A Production Inventory Model with Constant Production Rate, Linear Level Dependent Demand and Linear Holding Cost

Abstract

In this paper, a production inventory model is proposed which considers products with limited life and a little amount of decay. In real life problem, there are many scenarios that happened in production inventory which were not taken into consideration by Shirajul Islam and Sharifuddin [19], who formulated a production inventory model and considered both the holding cost and the production rate to be constant. They assumed that the demand is a linear level dependent. Their paper has been modified and extended by considering the holding cost to be linearly dependent on time and the demand rate during production is assumed to be smaller than the demand rate after production. The proposed production inventory model is formulated using systems of differential equations including initial and boundary conditions and typical integral calculus were also used to analyze the inventory problems. These differential equations were solved to give the best cycle length of the model to minimize the inventory cost. A mathematical theorem and proof are presented to establish the convexity of the cost function. From the numerical examples giving to illustrate the application of the model, a Newton-Raphson method has been used to determine the optimal length of ordering cycle to be 0.54814, optimal cycle time=2.3014 (840days), optimal quantity=32.9675 and total optimal average inventory cost per unit time=18.253 and accompanied by sensitivity analysis to see the effects of the parameter changes.