Constrained Periodic-Review Probabilistic Inventory Model with Increasing Holding Cost for Two Different Cases of the Relational Function

This paper proposed a multi-item multi-source probabilistic periodic review inventory model under a varying holding cost constraint with zero lead time when: (1) the stock level decreases at a uniform rate over the cycle. (2) some costs are varying. (3) the demand is a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Rayleigh, Erlang distributions). The objective function under a constraint is imposed here in crisp and fuzzy environment. The objective is to find the optimal maximum inventory level for a given review time that minimize the expected annual total cost. Furthermore, a comparison between given distributions is made to find the optimal distribution that achieves the model under considerations. Finally, a numerical example is applied.

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Multi-Source Backlogged Probabilistic Inventory Model for Crisp and Fuzzy Environment

JOURNAL OF ADVANCES IN MATHEMATICS ◽

10.24297/jam.v14i2.7365 ◽

2018 ◽

Vol 14 (2) ◽

pp. 7729-7743

Author(s):

H. A. Ferganya ◽

O. M. Hollahb

Keyword(s):

Random Variable ◽

Inventory Model ◽

Inventory Level ◽

Periodic Review ◽

Fuzzy Environment ◽

Holding Cost ◽

Annual Total ◽

Probabilistic Inventory Model ◽

Erlang Distributions ◽

Periodic Review Inventory

This paper proposed a multi-item multi-source probabilistic periodic review inventory model under a varying holding cost constraint with zero lead time when: (1) the stock level decreases at a uniform rate over the cycle. (2) some costs are varying. (3) the demand is a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Rayleigh, Erlang distributions).The objective function under a constraint is imposed here in crisp and fuzzy environment. The objective is to find the optimal maximum inventory level for a given review time that minimize the expected annual total cost. Furthermore, a comparison between given distributions is made to find the optimal distribution that achieves the model under considerations. Finally, a numerical example is applied.

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A Probabilistic Inventory Model with Two-Parameter Exponential Deteriorating Rate and Pareto Demand Distribution

International Journal of Scientific Research and Management ◽

10.18535/ijsrm/v6i5.m01 ◽

2018 ◽

Vol 6 (5) ◽

Author(s):

Hala Aly Fergany ◽

Osama Mahmoud Hollah

Keyword(s):

Random Variable ◽

Inventory Model ◽

Inventory Systems ◽

Systems Science ◽

Inventory Level ◽

Periodic Review ◽

Deterministic Models ◽

Demand Distribution ◽

Deterioration Rate ◽

Probabilistic Inventory Model

Although the deterioration is one of the main problems that have been investigated in the inventory systems science the last twenty years ago but Most deteriorating inventory studies focused on deterministic models. This paper presents a Constraint Deteriorating Probabilistic Periodic Review Inventory Model (CDPPRIM); a model is applicable when: (1) the demand is a random variable that follows Pareto distribution without lead-time, (2) some costs are varying, (3) shortages are permitted, and (4) the deterioration rate follows exponential distribution.The objective function under a constraint is imposed here in crisp and fuzzy environment. A numerical analysis method (Newton's method) is used to solve the model. The main objective is to find the optimal values of four decision variables (maximum inventory level, stock-out time, the deteriorating time and review time), which minimize the expected annual total cost under the assumptions. At the end, the paper explains the model through an application.

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