Inventory Model with Fixed Shelf Life under Generalized Non-Increasing Demand

Han-Wen Tuan,Kuo-Chen Hung,Gino K Yang

doi:10.3390/math9212735

Abstract

In this paper, we develop an economic order quantity (EOQ) model for fixed shelf-life items and a non-increasing demand. The objective of this model is to maximize the total profit. We find the criterion to decide (i) the interior maximum solution or (ii) the boundary maximum solution. Eight numerical examples are given to illustrate all possible scenarios of this generalized model. Our results identify a scenario for which the maximum profit is always negative. This is highly relevant for firms in the public sector operating at a financial loss.

Highlights

We extend the inventory model of Avinadav and Arponen [13] from a special form of polynomial type demand to a generalized version of any non-increasing demand
We extend the inventory model proposed by Avinadav and Arponen [13] from polynomial-type decreasing demand to any non-increasing demand
The significant finding of our paper is to point out that sometimes a negative maximum profit model is reasonable which is verified by our Theorem 2

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. When an item is fresh, its perceived quality is considered perfect They constructed an inventory model with polynomial-type demand which is proportional to the remaining time to full shelf-life duration. Herbon [19] examined an inventory model with a perishable product with a fixed shelf life, and a dynamic pricing policy to study consumer sensitivity to price and freshness. Chuang and Lin [21] studied a two-echelon inventory model with a supplier and one retailer to decide the optimal solutions for selling price under a fixed shelf-life and a ramp type demand with shortages. Avinadav [34] formulated a two-echelon supply chain with a manufacturer and a retailer to examine conditions where the demand is related to the age of the product on a shelf-life, sales effort, and selling price.

A Literature Review among Models

Notation and Assumptions

Proposed Modification

Numerical Examples

Direction for Future Research and Managerial Insights

Conclusions