Stochastic decomposition in production inventory with service time

Krishnamoorthy, A.; Narayanan, Viswanath C.

doi:10.1016/j.ejor.2013.01.041

Cited by 59 publications

(42 citation statements)

References 10 publications

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“…Had reneging of customers been incorporated when inventory level is zero, then the lead time parameter would have appeared in the stability condition. (These remarks are applicable to a very recent paper by Krishnamoorthy and Viswanath C. Narayanan [32]. In the product form one factor is the number of customers in classical M/M/1 queue.…”

Section: Sivakumar and Arivarignanmentioning

confidence: 80%

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A survey on inventory models with positive service time

2011

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Section: Sivakumar and Arivarignanmentioning

confidence: 80%

“…When production time to produce one unit of item has exponential distribution they compute a number of optimal design oriented performance measures. The work of Krishnamoorthy and Viswanath C. Narayanan [32], which was mentioned earlier, considers a more general production process distribution.…”

Section: Retrial Inventory With Productionmentioning

confidence: 98%

A survey on inventory models with positive service time

2011

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“…Proof This is obvious when we arrive at (20) and see that the specific value of λ(·) does not matter. The specific μ(i) are canceled in the early steps of the proof already.…”

Section: Finite Capacity Loss Systemsmentioning

confidence: 94%

“…2 encompasses this system. [20] studied an inventory system under (r, S)-policy, which provides items for an exponential server, who processes items on-demand. When inventory is depleted arriving demand is rejected (lost sales).…”

Section: Examplementioning

confidence: 99%

Loss systems in a random environment: steady state analysis

Krenzler

Daduna

2014

Queueing Syst

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We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove a product-form steady state distribution of the joint queueingenvironment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, for example, from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, for example, of queueing-inventory processes. We investigate further classical loss systems, where, due to finite waiting room, loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise.Keywords Queueing systems · Random environment · Product form steady state · Loss systems · M/M/1/∞ · M/M/m/∞ · M/M/m/N · Inventory systems · Availability · Lost sales Mathematics Subject Classification Primary 60K · 60J10 · 60F05 · 60K20 · 90B22 · 90B05

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“…Subsequently several authors made the above assumption in their investigations to come up with product form solution, the details of which could be seen below. Krishnamoorthy and Viswanath [6] subsume Schwarz et al [5] by extending the latter to production inventory with positive service time. References [7] of Sivakumar and Arivarignan, [8] of Krishnamoorthy and Narayanan, [9] of Deepak et al, [10] of Schwarz and Daduna, [11] of Schwarz et al, and [12] of Krenzler and Daduna are a few other significant contributions to inventory with positive service time.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Multiserver Queueing-Inventory System

Krishnamoorthy

Manikandan

Shajin

2015

Advances in Operations Research

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We attempt to derive the steady-state distribution of the / / queueing-inventory system with positive service time. First we analyze the case of = 2 servers which are assumed to be homogeneous and that the service time follows exponential distribution. The inventory replenishment follows the ( , ) policy. We obtain a product form solution of the steady-state distribution under the assumption that customers do not join the system when the inventory level is zero. An average system cost function is constructed and the optimal pair ( , ) and the corresponding expected minimum cost are computed. As in the case of / / retrial queue with ≥ 3, we conjecture that / / for ≥ 3, queueing-inventory problems, do not have analytical solution. So we proceed to analyze such cases using algorithmic approach. We derive an explicit expression for the stability condition of the system. Conditional distribution of the inventory level, conditioned on the number of customers in the system, and conditional distribution of the number of customers, conditioned on the inventory level, are derived. The distribution of two consecutive to transitions of the inventory level (i.e., the first return time to ) is computed. We also obtain several system performance measures.

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Stochastic decomposition in production inventory with service time

Cited by 59 publications

References 10 publications

A survey on inventory models with positive service time

A survey on inventory models with positive service time

Loss systems in a random environment: steady state analysis

Analysis of a Multiserver Queueing-Inventory System

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