Inventory analysis for deteriorating items deploying preserrvation technology with time dependent quadratic demand function

Abstract

The effect of deterioration is very important in many inventory systems. Most of the physical goods undergo decay or deterioration over time. Preservation technology is a system which helps to reduce the rate of deterioration of the deteriorating items. The preservation technology has a significance and it can increase the life of some products. In the present study, two individual model Inventory Model Without Preservation Technology (IMWOPT) and Inventory Model With Preservation Technology (IMWPT) have been formulated. The model IMWOPT consists of ordering cost, holding cost and purchase cost. On the other hand, the model IMWPT consists of ordering cost, holding cost, purchase cost, reduced deterioration rate and preservation technology cost. Both of these model has been developed by the sense of time dependent quadratic demand function and variable deterioration rate. The reason for considering the variable deterioration rate and time dependent demand rate is due to change in deterioration rate with respect to time. The development of these models is to minimize the total average cost per unit time. In order to validate the models, numerical examples have been considered. Then the sensitivity of several major parameters quadratic functions is analyzed using MATLAB. The optimal solutions with the effects of major parameters have been represented graphically and in tabular form. From the numerical results of IMWOPT and IMWPT, it is evident that the values of parameters of quadratic demand function, ordering cost, holding cost, purchase cost and deterioration rate per unit time increase and decrease then the total cost per unit time increase and decrease respectively. Consequently, from the numerical results of IMWPT the values of reduced deterioration rate per unit time increase then the total cost per unit time decrease as well as the values of reduced deterioration rate per unit time decrease then the total cost per unit time increase and due to increase and decrease of preservation technology cost per unit time total cost per unit time increase and decrease respectively. Finally, comparison of both model has been discussed. It is observed that IMWPT is better than IMWOPT model.