On (<i>s</i>, <i>S</i>) inventory system with random lead time and repeateddemands

Ushakumari, P. V.

doi:10.1155/jamsa/2006/81508

Cited by 26 publications

(12 citation statements)

References 10 publications

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“…By fixing all the parameters except the arrival rate λ, it is clear from Figure 5.1 that the cost function is convex A. Krishnamoorthy and K. P. Jose 15 (model with buffer size equal to the maximum inventory level S) can be considered as the best model for practical applications. As indicated in the introduction, Ushakumari [10] obtained analytical solution to inventory system with retrial of unsatisfied customers. However, she considered a system A.…”

Section: Interpretations Of the Graphsmentioning

confidence: 99%

“…Retrials of failed components for service were introduced into the reliability of k-out-of-n system by Krishnamoorthy and Ushakumari [8]. Artalejo et al [9] were the first to study inventory policies with positive lead-time and retrial of customers who could not get service during their earlier attempts to access the service station; it may be noted that recently Ushakumari [10] obtained analytical solution to this model. So far, very little investigation is done in retrial inventory with service time.…”

Section: Introductionmentioning

confidence: 99%

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

Krishnamoorthy

Jose

2007

Journal of Applied Mathematics and Stochastic Analysis

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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.

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Section: Interpretations Of the Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Krishnamoorthy

Jose

2007

Journal of Applied Mathematics and Stochastic Analysis

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“…J. R. Artalejo and A. Krishnamoorthy [8] have studied (s,S) inventory systems with repeated attempts and P.V. Ushakumari [13] considering random lead time. A .Krishnamoorthy and K.P.Jose [10] have studied the system with positive lead time, loss and retrial of customers.…”

Section: Introductionmentioning

confidence: 99%

Two Server (s, S) Inventory System with Positive Service Time, Positive Lead Time, Retrial Customers and Negative Arrivals

P¹,

Subramanian²

2013

IJCA

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This paper deals with a two server (s,S) inventory system with positive service time, positive lead time, retrial of customers and negative arrivals. In this system, arrival of customers form a Poisson process, lead time and service time are exponentially distributed. The system starts with S units of inventory on hand. Each arriving customer is served a single unit of the item by any one of the servers. When the inventory level reaches s, an order is placed for (S-s) units. If the inventory level is zero or both servers are busy, then the arriving customer goes to orbit and becomes a source of repeated calls. Assume that the capacity of the orbit is infinite. The negative arrival plays an important role in this paper and it controls the congestion in the orbit by removing one customer from the orbit and further it is assumed that it removes the customer from the orbit only if inventory level is zero or both servers are busy. It is also assumed that the access from orbit to the service facility is governed by the classical retrial policy. This model is solved by using Direct Truncation Method. Numerical and graphical studies have been done for analysis of mean number of customers in the orbit, average inventory level, Truncation level, mean number of busy servers and system performance measures. A suitable cost function is defined.

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“…We assume that the demands that occurred during stock-out enters into the orbit and retry for their demands after a random time. The concept of retrial demands in inventory was introduced in [6] and only few papers [21,20] have appeared in this area. However, considerable interest is shown in the study of Queueing models with retrial customers [8,[3][4][5]11].…”

Section: Introductionmentioning

confidence: 99%

A perishable inventory system with retrial demands and a finite population

Sivakumar

2009

Journal of Computational and Applied Mathematics

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Positive lead time Retrial demand Finite population a b s t r a c tIn this article, we consider a continuous review perishable inventory system with a finite number of homogeneous sources of demands. The maximum storage capacity is S. The life time of each items is assumed to be exponential. The operating policy is (s, S) policy, that is, whenever the inventory level drops to s, an order for Q(= S − s) items is placed. The ordered items are received after a random time which is distributed as exponential. We assume that demands occurring during the stock-out period enter into the orbit. These orbiting demands send out signal to compete for their demand which is distributed as exponential. The joint probability distribution of the inventory level and the number of demands in the orbit are obtained in the steady state case. Various system performance measures are derived and the results are illustrated numerically.

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On (s, S) inventory system with random lead time and repeateddemands

Cited by 26 publications

References 10 publications

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

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

Two Server (s, S) Inventory System with Positive Service Time, Positive Lead Time, Retrial Customers and Negative Arrivals

A perishable inventory system with retrial demands and a finite population

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