Inventory with Positive Service Time: a Survey

Krishnamoorthy, A.; Shajin, Dhanya; Narayanan, Viswanath C.

doi:10.1002/9781119755234.ch6

Cited by 38 publications

(22 citation statements)

References 102 publications

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“…queueing theory in combination with inventory theory) is also overwhelming. For a recent review we refer to Krishnamoorthy, Shajin and Narayanan [18].…”

Section: Related Literature and Own Contributionsmentioning

confidence: 99%

Load balancing in a network of queueing-inventory systems

Otten¹

2022

Preprint

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We study a supply chain consisting of production-inventory systems at several locations which are coupled by a common supplier. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted ('lost sales'). To satisfy a customer's demand a server at the production system needs raw material from the associated local inventory. The supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. The routing of items depends on the on-hand inventory at the locations with the aim to obtain 'load balancing'. We show that the stationary distribution has a product form of the marginal distributions of the production subsystem and the inventory-replenishment subsystem. For the marginal distribution of the production subsystem we derive an explicit solution and for the marginal distribution of the inventory-replenishment subsystem we derive an explicit solution resp. a recursive algorithm for some special cases.

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“…queueing theory in combination with inventory theory) is also overwhelming. For a recent review we refer to Krishnamoorthy, Shajin and Narayanan [18].…”

Section: Related Literature and Own Contributionsmentioning

confidence: 99%

Load balancing in a network of queueing-inventory systems

Otten¹

2022

Preprint

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“…• Service of a customer needs a piece of raw material available in an associated inventory (for a review of research on these models see e.g. Krishnamoorthy and his coauthors [KSN21]).…”

Section: Related Literature and Own Contributionsmentioning

confidence: 99%

Stability of queueing-inventory systems with different priorities

Otten¹,

Daduna²

2022

Preprint

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We study a production-inventory system with two customer classes with different priorities which are admitted to the system following a flexible admission control scheme. The inventory management is according to a base stock policy and arriving demand which finds the inventory depleted is lost (lost sales). We analyse the global balance equations of the associated Markov process and derive structural properties of the steady state distribution which provide insights into the equilibrium behaviour of the system. We derive a sufficient condition for ergodicity using the Foster-Lyapunov stability criterion. For a special case we show that the condition is necessary as well.

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“…Subsequently, these systems were called queuing-inventory systems (QIS) [6,7]. The theory of QISs has been intensively developed over the past three decades, and its state of the art is described in detail in the review papers [8,9].…”

Section: Introductionmentioning

confidence: 99%

Double Sources Queuing-Inventory System with Hybrid Replenishment Policy

2022

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A hybrid replenishment policy in double sources queuing-inventory system is proposed. If the inventory level drops to the reorder point s, then a regular order of the fixed volume Q = S − s is generated to a slow and cheap source, where S denotes the maximum size of the system’s warehouse. If the inventory level falls below a certain threshold value r, where r < s, then the system instantly cancels the regular order and generates an emergency order to a fast and expensive source where the replenishment quantity should be able to bring the inventory level back to S at the replenishment epoch. In addition to consuming customers, the system also receives destructive customers that do not require inventory but destroy them. The stability condition for the system under study is found, steady-state probabilities are calculated, and formulas for finding performance measures are proposed. The problem of minimizing the total cost of the system under the proposed hybrid replenishment policy is solved by choosing the appropriate values of the order point and the threshold value.

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Inventory with Positive Service Time: a Survey

Cited by 38 publications

References 102 publications

Load balancing in a network of queueing-inventory systems

Load balancing in a network of queueing-inventory systems

Stability of queueing-inventory systems with different priorities

Double Sources Queuing-Inventory System with Hybrid Replenishment Policy

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