# Inventory models for perishable items with inventory level dependent demand rate

Yongrui Duan, Guiping Li, James M. Tien, Jiazhen Huo

Research output: Contribution to journalArticle

29 Citations (Scopus)

### Abstract

This paper presents inventory models for perishable items with inventory level dependent demand rate. The models with and without backlogging are studied. In the backlogging model, it is assumed that the backlogging rate is dependent on the waiting time and the amount of products already backlogged simultaneously. Two cases that holding inventory is profitable or not are studied, respectively. The smallest shelf space to ensure shortage not occur when holding inventory is not profitable is obtained. In the model without backlogging, it is assumed that the remaining stock at the end of the inventory cycle is disposed of with salvage value. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution of these models are investigated. At last, some numerical examples are presented to illustrate the effectiveness of the proposed model. The model in this paper is generalization of present ones. In particularly, the model is reduced to Padmanabhan and Vrat's when δ 1=0, and Dye and Ouyang's when δ 2=0. If S=s and δ 2=0, it is Chang, Goyal and Teng's model.

Original language English 5015-5028 14 Applied Mathematical Modelling 36 10 https://doi.org/10.1016/j.apm.2011.12.039 Published - Oct 1 2012

### Fingerprint

Inventory Model
Backlogging
Dependent
Model
Demand
Salvaging
Shortage
Dyes
Waiting Time
Existence and Uniqueness
Optimal Solution
Cycle
Necessary Conditions
Numerical Examples
Sufficient Conditions

### Keywords

• Backlog
• Inventory dependent demand
• Inventory model
• Perishable

### ASJC Scopus subject areas

• Applied Mathematics
• Modeling and Simulation

### Cite this

Inventory models for perishable items with inventory level dependent demand rate. / Duan, Yongrui; Li, Guiping; Tien, James M.; Huo, Jiazhen.

In: Applied Mathematical Modelling, Vol. 36, No. 10, 01.10.2012, p. 5015-5028.

Research output: Contribution to journalArticle

Duan, Yongrui ; Li, Guiping ; Tien, James M. ; Huo, Jiazhen. / Inventory models for perishable items with inventory level dependent demand rate. In: Applied Mathematical Modelling. 2012 ; Vol. 36, No. 10. pp. 5015-5028.
title = "Inventory models for perishable items with inventory level dependent demand rate",
abstract = "This paper presents inventory models for perishable items with inventory level dependent demand rate. The models with and without backlogging are studied. In the backlogging model, it is assumed that the backlogging rate is dependent on the waiting time and the amount of products already backlogged simultaneously. Two cases that holding inventory is profitable or not are studied, respectively. The smallest shelf space to ensure shortage not occur when holding inventory is not profitable is obtained. In the model without backlogging, it is assumed that the remaining stock at the end of the inventory cycle is disposed of with salvage value. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution of these models are investigated. At last, some numerical examples are presented to illustrate the effectiveness of the proposed model. The model in this paper is generalization of present ones. In particularly, the model is reduced to Padmanabhan and Vrat's when δ 1=0, and Dye and Ouyang's when δ 2=0. If S=s and δ 2=0, it is Chang, Goyal and Teng's model.",
keywords = "Backlog, Inventory dependent demand, Inventory model, Perishable",
author = "Yongrui Duan and Guiping Li and Tien, {James M.} and Jiazhen Huo",
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AU - Duan, Yongrui

AU - Li, Guiping

AU - Tien, James M.

AU - Huo, Jiazhen

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N2 - This paper presents inventory models for perishable items with inventory level dependent demand rate. The models with and without backlogging are studied. In the backlogging model, it is assumed that the backlogging rate is dependent on the waiting time and the amount of products already backlogged simultaneously. Two cases that holding inventory is profitable or not are studied, respectively. The smallest shelf space to ensure shortage not occur when holding inventory is not profitable is obtained. In the model without backlogging, it is assumed that the remaining stock at the end of the inventory cycle is disposed of with salvage value. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution of these models are investigated. At last, some numerical examples are presented to illustrate the effectiveness of the proposed model. The model in this paper is generalization of present ones. In particularly, the model is reduced to Padmanabhan and Vrat's when δ 1=0, and Dye and Ouyang's when δ 2=0. If S=s and δ 2=0, it is Chang, Goyal and Teng's model.

AB - This paper presents inventory models for perishable items with inventory level dependent demand rate. The models with and without backlogging are studied. In the backlogging model, it is assumed that the backlogging rate is dependent on the waiting time and the amount of products already backlogged simultaneously. Two cases that holding inventory is profitable or not are studied, respectively. The smallest shelf space to ensure shortage not occur when holding inventory is not profitable is obtained. In the model without backlogging, it is assumed that the remaining stock at the end of the inventory cycle is disposed of with salvage value. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution of these models are investigated. At last, some numerical examples are presented to illustrate the effectiveness of the proposed model. The model in this paper is generalization of present ones. In particularly, the model is reduced to Padmanabhan and Vrat's when δ 1=0, and Dye and Ouyang's when δ 2=0. If S=s and δ 2=0, it is Chang, Goyal and Teng's model.

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