Variable demand model for periodically reviewing with allowing refunding parts of the orders

AbstractDepending on a field study for one of the largest iron and paints warehouses in Egypt, this paper presents a new multi-item periodic review inventory model considering the refunding quantity cost. Through this field study, we found that the inventory level is monitored periodically at equal time intervals. Returning a part of the goods that were previously ordered is permitted. Also, a shortage is permissible to occur despite having orders, and it is a combination of the backorder and lost sales. This model has been applied in both crisp and fuzzy environments since the fuzzy case is more suitable for real-life than crisp. The Lagrange multiplier technique is used for solving the restricted mathematical model. Here, the demand is a random variable that follows the normal distribution with zero lead-time. Finally, the model is followed by a real application to clarify the model and prove its efficiency.

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

JOURNAL OF ADVANCES IN MATHEMATICS ◽

10.24297/jam.v15i0.7364 ◽

2018 ◽

Vol 15 ◽

pp. 8051-8069

Author(s):

H. A. Ferganya ◽

Osama Mahmoud Hollah

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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Optimization Of (s, S) Periodic Review Inventory Model With Uncertain Demand And Lead Time Using Simulation

International Journal of Management & Information Systems (IJMIS) ◽

10.19030/ijmis.v15i1.1597 ◽

2011 ◽

Vol 15 (1) ◽

Cited By ~ 2

Author(s):

Raida Abuizam

Keyword(s):

Lead Time ◽

Inventory Model ◽

Inventory Level ◽

Periodic Review ◽

Expected Cost ◽

Ordering Policy ◽

Long Time ◽

Risk Simulation ◽

Optimal Values ◽

Periodic Review Inventory

This paper presents the use of Palisade @RISK simulation and RISKOptimizer to minimize the expected cost of inventory per period over a long time horizon. An (s, S) ordering policy will be used in this analysis. In an (s, S) ordering policy, an order is placed at the beginning of any period in which beginning inventory is less than s. The order size is the amount needed to bring the inventory level up to S. This paper illustrates a comparison between the use of @RISK simulation with trial values of (s, S) and the use of RISKOptimizer to find optimal values of (s, S) that minimize the expected cost of inventory over a period of time in a periodic review inventory model.

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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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Determination of Optimal Reserve between Two Machines in Series with the Repair Time has Change of Distribution after the Truncation Point

GIS Business ◽

10.26643/gis.v14i6.14581 ◽

2019 ◽

Vol 14 (6) ◽

pp. 577-585

Author(s):

T. Vivekanandan ◽

S. Sachithanantham

Keyword(s):

Real Life ◽

Random Variable ◽

Repair Time ◽

Inventory Level ◽

Optimal Size ◽

Truncation Point ◽

In Series ◽

Optimal Reserve ◽

Optimal Inventory Level ◽

Two Machines

In inventory control, suitable models for various real life systems are constructed with the objective of determining the optimal inventory level. A new type of inventory model using the so-called change of distribution property is analyzed in this paper. There are two machines M1 and M2 in series and the output of M1 is the input of M2. Hence a reserve inventory between M1 and M2 is to be maintained. The method of obtaining the optimal size of reserve inventory, assuming cost of excess inventory, cost of shortage and when the rate of consumption of M2 is a constant, has already been attempted. In this paper, it is assumed that the repair time of M1 is a random variable and the distribution of the same undergoes a change of distribution after the truncation point X0 , which is taken to be a random variable. The optimal size of the reserve inventory is obtained under the above said assumption . Numerical illustrations are also provided.

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