The M/M/1 queue with inventory, lost sale, and general lead times

Saffari, Mohammad; Asmussen, Søren; Haji, Rasoul

doi:10.1007/s11134-012-9337-3

Cited by 68 publications

(42 citation statements)

References 8 publications

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“…[15] considered a M/M/1 queuing system with a (s, q) inventory policy and the possibility of lost sales, in which the demands arrive according to a Poisson's distribution and service times modeled by an exponential probability distribution. The aim of the study is to obtain reorder points and optimal quantities order for several cases.…”

Section: Stochastic Demand and Lead Time Modelingmentioning

confidence: 99%

Inventory Routing Problem with Stochastic Demand and Lead Time: State of the Art

Roldán

Basagoiti

Onieva

2014

Advances in Intelligent Systems and Computing

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Abstract. The integration of the different processes that conform the supply chain (SC) is fundamental to obtain a better coordination level. The inventory control and its distribution, are the processes that researches have found as the key in the loss of efficiency and effectiveness in the field of logistics, affecting so the synchronization in the SC management. In order to analyze the recent developments in the integration of these processes, this paper analyzes the state of the art of the progress in information management in the SC, the relationship of inventory policies and the demand information, modeling demand and use of optimization methods in the search for the appropriate solutions.

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Section: Stochastic Demand and Lead Time Modelingmentioning

confidence: 99%

Inventory Routing Problem with Stochastic Demand and Lead Time: State of the Art

Roldán

Basagoiti

Onieva

2014

Advances in Intelligent Systems and Computing

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“…A rich literature on queueing systems with inventory was developed in recent years, and with various approaches; but when it comes to computing the stationary distribution of inventory and/or workload states (which will interest us in this paper), the topic seems to be less investigated. We would like to mention the book of Sahin [17], and papers like [7,12,16,18,19], which are more oriented towards lost sale problems.…”

Section: Introductionmentioning

confidence: 99%

A Queueing Model With Randomized Depletion of Inventory

Albrecher

Boxma²,

Essifi³

et al. 2016

Prob. Eng. Inf. Sci.

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Abstract. In this paper we study an M/M/1 queue, where the server continues to work during idle periods and builds up inventory. This inventory is used for new arriving service requirements, but it is completely emptied at random epochs of a Poisson process, whose rate depends on the current level of the acquired inventory. For several shapes of depletion rates, we derive differential equations for the stationary density of the workload and the inventory level and solve them explicitly. Finally numerical illustrations are given for some particular examples, and the effects of this depletion mechanism are discussed.

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“…Order Penetration Point is boundary between Make-to-order and Make-tostock. Saffari et al (2013) considered an M/M/1 queuing system under (r, Q) inventory policy and in presence of lost sales. They derived the stationary distributions of the joint queue length (number of customers in the system) and on-hand inventory.…”

Section: Introductionmentioning

confidence: 99%

Multi-Objective Soft Computing-Based Approaches to Optimize Inventory-Queuing-Pricing Problem under Fuzzy Considerations

Alinezhad¹,

Mahmoudi²,

Hajipour³

2016

Industrial Engineering and Management Systems

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Due to uncertain environment, various parameters such as price, queuing length, warranty, and so on influence on inventory models. In this paper, an inventory-queuing-pricing problem with continuous review inventory control policy and batch arrival queuing approach, is presented. To best of our knowledge, (I) demand function is stochastic and price dependent; (II) due to the uncertainty in real-world situations, a fuzzy programming approach is applied. Therefore, the presented model with goal of maximizing total profit of system analyzes the price and order quantity decision variables. Since the proposed model belongs to NP-hard problems, Pareto-based approaches based on non-dominated ranking and sorting genetic algorithm are proposed and justified to solve the model. Several numerical illustrations are generated to demonstrate the model validity and algorithms performance. The results showed the applicability and robustness of the proposed soft-computing-based approaches to analyze the problem.

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The M/M/1 queue with inventory, lost sale, and general lead times

Cited by 68 publications

References 8 publications

Inventory Routing Problem with Stochastic Demand and Lead Time: State of the Art

Inventory Routing Problem with Stochastic Demand and Lead Time: State of the Art

A Queueing Model With Randomized Depletion of Inventory

Multi-Objective Soft Computing-Based Approaches to Optimize Inventory-Queuing-Pricing Problem under Fuzzy Considerations

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