A survey on inventory models with positive service time

Krishnamoorthy, A.; Lakshmy, B.; Manikandan, R.

doi:10.1007/s12597-010-0032-z

Cited by 95 publications

(36 citation statements)

References 30 publications

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“…Continuous review (R, Q) policy was assumed for the inventory system and lead-times were considered to be exponentially distributed. Krishnamoorthy et al [38] performed a detailed review of inventory models involving positive service time. Krishnamoorthy and Viswanath [39] investigated an (S, s) production-inventory system and presented an explicit product form solution for the steady-state probability vector, using a simple approach.…”

Section: Literature Reviewmentioning

confidence: 99%

Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations

Sadjadi

Makui

Dehghani

et al. 2016

Applied Mathematical Modelling

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Please cite this article as: S.J. Sadjadi, A. Makui, E. Dehghani, M. Pourmohammad, Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations, Appl. Math. Modelling (2015), doi: http://dx. ABSTRACTThis paper studies a three-level supply chain network, which includes a single supplier, multiple potential distribution centers (DCs) and multiple retailers. The problem is to optimize the facility location, allocation retailers' demands, and inventory replenishment decisions simultaneously such that the total expected costs of location, transportation and inventory are minimized. In order to make the problem more realistic, we consider uncertain demand and leadtime, which follow Poisson and Exponential distributions, respectively. Hence, a queueing approach is used to obtain the amount of annual ordering, purchase and shortage as well as the mean inventory in the steady-state condition. Then, according to the results of queuing analysis, we propose a mixed integer nonlinear programming model (MINLP) to address the locationinventory problem. Moreover, the expected mean inventory is calculated using two different methods and the results are also compared through different criteria.

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Section: Literature Reviewmentioning

confidence: 99%

Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations

Sadjadi

Makui

Dehghani

et al. 2016

Applied Mathematical Modelling

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“…At a first glance, the construction may seem to produce a narrow class of examples, but this is not so: All reversible V fulfill the partial balance condition (21).…”

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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“…A review paper by Krishnamoorthy et al [4] provides the details of the research developments on queueing theory with positive service time. Schwarz et al [5] were the first to produce product form solutions for single server queueinginventory problem with exponentially distributed service time as well as lead time and Poisson input of customers.…”

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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A survey on inventory models with positive service time

Abstract: A detailed review of inventory models involving positive service time is given. These include classical and retrial cases. Also contributions to production inventory with service time is indicated towards the end. In addition directions for future work are indicated.

Cited by 95 publications

References 30 publications

Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations

Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations

Loss systems in a random environment: steady state analysis

Analysis of a Multiserver Queueing-Inventory System

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