Double-Sources Queuing-Inventory Systems with Finite Waiting Room and Destructible Stocks

Melikov, Agassi; Mirzayev, Ramil; Sztrik, János

doi:10.3390/math11010226

Cited by 8 publications

(4 citation statements)

References 39 publications

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“…The system is a QBD process thus it will be stable if and only if πAe < πCe. The stability condition is given in the Equation (20). The proof of Theorem 2 can be performed similar to Theorem 1 in the Equation ( 6).…”

Section: Model-1 With (S S)-type Replenishment Policymentioning

confidence: 98%

“…QIS models with destructive customers hardly have been studied, although, as indicated above, they are accurate models of systems in real life. In papers [17][18][19][20], the authors assumed that the arrival of destructive customers causes the level of the inventory is reduced only by one. However, there are many realistic QISs in which upon arrival of destructive customers all items damage together.…”

Section: Introductionmentioning

confidence: 99%

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Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Ozkar,

Melikov,

Sztrik

2023

Mathematics

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We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an infinite buffer. The service time of a consumer customer follows a phase-type distribution. The system receives negative customers which have Poisson flows and as soon as a negative customer comes into the system, he causes a consumer customer to leave the system, if any. One of two inventory policies is used in the systems: either (s,S) or (s,Q). If the inventory level is zero when a consumer customer arrives, then this customer is either lost (lost sale) or joins the queue (backorder sale). The system is formulated by a four-dimensional continuous-time Markov chain. Ergodicity condition for both systems is established and steady-state distribution is obtained using the matrix-geometric method. By numerical studies, the influence of the distributions of the arrival process and the service time and the system parameters on performance measures are deeply analyzed. Finally, an optimization study is presented in which the criterion is the minimization of expected total costs and the controlled parameter is warehouse capacity.

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Section: Model-1 With (S S)-type Replenishment Policymentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Ozkar,

Melikov,

Sztrik

2023

Mathematics

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“…In this subsection, we derive the closed-form approximate solution for the steady-state probabilities of the investigated 2D CTMC by using a space merging approach; see [23]. This approach is highly accurate for systems with rare catastrophes, i.e., it is assumed that κ ≪ min(λ + , λ − , µ).…”

Section: An Approximate Approachmentioning

confidence: 99%

Queuing-Inventory System with Catastrophes in the Warehouse: Case of Rare Catastrophes

Melikov,

Poladova,

Sztrik

2024

Mathematics

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A model of a single-server queuing-inventory system (QIS) with a limited waiting buffer for consumer customers (c-customers) and catastrophes has been developed. When a catastrophe occurs, all items in the system’s warehouse are destroyed, but c-customers in the system are still waiting for replenishment. In addition to c-customers, negative customers (n-customers) are also taken into account, each of which displaces one c-customer (if any). The policy (s, S) is used to replenish stocks. If, when a customer enters, the system warehouse is empty, then, according to Bernoulli’s trials, this customer either leaves the system without goods or joins the buffer. The mathematical model of the investigated QIS is constructed in the form of a continuous-time Markov chain (CTMC). Both exact and approximate methods for calculating the steady-state probabilities of constructed CTMCs are proposed and closed-form expressions are obtained for calculating the performance measures. Numerical evaluations are presented, demonstrating the high accuracy of the developed approximate formulas, as well as the behavior of performance measures depending on the input parameters. In addition, an optimization problem is solved to obtain the optimal value of the reorder point to minimize the expected total cost.

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“…The emergency supply has a zero lead time but incurs an extra cost has been assumed. Two models of double-source queueing-inventory systems have been studied where instant destruction of inventory is possible in Melikov et al (2023). Replenishment of stocks from various sources occurs as following.…”

Section: Introductionmentioning

confidence: 99%

MAP/PH/1 Üretim Envanter Modeli

Ozkar

2023

UUJFE

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In this study, a production inventory model with phase type service times where customers join the system occur according to a Markovian arrival process is discussed. When the inventory level is positive, if an arriving customer finds the server idle gets into service immediately. Served customer leaves the system and the on-hand inventory is decreased one unit of item at service completion epoch. Otherwise, the customer enters into a waiting space (queue) of infinite capacity and waits for get served. The production facility produces items according to an (s,S) policy. The production is switched on when the inventory level depletes to s and the production remains on until the inventory level reaches to the maximum level S. Once the inventory level becomes S, the production process is switched off. Applying the matrix-geometric method, we carry out the steady-state analysis of the production inventory model and perform a few illustrative numerical examples includes the effect of parameters on the system performance measures and an optimization study for the inventory policy.

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Double-Sources Queuing-Inventory Systems with Finite Waiting Room and Destructible Stocks

Cited by 8 publications

References 39 publications

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Queuing-Inventory System with Catastrophes in the Warehouse: Case of Rare Catastrophes

MAP/PH/1 Üretim Envanter Modeli

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