An Inventory Model under Trapezoidal Type Demand, Weibull-Distributed Deterioration, and Partial Backlogging

Lianxia Zhao

doi:10.1155/2014/747419

Abstract

This paper studies an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate, in which shortages are allowed and partially backlogging depends on the waiting time for the next replenishment. The inventory models starting with no shortage is are to be discussed, and an optimal inventory replenishment policy of the model is proposed. Finally, numerical examples are provided to illustrate the theoretical results, and a sensitivity analysis of the major parameters with respect to the optimal solution is also carried out.

Highlights

This paper studies an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate, in which shortages are allowed and partially backlogging depends on the waiting time for the replenishment
The effect of deteriorating for items cannot be disregarded in many inventory systems and it is a general phenomenon in real life
Wee [3] developed an inventory model with quantity discount, pricing, and partial backordering when the product in stock deteriorates with time

Summary

Introduction

The effect of deteriorating for items cannot be disregarded in many inventory systems and it is a general phenomenon in real life. Wu et al [2] studied an inventory model with a Weibull-distributed deteriorating rate for items and assumed the demand rate with a continuous function of time. Wu [9] considered an inventory model with Weibull distribution deterioration and ramp type demand rate in which shortages are allowed and the backlogging rate is dependent on waiting time. Skouri et al [12] considered an inventory model with general ramp type demand rate, partial backlogging, and Weibull deterioration rate. Cheng et al [15] considered an inventory model for time-dependent deteriorating items with trapezoidal type demand rate and partial backlogging. We consider an inventory model with Weibull-distributed deterioration items, trapezoidal type demand rate, and time-dependent partial backlogging.

Notations and Assumptions

Model Formulation

Numerical Example

Findings

Conclusion