Optimal Replenishment Policy for Weibull-Distributed Deteriorating Items with Trapezoidal Demand Rate and Partial Backlogging

Lianxia Zhao

doi:10.1155/2016/1490712

Abstract

An inventory model for Weibull-distributed deteriorating items is considered so as to minimize the total cost per unit time in this paper. The model starts with shortage, allowed partial backlogging, and trapezoidal demand rate. By analyzing the model, an efficient solution procedure is proposed to determine the optimal replenishment and the optimal order quantity and the average total costs are also obtained. Finally, numerical examples are provided to illustrate the theoretical results and a sensitivity analysis of the major parameters with respect to the stability of optimal solution is also carried out.

Highlights

Deteriorating is a general phenomenon for many products, in that fruits or vegetables are spoiled directly while alcohol undergoes physical depletion over time, and electronic products deteriorate through a gradual loss of potential utility as time passed
Zhao [23] studied an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate and partial backlogging in which the model begins with no-shortage
In real situation, customers will respond differently in case of shortages, either to wait until replenishment or to look for alternative products, in this paper, we study an inventory model beginning with shortage, Weibull-distributed deterioration items, trapezoidal type demand rate, and time-dependent partial backlogging

Summary

Introduction

Deteriorating is a general phenomenon for many products, in that fruits or vegetables are spoiled directly while alcohol undergoes physical depletion over time, and electronic products deteriorate through a gradual loss of potential utility as time passed. Skouri et al [10] considered a model with general ramp-type demand rate, partial backlogging, and Weibull deterioration rate. Pal et al [12] considered a production inventory model for deteriorating items with ramp-type demand rate under the effect of inflation and shortages under fuzziness. Cheng et al [19] extended the model to be of time-dependent deteriorating items with trapezoidal type demand rate and partial backlogging. Zhao [23] studied an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate and partial backlogging in which the model begins with no-shortage. In real situation, customers will respond differently in case of shortages, either to wait until replenishment or to look for alternative products, in this paper, we study an inventory model beginning with shortage, Weibull-distributed deterioration items, trapezoidal type demand rate, and time-dependent partial backlogging.

Notations and Assumptions

Inventory Model Starting with Shortage

Numerical Examples and Sensitivity Analysis

Conclusion