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 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.

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.

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.

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 A Perishable Inventory System with Postponed Demands and Multiple Server Vacations

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
R. Jayaraman ◽  
B. Sivakumar ◽  
G. Arivarignan
Keyword(s):  
Steady State ◽  
Joint Probability ◽  
Life Time ◽  
Inventory System ◽  
Inventory Level ◽  
Joint Probability Distribution ◽  
Single Server ◽  
Cost Rate ◽  
Stochastic Inventory ◽  
Number Of Customers

A mathematical modelling of a continuous review stochastic inventory system with a single server is carried out in this work. We assume that demand time points form a Poisson process. The life time of each item is assumed to have exponential distribution. We assume(s,S)ordering policy to replenish stock with random lead time. The server goes for a vacation of an exponentially distributed duration at the time of stock depletion and may take subsequent vacation depending on the stock position. The customer who arrives during the stock-out period or during the server vacation is offered a choice of joining a pool which is of finite capacity or leaving the system. The demands in the pool are selected one by one by the server only when the inventory level is aboves, with interval time between any two successive selections distributed as exponential with parameter depending on the number of customers in the pool. The joint probability distribution of the inventory level and the number of customers in the pool is obtained in the steady-state case. Various system performance measures in the steady state are derived, and the long-run total expected cost rate is calculated.

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