s):  
Ji Hwan Cha ◽  
Maxim Finkelstein
Keyword(s):  
Complex Systems ◽  
Preventive Maintenance ◽  
Life Extension ◽  
Optimal Solutions ◽  
Numerical Examples ◽  
Cost Rate ◽  
Noticeable Increase ◽  
Novel Approach ◽  
Long Run ◽  
Useful Life

We consider life extension models for critical, complex systems with relatively long lifecycles. In contrast to traditional optimal preventive maintenance that usually minimizes the corresponding long run cost rate, a finite number of preventive maintenances are performed to increase the expected lifetime of these systems in an optimal way. The cases of periodic and aperiodic preventive maintenance actions are discussed. The proposed novel approach to life extension allows for simple sensitivity analysis with respect to parameters of the model. The obtained optimal solutions can result in a noticeable increase in the useful life of complex systems. Our findings are illustrated by numerical examples.

Sign in / Sign up

Export Citation Format

Share Document